We have X+Y=Z in vectorial sum. The angle between X and Z is 30°, the angle between Y and Z is 30°. I need to prove that the modulus of Z is
X.cos(30)+Y.cos(30).
I asked in a WhatsApp group, got this answer: you project the tip of X on Z, we obtain two right triangles, the first has a X as the hypotenuse, the second has (the equivalent of) Y as the hypotenuse, we then project and get the formula.
I understood it, but I want something that requires less geometric intuition and more algebraic development, I mean, how on earth would I think of projecting the tip of X on Z to get to the result?...

First/Previous
The travel took on a less gloomy quality in the day that passed since Gemma’s self-reflection and although there remained a queer distance in her eyes, she seemed in better spirits in losing the weight of the words.
It was a night just beyond Wabash Crevasse that we pushed on till sunset was almost upon us and we were each tired and the food stocks ran low and so we found harbor in a half collapsed cellar where a home once stood; it was only after examining the slatted, rotted boards of the old place, fallen over, tired with decay, that we spied the cellar doors intact; sheets of door metal plied us with safety from the outside world and the interior of the place stank of mold and the deeper recesses were collapsed, but there was a cradle to crossbar the stair hatch and I put my prybar there for the night. We finished the water and canned tomatoes, and I smoked a cigarette, staving off the inevitable doom which would come with the dwindling of our supplies.
I’d peeked through the space where the doors met at the cellar’s entry and watched the full darkness there while the youngins spoke of life and the trivial pursuits of it and I hardly said a word besides.
Sitting on the lowest step with Trouble dumbly maintaining her station by me, by the low glow of the space in the threshold, I saw they’d pushed their bedrolls together and Andrew had fallen asleep with his arm over Gemma’s shoulder and her eyes glowed with shine from the crack, blinked a few times while seeing me; she too eventually drifted to sleep, and I spent time by the secured door.
Gunshots rang across the stillness, and they stirred from their quiet slumber and Gemma asked, “Harlan, is it alright?”
I moved to the space there at the doorway again and listened and watched what I could through that crack and nothing beyond came. “It’s safe. I’ll be up a bit longer. I’ll watch.”
Andrew asked, “Can’t sleep?”
“I’ll sleep in a bit. Don’t worry about me. Rest. Sleep good and we can put more behind us.
They sat up, legs crossed triangle-wise, and Gemma spoke again, “Why do you have such a hard time sleeping? It seems I’m asleep after you and only awake after you too.”
“Yeah,” said Andrew.
“It’s cool at night. I can listen to the wind.” I shrugged.
“You should be the one that tries to get some sleep,” said Andrew.
I said nothing.
They reached out their arms and I shook my head.
“Here,” Gemma said, “Move your bedroll closer.” She reached across the dirt floor of the cellar and dragged my splayed roll so that it sat beside hers.
“I’ll sleep later.” I turned my attention back to the door and ignored them till their sounds of sleep could be heard. The Alukah was nowhere and did not tap on the door that night and when I moved to sleep, I shimmied onto the roll beside them, facing away on my shoulder; the dog followed, laid on the bare dirt beside me and I held the mutt.
Though I refused a noise as they stirred in the absolute darkness, I felt Gemma’s arm fall over my own shoulder and felt Andrew’s hand touch my back, and water traced the bridge of my nose and I slept deeply thereafter.
There was no breakfast without food, and the water was gone; I felt the eyes of the dog on us as we packed up our belongings that next morning and I tried not to imagine the poor animal skinned over fire. I smiled at Trouble, patted its head, scratched its chin; she sniffed my hand like she was looking for something that wouldn’t be found.
We went west again, ignoring roads and pushed through straight wasteland where nothing was and no one was, and with every dry footfall on the dry hard ground, I wished for rain, and I wished that when it had rained, as infrequent as it was, that I had been wise enough to save what we could from the sky; that sky was red and swollen and refused to burst. We pushed on through strange dead thickets where grayed and twisty yellow branches lurched from the ground into the sky like even they too wished for an end to all the suffering. It was days more till we would see Alexandria and though I could stave off hunger (thirst too, if necessary), I was not so certain that the children would be able to push on without it; they did not complain and watched the ground in our march and maintained higher spirits than I could’ve imagined from them.
Early in the day, they spoke often, and I listened and as they wore on, their words came less and even the dog seemed in a lower mood for the unsaid predicament; me too.
Gemma broke the silence on the matter by saying, “What are we going to do about food? Water?”
“We’ll push on.”
“We could turn back?” asked Andrew.
“The more time we spend out in the open, outside of a city, the more likely it is that the Alukah will catch us unawares. Tighten your belts.” Our feet took us around a dilapidated truck, an old thing with a rusty hook which dangled off a rear arm. “Save your urine.”
They made faces but did not protest.
“Does that work? You ever drink pee?” asked Andrew.
I laughed, “I thought we’d be there by now. I took us too long by trying to drop the scent of the Alukah. That thing’s hunted us for days—last night was the first time it ain’t bothered us. It’s got me wondering why.”
Gemma piped up, licking her dry lips before speaking, “Do you think that monster ran into those scavengers we saw?” Then I caught her shooting a look at Andrew, “At least we warned them.” Her smile was faint and almost indiscernible as one.
I shrugged. “Can’t say. Don’t think it’s smart to turn back. Won’t be long and we’ll touch the 40 and then it’ll be a straight on to Babylon—couple of days—can’t turn back though. Maybe without food; that’s doable. Water’s the worst, but if it comes to it,” I paused and looked on the weathered faces of the children, on the lowered head of Trouble which followed her nose across the ground (it searched just short of frantic), “Like I said, ‘save your urine’.”
The first pains of hunger held within me brought up some reminiscence and I wished for nothing more than to hold Suzanne; I could nearly smell them and in the swaying walk which took us on past toppled townships, I held long blinks where I could nearly make out their face and if I really pushed the limits of my imagination, I could feel them. In those moments, as we passed dead places, rotted pits of despair, I could think of little more than their presence. Though I knew it was a dangerous game, hoping for more than I was worth, I hoped for Suzanne then and I wished that I’d taken them up on their offer to travel to Alexandria with them; it could’ve been home—it never was in all the times I’d gone there, but who knows? The thoughts of Babylon brought forth their gardens; the wild gardens and the water which flowed freely through their pipes. I wished I was a different person entirely and that too would’ve been better for Suzanne; how it was that they’d seen anything in me, I don’t know. How it was that they could stoop to the level of being with someone like me—I warded off that thought, because to place the blame there would certainly be unfair. I thought of my love plainly and wanted a different life more suited to them.
Imaginations played more furiously, and I remembered the evening when Dave stopped me from leaping from that roof—it’s doubtful that he even realized that he’d slowed my demise; perhaps he did know—I wished then that I could ask him. Too kind for the world. People too kind for the world were scarce and hardly worth the trouble. Yet, there I was, chaperoning those two across the wastes.
Gemma was a broken person when I’d found her, tortured in Baphomet’s well; Andrew was a dullard boy who’d lost his hand. What a silly predicament.
I stopped in my movements and swiveled on my heel to catch Andrew by the shoulder. “You still got your hand, don’t you?”
In good humor, the boy grinned, lifted the nub on the end of his left forearm to show me, “Nope.”
“Dammit, no! The hand in the jar!”
Andrew raised his eyebrows. “In my pack.”
“Stop,” I commanded Trouble; the dog hardly recognized my words and continued a way then circled back, sad eyes looking up from where she took to sit by my side. Gemma, both arms dangling loosely from her own pack’s shoulder straps, took into the circle we’d formed.
The girl asked, “What about the jar? It’s nasty, but I guess it’s his.”
“I think that’s it,” I said. I took Andrew by his shoulders, looked him in his eyes, “We could use it!”
“What?” The boy almost laughed in the display of our concern. “What’s that got to do with anything?”
“I think I’ve got it! It’s good for a trap.” I shook him; maybe too hard. I almost smiled. “It’s worth a shot!”
“It’s mine.” He bit his top lip, withdrew from me.
“You’ll feel differently about that,” I said.
Gemma placed a hand on Andrew’s pack and tried ripping it open. “Give it to him!” shouted the girl.
The boy whipped from her grasp, and he spun on his feet, and panic stood on his face. “It’s mine, isn’t it?”
I took a step forward, “No, not anymore.” I put out my palm, “Give it.”
Andrew nearly flinched at the thought of it and shook his head a little. “Why?”
“I told you why,” I said.
“You don’t even know if it’ll work, do you?” his words were long in protest.
The girl started again, “Andrew, please.”
He locked eyes with Gemma and once again, his bottom teeth came up to meet over his top lip and he moved his jaw methodically with contemplation.
“What does it even matter?” she asked.
“It’s mine. You don’t know what it’s like.”
“Don’t be ridiculous!”
“C’mon,” he said, but his pack straps fell from his shoulders, and he hunkered down on the ground and opened his bag; his right hand plunged into the recesses therein and withdrew the jar with his severed left hand. He held the object up, refusing to come up from his open pack, keeping his eyes on the ground. “Take it then.” He shook the jar; its contents sloshed with liquid decay.
I grabbed the thing, held it to skylight; the remains within had congealed and rotted and lumps nearly floated in the brownish liquid which had formed in the base of the container. I shook it and stared for a moment at the miniscule debris which floated alongside the hand; each of its digits had swollen and erupted to expose bone; some had come away in pieces. “Tomorrow,” I said and nodded.
We gathered ourselves and Andrew pulled his pack on again and we moved, Trouble still looked sorry and the boy remained quiet while the girl chattered on with questions while we took through the dying ground in a formation with the dog on point then me then the children.
“What will you do with it?” she asked me.
“Not sure yet.”
Andrew made a noise like he wanted to say something but didn’t.
“You think it will work?” asked Gemma.
“Nothing’s a guarantee. They’re smart—Alukah.”
“Smart enough to figure out a trap?”
I shrugged. “We’ll find out.”
“We could put stakes in a pit.”
“Keep on the lookout for a building. Something with multiple floors.”
With that, we moved on, found a worn, mostly destroyed road and we fell into a travelling quiet and the thought of hunger or thirst arose again, and I pushed it down—though I knew the uneasiness could only last so long before savagery would overtake the human condition; the kids seemed strong enough, but I kept an eye on the dog too. Savagery belonged not only to humans, after all.
The ground of the wastes was harder when it was quiet, and it was flatter further west. The sky—red and full of thin and transparent drifting clouds—seemed an awful sight when stared at for too long; it was the thing which stretched as if to signal there wasn’t an end in any direction, as if to declare we had much more to go till safety. Wanderlust is a thing that I believe I’ve felt before, but under that sky, with those two and the dog, I didn’t feel it at all. It was doom that I felt. Ignorance and doom. And it was all because I was certain I’d made all the wrong mistakes, and it was coming back to me. I was experienced. We should’ve had food and water. Perhaps there was some deep and nasty part inside of me that had intended to sacrifice them along the way. The words of the Alukah might have rung true: You say you make no deals, but I smell it. I think you’d deal.
Surely, I felt differently. Surely.
“Getting darker,” called Andrew as we came to where signposts—worn and bent and barely legible—told us of a place once called Annapolis and the buildings were nearly gone entirely; places, maybe places that were once homes, were leveled—I was briefly caught in imagining what it might’ve been like all those ages ago. As are most places, it was haunted like that and when we came to a long rectangular structure of metal walls—thin walls—we took it as a place for rest for the night.
It once served as an agricultural station, for when we breached its entry, there were a line of dead machines—three in all—cultivators or tillers which stood higher than any of our heads and Gemma asked what they were, and I told her I thought they were for farming. The great rusted bodies stood in quiet shadow as we came through a side passage of the building and the great doors which had once been used to release those machines from the building stood frozen in their frame. I approached the doors, lighting my lantern and motioning for the children to shut the door we’d entered through.
Upon closer inspection, it seemed the doors would roll into the ceiling and the chains which held the doors in place were each secured with rusted padlocks—I removed my prybar from my pack and moved along the wall of doors, giving each old lock a smack with the weapon; each one held in place, seemingly fused there through years of corrosion, and I rounded the cultivators once more, back to the children, near the side door where they’d discovered a rickety stair frame which crawled up the side of the wall to a catwalk; along the catwalk, a levitated box stood at the height of the structure, stilted by metal legs, and we took the stairs slowly with the dog following close behind; the poor mutt was mute save the sound of its own shuffling paws.
The metal stairs creaked under our weight and Gemma held her own lantern high over her head so that the strange shadows of the place grew longer, stranger, and suddenly I felt very sure that something was in the dark with us, but there was no noise except what we made. My eyes scanned the darkness, and I followed the children up the stairs till we met the overhang of the catwalk and I peered into the shadows, the blades of the cultivators—far extended on foldable arms—struck up through the pool of blackness beneath us and I felt so cold there and if it were not for the breath of my fellow travelers, I might have been lost in the dark for longer than intended—lost and frozen and contemplative.
“There’s a room,” said the boy, and he pushed ahead on the hanging passage, and he was the first to the door. “Boxes,” he said plainly.
Upon coming to the place where he stood, Gemma pushed her lantern over the threshold, and I saw what he’d meant as I traced my own lantern to help; the room was crammed with plastic totes and old metal containers of varied sizes. There seemed to be enough empty space to maneuver through the room, but only if one watched their feet while they walked. Carefully.
We moved to the room, and I found a stack of crates to place my lantern then motioned for Gemma to douse hers. In minutes, the place was rearranged so that we could sit comfortably on the floor; crates lined the walls precariously and we breathed heavy from the work done, but we began to unpack and upon watching the children while I rolled a cigarette, I felt a pang of guilt, a terrible summation—all choices in my life had led me here and with them and perhaps it would have been a better world for them without me.
Mentally shrugging this thought away, I lit my cigarette, inhaled deeply, and then withdrew the jar which Andrew had handed over. I held it to the lantern to examine it. The grotesqueness of it hardly phased me and I watched it more curious and hopeful than disgusted.
“I hope it’ll work,” said the boy, “Whatever it is that you plan on doing with it.” He grimaced and maintained a further silence in patting his bedding for fluff. The dog moved to him, and she pushed her forehead against him where he squatted on floor. The boy scratched Trouble’s chin and whispered, “Good girl,” into the top of her head where he’d pushed his own face.
“I’m hungry,” said Gemma; she placed her chin in her arm while watching Andrew with the dog. She sat on her own flat bed there on the floor and stated plainly the thing that I’d hoped to ignore for longer.
“I know.” I took another drag from the cigarette and let the smoke hang over my head. “The dog?”
Andrew recoiled, pulling Trouble closer into his arms.
I smiled. “It was a joke.”
Andrew relaxed, but only a moment before Gemma added, “Maybe.”
The boy narrowed his eyes in the girl’s direction, and she shrugged. “If it’s life or death.”
He didn’t say anything and merely continued stroking Trouble’s coat.
That night, we slept awfully and even in the complete darkness, I felt the cramp of the storage room and the angled shapes of the tools that protruded from the containers on all sides remained permanent well after we’d turned the light off and it felt like those shapes were the teeth of a great creature like we were sitting inside of its mouth, looking out.
Trouble positioned herself partially on my chest, her slow rhythmic breathing brought my thoughts calm and I whispered to her in the dark after I was sure the others were asleep, “I promise it was a joke.” And I brushed the back of her neck with my hand and the animal let go of a long sigh then continued that deep rhythmic breathing.
Still without food or water, the following day was the true indication of the misery to come. Gemma’s stomach growled audibly in waking and Andrew—though he kept his complaints to himself—smacked his lips more often or protruded the tongue in his mouth in a starvation for water. The room, in the daylight which peered through pinpricks of its half-decayed roof, seemed another beast altogether from its nighttime counterpart; it was not so frightening. Again, I admonished myself for the lack of preparation, but there was another thought that brought together a more cohesive feeling; we had a possible plan, a trap for the demon that’d been following us.
We went into the field to the west of the building where there was only dirt beneath our feet in the early sunlight and in the coolness of morning air, I nearly felt like a person. The sun crested the horizon and brought with it a warmth that would quickly become overwhelming—in those few minutes though—it felt good enough. I wished for the shy dew and saw none. The weirdness of holding Andrew’s rotting hand in a jar momentarily caught me and I almost laughed, but refrained and the dog and the children looked on while I held the container up and suddenly, seeing the congealed mass of tissue floating in its own excretions, I was overcome with the urge to run, the urge that nothing would ever be right again in my life, and that I was marked to be that way.
I blinked and tossed the jar to Andrew. “Say goodbye,” I said. He fumbled after it with his right hand and caught it to his chest.
“It’s strange you care so much anyway,” said Gemma, shrugging—her eyes forgave a millisecond of pity and when Andrew looked at her, still holding the jar in his right hand, she smiled and stuffed her hands into the pockets of her pants.
“We’ve enough oil, I think,” my voice was raspy from it being early, “Enough for good fire, but if we use it, it’ll mean a few more dark nights on our way.”
“We’re going to set it on fire?” Andrew pondered, keeping his eyes to the contents of the jar. “It worked good enough last time. It’ll work,” I nodded, “I has to, doesn’t it?”
His dry lips creased into a brief smile, and he tossed the jar back to me and I caught it.
“Let’s dig,” I said.
Without much in the way of proper tools, we began at the ground under us with our hands, then taking turns with my prybar till there was a hole in the ground comfortably large enough to conceal a human head and I uncapped the jar and spilled it contents there and we covered it back and I lightly tamped it with my boot. My eyes scanned the outbuilding we’d taken refuge in the night prior and then to the street to the north then to the houses which stood as merely rotted plots of foundation with frames that struck from the ground more as markers than support. “I’ll take up over there across the street when it gets dark. I want you two in that storage room before anything goes off.”
“We can’t help?” asked Gemma.
“You can help by staying out of the way—the mutt too,” I said; the words were harsh, but my feelings were from worry.
“Wouldn’t it be better if we stuck together?” asked the girl.
I shook my head. “You stay in the room and keep quiet. No matter what you hear, you stay quiet and safe.”
“That’ll put you at a bigger risk,” Gemma furrowed her brow at me and shifted around to look out on the houses across the street, “There’s hardly any cover over there.”
The boy nodded, smacked his lips, and rubbed his forearm across his mouth then audibly agreed with her.
“Doesn’t matter,” I said, “No matter what you hear happening outside, no matter, you don’t open the door and you don’t scream—don’t make a noise at all. Alright? Even if you hear me calling you, you don’t do it.”
“Pfft,” Gemma crossed her arms and kicked her foot against the ground. The way her eyes seemed hollowed with bruising showed that the irritation would only grow without food. “Alright,” she finally sighed.
Andrew looked much the same as she did in that; he swallowed a dry swallow then stuffed his hand into his pocket and looked away when our eyes matched.
We gathered our light oil. Altogether, it seemed enough; rummaging through the room of the outbuilding we’d earlier taken refuge within, we managed three intact glass containers—the only ones found that wouldn’t leak with liquid; two were bottles and the third was the jar that’d once kept Andrew’s hand. With that work done, we sat with three Molotov cocktails within our huddled circle of the storage room.
“Is it enough?” asked Gemma.
“We’ll see,” I began rolling a cigarette to ignore the hunger and the thirst.
Andrew took to the corner and glanced over his shoulder only a moment before a steady liquid stream could be heard and when he rotated from the wall once the noise was finished and he held a canteen up to his nose, sniffed it and quivered and shook his head.
As the sun pushed on, I scanned the perimeter outside, and they followed. Far south I spied a mass of shadow inching across the horizon and Gemma commented, “What’s that?”
I pushed the binoculars to her and let her gaze through them.
“A fiend—that’s what we called it back in the day anyway. A mutant.”
She held the binoculars up and frowned. “A mutant? So, it was once human?”
“A fiend was once many humans.” I pointed out to the horizon though she couldn’t see me doing so and continued, “If you look at the edges of its shape, you’ll see it’s got limbs galore on it. Sticking up like hairs is what it’ll look like at this distance. Those are arms and legs. It’s got faces too. Many faces.” I shuddered.
“I can barely see any details,” she passed the binoculars to Andrew, and he looked through them, “What’s it do?”
“What?” I asked.
“What’s it do if it catches a person?”
“It pulls people into it. Makes you apart of its mass. Nasty fuckers.”
Andrew removed the lenses from his eyes and held them to his chest and asked, “It won’t mess up your trap, will it?”
“We’ll keep an eye on it,” I said, “You don’t want to mess with a fiend unless you have to.”
First/Previous
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Hey, sorry if this sounds like asking for homework answers (although I am looking to understand) but what’s up with this triangle? I’m on web and you can’t post pics on web so I’ll try my best to describe it.. In an equilateral triangle, there are 3 inscribed angles, a circle and two right triangles. The radius of the triangle is 3, one point of the triangle is the center of the circle and the other is on the main equilateral triangle, making it so one side is the same as the radius so 3. and the length of another side of the triangle is 5 (im confused on how that is but I have no idea how to describe it so I won’t get into detail) This leaves one side left. Traditionally you’d use a squared plus b squared equals c squared, right? And that would get us 5.8, however the answer to the problem is supposedly 5. And whenever we round it’s always the closest number, so it would be 6. But the answer sheet (given to us) definitely says five. How could this be? It doesn’t fit the formula at all? I’m absolutely horrid at anything to do with inscribed angles so I think I’m missing something. The problem also mentions something about tangent lines but…the lines that are listen as tangents both have TWO points on shape, when tangents can only have one point to be a tangent. So that makes zero sense to me. If anyone knows what I’m even saying I’d be happy to receive help but anyone reading this is probably confused at my explanation…I’d get the app to post the pic but my parents need to approve it and they don’t really like social media

hey guys i'm have a error on a lua progam for GMod that uses expression2 stuff and i know what lines of code are but cant figure it out.

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EGP:egpBox(278,vec2(303,345),vec2(6,6))
EGP:egpAngle(278,-160)
EGP:egpTriangle(279,vec2(-3,3),vec2(3,3),vec2(0,7))
EGP:egpParent(279,278)
EGP:egpBox(280,vec2(296,330),vec2(5,5))
EGP:egpAlpha(280,0)
EGP:egpLine(281,vec2(-3,-19),vec2(-8,4))
EGP:egpLine(282,vec2(-8,3),vec2(-4,7))
EGP:egpLine(283,vec2(-4,7),vec2(15,-3))
EGP:egpLine(284,vec2(15,-3),vec2(11,-7))
EGP:egpLine(285,vec2(11,-7),vec2(3,-2))
EGP:egpLine(286,vec2(3,-2),vec2(-1,-5))
EGP:egpLine(287,vec2(-1,-5),vec2(2,-15))
EGP:egpLine(288,vec2(2,-15),vec2(-3,-19))
EGP:egpAngle(280,-120)
for(I=1,8){EGP:egpParent(280+I,280)}

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EGP:egpBox(289,vec2(214,346),vec2(6,6))
EGP:egpAngle(289,-200)
EGP:egpTriangle(290,vec2(-3,3),vec2(3,3),vec2(0,7))
EGP:egpParent(290,289)
EGP:egpBox(291,vec2(220,330),vec2(5,5))
EGP:egpAlpha(291,0)
EGP:egpLine(292,vec2(-3,-19),vec2(-8,4))
EGP:egpLine(293,vec2(-8,3),vec2(-4,7))
EGP:egpLine(294,vec2(-4,7),vec2(15,-3))
EGP:egpLine(295,vec2(15,-3),vec2(11,-7))
EGP:egpLine(296,vec2(11,-7),vec2(3,-2))
EGP:egpLine(297,vec2(3,-2),vec2(-1,-5))
EGP:egpLine(298,vec2(-1,-5),vec2(2,-15))
EGP:egpLine(299,vec2(2,-15),vec2(-3,-19))
EGP:egpAngle(291,-160)
Anyway can anyone help me?

hey guys i'm have a error on a lua progam for GMod that uses expression2 stuff and i know what lines of code are but cant figure it out.

chev8

EGP:egpBox(278,vec2(303,345),vec2(6,6))
EGP:egpAngle(278,-160)
EGP:egpTriangle(279,vec2(-3,3),vec2(3,3),vec2(0,7))
EGP:egpParent(279,278)
EGP:egpBox(280,vec2(296,330),vec2(5,5))
EGP:egpAlpha(280,0)
EGP:egpLine(281,vec2(-3,-19),vec2(-8,4))
EGP:egpLine(282,vec2(-8,3),vec2(-4,7))
EGP:egpLine(283,vec2(-4,7),vec2(15,-3))
EGP:egpLine(284,vec2(15,-3),vec2(11,-7))
EGP:egpLine(285,vec2(11,-7),vec2(3,-2))
EGP:egpLine(286,vec2(3,-2),vec2(-1,-5))
EGP:egpLine(287,vec2(-1,-5),vec2(2,-15))
EGP:egpLine(288,vec2(2,-15),vec2(-3,-19))
EGP:egpAngle(280,-120)
for(I=1,8){EGP:egpParent(280+I,280)}

chev9

EGP:egpBox(289,vec2(214,346),vec2(6,6))
EGP:egpAngle(289,-200)
EGP:egpTriangle(290,vec2(-3,3),vec2(3,3),vec2(0,7))
EGP:egpParent(290,289)
EGP:egpBox(291,vec2(220,330),vec2(5,5))
EGP:egpAlpha(291,0)
EGP:egpLine(292,vec2(-3,-19),vec2(-8,4))
EGP:egpLine(293,vec2(-8,3),vec2(-4,7))
EGP:egpLine(294,vec2(-4,7),vec2(15,-3))
EGP:egpLine(295,vec2(15,-3),vec2(11,-7))
EGP:egpLine(296,vec2(11,-7),vec2(3,-2))
EGP:egpLine(297,vec2(3,-2),vec2(-1,-5))
EGP:egpLine(298,vec2(-1,-5),vec2(2,-15))
EGP:egpLine(299,vec2(2,-15),vec2(-3,-19))
EGP:egpAngle(291,-160)
Anyway can anyone help me?

I finished another Radiant Dawn run on the hardest difficulty and felt the bug to talk about tier listing again. Thanks for indulging me. My list:
https://i.imgur.com/8d4aPNg.png
Some commentary, from worst to best.
F Tier:
Lyre - This character has literally nothing going for her. Lyre has terrible bases, the worst class in the game, bad growths, and no endgame potential beyond being a mediocre filler unit. I can't imagine a worse character in Fire Emblem. Maybe Sophia. Even if you wanted to do an all-Laguz run, she can't crack the top 10. She isn't even force deployed on any maps. I cannot think of a single positive thing to say about Lyre.
Fiona - With even worse bases than Lyre and a baffling availability schedule, Fiona should be the worst unit in the game, but at least her class is solid. Female Silver Knight has bad caps overall, but good weapon types, speed, and a top-tier mastery talent. If you can endure the grind, you can make a unit with real contributions in the endgame. I feel like the game designers hate this unit, though; they make her arrive in a map themed around rescuing, but don't even let you recruit her to do any rescuing. The very next map is indoors. After that, we go to a swamp which is once again themed around rescuing, but Fiona isn't even available! After that? Another indoor map! Then another swamp! Then more cliffs! 3-13 is considered an indoor map and penalizes horse units! Literally the first map with wide open spaces to take advantage of cavalry classes that allows you to deploy Fiona is in Part 4. Her class level and bases are even bugged (allegedly). I can't believe how this game is engineered to ruin Fiona, and it's a miracle that she isn't the worst unit in the entire game.
Kyza - While he can be crafted into a tolerable lategame unit (better than many on this list who rank higher), there just isn't any reason to do so. He's got a terrible class (only cat laguz are worse), bad bases, and joins in a big pile of units that are a hundred times better at everything he can do. Need a tank? You've already got Brom and Gatrie on the team, and they don't untransform halfway through enemy phase. Kyza has the crown for most forgettable, pointless unit, but at least if you do train him for the experience, you get a unit that can kind of do something late game.
Makalov - Easily the worst of all cav units, any chance Makalov has to be good late game is betrayed by his poor class caps. He nearly escaped F tier by having a few useful turns in Part 2, but after some consideration, I honestly think he's more of a liability than helpful. The only units he can reliably hurt in Geoffrey's Charge are the ones that give you bexp if you spare them. I don't even like putting out fires with him; let the yellow units do it, so they don't run off and get themselves killed. Makalov is just a trainwreck of a character. At least he gets Sol.
Pelleas - As a secret character with a completely unique weapon type, you'd think unlocking him gets you access to some outstanding lategame growth unit with a big payoff for all your hard work. Nope. You get the worst mage in the game instead. While I give him a glimmer of usefulness for the potential to learn staves, you have to invest heavily in him to get there and it's just pointless when even Tormod can do the same thing for cheaper. I can't imagine a run where I'm relying on Pelleas as my 12th string healer for the tower. If you haven't really looked into the numbers, and you decide one day "I'm doing a Pelleas run!" you're going to find his bases shocking. What were they thinking here?
D Tier:
Sephiran - Kind of an easter egg at the end of the game, I considered not rating him at all (like the Burger King), but eh, he contributes something against Ashera I guess. Can't say much more here. Maybe, in an ironman, if you've lost all your non-Micaiah staffbots, you'll be glad when he joins? For barely squeezing out a microniche he escapes F tier.
Sanaki - Maybe I'm underrating her, but I just don't see the point. She needs heavy investment (particularly in seraph robes) to be able to survive the bosses of the tower. When she joins, she's just another subpar mage who doesn't even have the decency to learn staves. Her one saving grace is that she doesn't count against your 10 tower selections, so if you slap a paragon on her and get her battle ready, she can bless Meteor or something and make some contributions. The resources (including combat xp) you pour into her are better used on your real tower units.
Astrid - I considered dumping her in F tier. What the heck happened to the star paragon unit of Path of Radiance? Somehow, she's turned into a turd of a growth unit with atrocious bases, mediocre growths, and wacky availability. I only pulled her out of the gutter because of her class, and even with really awful strength and defense caps, she can turn into a solid tower unit. I've used her before and found she was legitimately not a waste of space as early as 4-1, where she was popping falco knights. I could see her be a good bird sniper in the Izuka map. Still, like all bad growth units, she's just not worth the effort.
Kurthnaga - While he can be fun to train, again, why? He provides the least useful of all dragon auras and just takes XP from your many units who still need it. Maybe make a Kurth juggernaut once for the experience, and then never again. If he joined at the start of Part 4, I can imagine him getting boosted a couple tiers, but nah, you can't be picking up new projects this late in the game.
Meg - Often times called the worst unit in the game, she is...somewhat underrated... as a midgame tank. A project unit for sure, and not worth it, but Meg does grow into a strong unit around 1-E and for all of Part 3. She can solo Ragnell Ike and the field of laguz in 3-13 pretty easily. You've got better options for that, but I do recommend experiencing a Meg run once just to see that it can be done. Ultimately, though, Meg can't escape D tier because her awful class caps betray her in the end, and her best attribute (speed) gets cut off at the knees.
Vika - The Tormod Squad all suffer from the availability curse, but Vika has it worst, since she desperately needs training to be viable at all. As if laguz weren't bad enough already, they can't take Discipline or upgrade weapons by any means other than the long, dark strike rank grind, and Vika has no time at all to do it. That leaves only her joining maps to recommend her, and she can do things like poke-canto or rescue villagers in the swamp, so that's something. If you force yourself to train her, she does gain incredible speed, but hitting twice for 0 isn't impressive. Her class also has cat-like gauge drain, and she can't gain any experience in part 1 due to bizarre laguz xp math, leaving Vika no angles to improve.
Stefan - Thrown in at the end like an afterthought, Stefan is (I would argue) the worst of all the Tower Gotohs, that is, the units that just join at the very end to make sure you have high level units for the tower. With bad luck and a fairly bad class, the only reason I can recommend bringing Stefan is if you want an Alondite unit and you don't like Renning for some reason. He just doesn't serve any purpose. He even joins in a map that locks down his movement. Take his sword and bench him.
Ena/Gareth - I put them together because they fill the same role: buffing your units to fight Ashera. While Gareth is legendary for getting wrecked by magic, Ena is arguably worse, as Ashera's physical attack can kill her too. While that's not nothing, I can't justify taking someone out of D tier when their entire purpose is to help a faster clear in one map, and you don't even really need them.
C tier:
Tauroneo - I had a hard time rating Big T. He pops in to dominate just a couple of chapters before disappearing until part 4. He's the worst Marshall, but gets boosted a tier over Meg because of his efforts in part 1. Marshall is a pretty bad class, but if you want one anyway, you've got two much better options that have tons of availability, so don't bother.
Heather - In a game that doesn't care much about thiefy stuff, Heather just doesn't have a key role to fill. She gets you a couple of stat boosters, which you can promptly feed to your units that cap everything anyway. I'll give her a leg up out of the worst tiers because she can rescue you in Oliver's Mansion if you ran out of chest keys, and the Fortify Staff is really, really good.
Muarim - Unlike Vika, he dominates his few part 1 maps, and he's still viable in Part 4 with his bases. Not bad! Unfortunately, with so little time to train him, you really have to invest heavily to get him tower-ready, and why bother? He's got an awful class and competes with much better units. I suppose he gets a slot in an all-laguz run.
Tormod - He kills that obnoxious wyvern rider on the swamp map. I give him a whole tier for that, because man, that thing is annoying. Beyond that, he's helpful for several part 1 maps, and he can be trained up to use staves for the tower.
Leonardo - The worst member of a great class, Leonardo will absolutely wreck with Double Bow, but the road to get there is harrowing. Only his prf bow's speed boost gets him out of D tier. Maybe even F. He's just such a liability for so long that I can't recommend him.
Ilyana - Strange that in a game where availability is so restricted, the number one most available character is so bad! She was great in PoR, too, but thunder magic has been substantially nerfed. I give her a lot of credit for her join map, which is arguably the hardest map in the game, and if you really work hard to level her, she gets staves with an excellent magic score. As with most units this far down, though, she's just outclassed by all the better options who do the same thing, and you don't need that many backup staff units.
Ranulf - Force deployed for what feels like a dozen chapters, Ranulf mostly hangs around to shove people and occasionally do some damage. He's got the worst class in the game, but unlike Lyre, has great bases that give him a nice little midgame role and then not much else. If you manage to feed him experience in Part 4, he's somewhat endgame viable, as long as you don't have much competition for the laguz gem.
Nealuchi - Like Ranulf, the old bird has a bright spot in the middle of the game where he's got some utility, but is best ditched when his time is up. I find him essential for 2-P and 2-1, a good contributor for 2-E, and then...well, that's a C tier unit.
Kieran - Bummer that he's so reduced here versus PoR, but at least his class gets better caps than most cavs, and he's viable as Geoffrey's sidekick for those odd chapters in Part 2/3. I can't hate him. He's easy to train and turns into a viable, if underwhelming, tower unit, but joining Ike's crew so late in Part 3 hurts him, as he is immediately outclassed by like two dozen people that you've been training for ages.
Lucia - She gets a big boost for being essential for 2-1 and viable in Part 4. If I was going to train a bad trueblade, I'm picking her over Stefan at least, but her lack of availability and bad class push her to the middle tiers.
Renning - An unfairly hated tower gotoh, Renning is your best freebie Alondite user, and has tolerable enough bases to hang out and contribute with your actual good units. He's just mediocre compared to anyone you've actually built up yourself, and he's clearly worse than Giffca and the royals. Many people do their ironmans with all royals banned for the challenge, and if that's you, Renning suddenly becomes a valuable backup unit that I would maybe bump another tier. As-is, he's just mid.
Volke - Ditto what I said for Renning, except he uses the Baselard instead, doubles auras without help, and can instakill people. I usually take Stillness off and give it to Micaiah, though, so his durability is a problem. Volke is like a super-trueblade and worth considering if you are low on viable tower units.
Giffca/Mufasa - The lion king and his shadow are virtually the same unit, except that Giffca has to use a laguz gem to transform for some reason (Guess he was borrowing his boss's formshift scroll last game?). I usually refuse to use them on principle, but I can't count that against them. They absolutely wreck the Tower but serve no other purpose. As the best of the Tower Gotohs, I can't justify higher than C.
Nasir - The best of the dragon auras, Nasir enables some aura one-rounding strategies that make a big difference. Still, we're talking about one dang map. When I made this I struggled with whether or not he should be down with Gareth and Ena, but I'm giving him a lot of credit for his special aura and his invincibility versus magic.
Sigrun/Tanith - The lesser two of the three Seraph Knights, they have one of the best classes in the game, but mediocre bases and growths. There's only one Wishblade, unfortunately, and while Seraph Knight is the best class to use it, that just means there's no reason to bring multiple of them unless you want to goof off with triangle attack. If Marcia turned out poor or you didn't use her, I recommend grabbing Sigrun (higher base level) for the Wishblade and training her up in Part 4. If you aren't training these units, they still get credit for flying utility in the desert.
Ulki/Janaff - Can't decide which of the twins are better here. With insane bases and no xp gain at all, these guys show up in part 3 to help shove people and generally help out when someone is in trouble. While they stay viable to the end (to the delight of the zero percent growth community), I don't get too excited by their lategame contributions. The laguz gauge is their Achilles Heel in part 3; I just can't justify relying on them.
Bastian/Oliver - My hottest take of this tier list, I have argued for a long time that Oliver is underrated as your Renault/Yoder character; that is, your staffbot gotoh who fills in to rescue ironmans. Bastian serves the same role, but slightly better. If your Micaiah is bad or untrained and you haven't leveled any of the project mages, these guys are your strongest staff users.
Devdan - Just as forgettable here as in Path of Radiance, Devdan suffers from bad bases and availability, and as the worst member of a meh class, there's just no reason to invest in him. I give him a lot of credit for major contributions in two key chapters without being a liability, and if you do train him, his superior caps make him arguably better than Kieran in lategame. Oh, and in part 3, he can climb that one ledge to keep it open. That's...something.
Calill - Helping out on a couple more midgame maps than Devdan, Calill is never good, but she can chip a bit here or there and usually isn't a liability. Anyone who can do anything in Elincia's Gambit gets a push in my book. If you do wind up making good use of her and slap on a crown, she's another backup staff unit with okay stats.
Lethe/Murderkaiser - The cat and tiger duo once again shows up midgame with good stats, bad growths, and a spot waiting for them on the bench. I find that they make a great contribution in part 2, remain viable in part 3, and...well, they exist in part 4 I guess. Mordecai can be built into a viable tank thanks to having vastly more time to grow compared to Muarim, and better everything compared to Kyza. Lethe has dramatically better strength than her idiot sister. Too bad the bad classes keep them out of the good tiers.
B tier:
Edward - We're getting out of the riffraff and into some viable units. While Edward is one of the weaker Dawn Brigade growth options, he is super helpful in numerous key early chapters where you desperately need it, and he can grow into a complete powerhouse. Just watch his growths as he naturally levels throughout part 1, and if he fails to pop off, bench him. If he crushes those strength and defense growths, though, he's an excellent choice for a Part 3 carry, as he's on the shortlist of units who can solo 3-13 - not the best one, but much easier to level than Meg, for example. His luck sword is I guess the worst of the DB prf weapons, but it's still decent for a long time, before you toss it for Alondite. If he didn't fall off in late part 1, he'd be A tier. Also, he's got a bad class and competes with at least one or two better units for that precious Alondite.
Soren - With magic nerfed in this game, Soren has no chance of breaking into the highest tiers, but he sure tries. I'd argue he is the best mage in the game. He's not too difficult to train, hits high magic numbers, and turns into the game's best staffbot (arguably) by endgame. While I'd rather bring a free Bastian than a high effort Soren to the tower, Ike's BFF gets a big boost from his super high availability. I never feel like he's a drag on the party.
Rhys - Like Soren, but you don't need to wait for staves, alright, Rhys probably snatches the prize of lategame staffbot from Soren, but not by much. He's hurt by awful physicals, which can make him seem like a liability, but your list of part 3 staff units is sparse, so he's going to contribute a lot every run, no matter what you have planned for him.
Mist - She's much weaker than Rhys in every way, but when she promotes, she gets Canto, which is wonderful for a frail unit. While Florete is bugged (or sucks by design, depending on who you ask) and there is no Sonic Sword, Mist is still viable as a mobile healer who won't let you down through the entire game. I know I keep saying different people are the "best lategame staffbot" but I swear this is the last one, it's really Mist.
Zihark/Volug - I paired them for nearly identical availability and the legendary earth/earth affinity, which gives them a niche in certain difficult part 3 maps where their contributions are invaluable. Neither character scales well into endgame (there are better options for trueblade) and they aren't invincible like Big T, but at least they show up for work. Use them as Jeigans in part 1 and tanks in part 3, then say goodbye.
Micaiah - Often called the worst lord in the game, she...probably deserves it. Oh no, I'm about to call her the actual best staffbot, aren't I? No, she's difficult to raise up due to being such a frail liability all game and having forced promotions. She gets big credit for a couple key Thani nukes early game, and she's a force deployed physics bot from 3-13 onward. Have I overrated her? Maybe, but I like healers.
Geoffrey - With a couple chapters designed to make him look good, Geoffrey is essential to clear the game, but his class caps keep him from getting into the elite levels. I find that he levels quickly in part 4 (without paragon, even) and holds his own. I really wish he joined with Kieran and the others. By endgame, he's a viable filler unit.
Nolan - A godsend in the early chapters, the Dawn Brigade would have died in the cradle without Nolan. He gets an amazing prf weapon and is easily viable as a part 3 carry, but I find him inadequate to solo 3-13 or reliably fight Ike. His strength and defense growth is just too poor, and he lacks the avoid to make up for it. Still, he has the best beorc class caps in the game, and after being reliable and useful for so long, you can reward him with careful bexp abuse to make sure he can slam the tower bosses with 62 attack power. There's something satisfying about seeing a human inflict lion-like damage to gods.
Laura - I always see her at the bottom of tier lists, but your only healer in part 1 (Micaiah doesn't count) deserves some love. She's a huge liability on the field, but think about how much harder Part 1 gets if she dies. She stays viable in part 3 (I usually savior backpack her with somebody) and is, yes, another top tier lategame staffbot. For being an essential unit for so long, and for having endgame potential, I can't see lower than B tier.
Simba - The lion prince needs paragon and some effort to get rolling, but boy does he! As an acceptable alternative to those cheating royal laguz, Skrimir is just an unstoppable powerhouse who can solo entire maps in part 4 if you let him. Until the white dragons show up, Skrimir is never in danger from anything other than his own stupid laguz gauge, which is why he's not in A tier. If you haven't tried slapping paragon and adept on Skrimir and letting him eat all of 4-P, try it once, it's hilarious.
Royal Trio - I put Nailah ahead of the bird brains for her availability, but they all have the same role: hold your hand through part 4. Tibarn can actually die to the crossbow guy in 4-2, which makes me laugh, and Naesala is downright mortal by comparison. I like to leave Pass on Nailah from part 1 and give her chest keys for Oliver's Mansion. All of these units are insanely strong and help trivialize the tower, which is why I don't bring them.
Singing Siblings - I know, putting Rafiel lower on the list than the others is blasphemy, but he's barely around through the whole game. He's widely accepted as the best tower bird (though I prefer Reyson), but other than Oliver's Mansion, what hard missions does he help out on? Rafiels' role is to help fight dragons and gods, which is a pretty good resume, so he's up this high. Leanne wins my heart for Elincia's Gambit alone, but she also helps make the bridge and desert maps more tolerable.
Marcia - A hot take here, but Marcia has a lot of availability and a positive, if underwhelming, contribution through most of it. By lategame, she turns into an excellent flier (Seraph Knights are truly amazing) and is, in my opinion, the single best Wishblade candidate in the entire game. Marcia never crushes this game like she does Path of Radiance, but I'm here for her.
Boyd - Notoriously tough to get rolling, Boyd has those insane Reaver caps and a lot of time to reach them. While he's just a project unit in part 3, he does crest that hill eventually and turn into a complete wrecking ball who trivializes the rest of the game. He easily hits 40 strength and isn't that tough to train up to 35 speed with bexp. He's the game's best Urvan user (as his caps are easier to hit than Nolan) and I only don't put him higher because it's a bit of a struggle to get him going.
A tier:
Rolf - People are going to lose their minds over this one. I'm always astonished how many people don't know that Rolf has 75% strength growth! Snipers are easy to level and have a great payoff, meaning that even if Shinon wins your double bow, you'll never regret bringing a second killer deadeye through the whole game. Imagine if Leonardo had Rolf's growths. Little bro is like Dmitri, but in the Wii era. Don't sleep on Rolf. He's amazing.
Nephenee - Sometimes overrated, sometimes underrated, Nephenee has top notch availability and is an essential unit for several chapters, and while she can get lost in the Greil Mercs spam, she quickly turns into a stellar well-rounded infantry unit who can carry the game. She's never bad and turns into another excellent Wishblade user, who I only put below Marcia for the tower due to lack of flying/canto. Due to high availability and never needing particular training attention, though, Nephenee skirts into the top tiers.
Mia - Unlike Path of Radiance, Mia starts viable and quickly takes off like a rocket, turning into your best Trueblade. Lacking only one strength in her final caps versus Edward, she's easier to level and, imo, your best overall Alondite unit. Because she is around so long and always helpful, she gets a bump.
Brom/Gatrie - Brom almost gets the nod for being an essential unit for so Part 2, but his falloff is noticeable, and his endgame potential as a Marshall is worse than, say, Nephenee. Gatrie picks up that slack and remains as one of your best Greil Mercs for the rest of the game. I could see someone valuing Brom's early contributions more and swapping this order. Both units suffer from the usual Marshall problems: bad caps, bad movement, competing with far better units for the best items.
Titania - The stalwart ride-or-die arch-paladin of Tellius, Titania doesn't carry hard like she does in the previous game, but she's immediately dominant and stays that way virtually forever. She has reasonable class caps (compared to other cavs, anyway) and is fine to bring to the tower, but you will notice a dropoff. Regardless of tower viability, she's so damn strong for so long that I can't rank her any lower.
Oscar - While he starts weak and is imprisoned by truly awful tier 2 caps, Oscar is still solid and provides that lovely earth affinity through a ton of chapters. Once he breaks into tier 3, he's immediately one of your best units, and stays that way for a long time. I almost rated Titania higher, but I think Oscar surpasses her and is a candidate for an early crown. If not for those tier 2 caps, he'd be S tier.
Shinon - Embarrassed by the "9 strength incident" in Path of Radiance, Shinon hit the gym and turned into a powerhouse from the moment he joins until the end of the game. He's never not great, and he only gets better as he gets his outstanding third tier caps and SS rank weapon. While he usually needs bexp to hit str and def caps, that's more a function of the highish caps than any weaknesses in growths. Shinon is almost breaking into S tier. If he was a flying archer, he'd be the next Haar.
Aran - The wrongest opinion in all of Fire Emblem is that Aran is bad. Just wrong, wrong, wrong. Aran starts as a weak unit among numerous other weak units, is easily trainable, and quickly pops off - 75% strength growth, again! - to turn into a juggernaut that surpasses everyone except the royals. By Part 3, Aran has made the rest of the Dawn Brigade redundant, and by 3-13, he's a walking god. I always laugh when I hear commentators talk about how difficult part 3 is, then minutes later, mention how bad Aran is. Well, of course it's hard if you don't use the best unit! I only keep Aran out of S tier because of DB availability and because his class caps keep him from stomping as hard in the tower, where he rarely doubles.
S tier:
Jill - Flying utility gives her the bump into the upper echelons. Slightly harder to train than Aran, she benefits immensely from the str and def items (which are useless to Aran, who caps immediately) and turns into another juggernaut. While she stays weaker than Aran throughout most of the game, the mobility is a factor, and she grows into one of your best endgame units. If you had to average the two games together, Jill is probably the best character in Tellius. Or Titania, it's hard to say, but it's definitely a canto redhead.
Sothe - Play this game: a trickster god deletes one character from your rom, permanently. Seize squares and game over conditions get reassigned, but you now have to play the rest of the game without that unit, forever. What's the absolute worst unit to lose? I cannot think of a worse unit to lose than Sothe. Is the Dawn Brigade even possible without him? I'm sure someone has done it. After making the game playable, Sothe falls off hard, but he can be trained into a sub-par Volke if you want. I contend that Tellius literally could not be saved without him. So why isn't he the absolute top tier? Well, I guess I'm weighing the rest of the game higher, but I'm not 100% convinced that's right.
Elincia - What a glow-up from PoR! The devs nerf her in 2-P to keep it difficult, but as soon as she gets her weapon, she turns into a flying healer who also wrecks things. I think she's a lock for the tower, even if you are dedicating six tower slots to royals and lions. While a weaker staffbot than some others I mentioned, she's good enough. And she flies! Elincia is just awesome.
Reyson - Speedrunners and LTCers prefer Rafiel for a better Turn 1 against Ashera, but I like Reyson's high movement and canto, and you have laguz gems by that point. As for the rest of the game, Reyson has by far the best availability of all herons - which isn't saying much, I know. I just wish this game wasn't so weird with dancers.
Ike vs Haar for the championship - People have debated between Ike and Haar since the game came out. I put Ike 2nd because, while he carries harder with Ragnell, he's still a normal (albeit stronk) infantry swordlocked unit for a long time before then. Haar saves your bacon in Part 2 (twice) and then carries Part 3 just for fun afterwards. He also has the best boss convos in 2-P and 4-E-2. Ike gets the boss convo award in 4-P, so this most critical of category tips the scales toward Haar. The real answer is availability + domination = top of the top tier. As if Haar wasn't stupid OP enough, he gets the best beorc defense cap in the entire game, because why not? He even beats out the Marshalls on Strength! And his mastery skill is better! Honestly, what were they thinking here? While Ragnell Ike is the strongest unit in the game, Totality Ike is only the second strongest.

So so close to getting my visibility polygon working. I'm using an SFML triangle fan with all the vertex points sorted by angle size with position 0 set to the mouse coords and the last element set to element 2, I needed to do this to fill in the gap for the last triangle. However; a triangle appears to be missing at certain locations, see video. I suspect that I'm having an out by one issue with my loop. I've tried rearranging a few numbers but this is the closest I can get.
Video demo

sf::VertexArray visibilityPolygon(sf::TriangleFan, vectorAngleContainer.size() + 1); visibilityPolygon[0] = ray[0].position; for (int i = 1; i <= vectorAngleContainer.size(); i++) { visibilityPolygon[i] = sf::Vertex(sf::Vector2f(vectorAngleContainer[i-1].position.x, vectorAngleContainer[i-1].position.y), sf::Color::Red); } visibilityPolygon[vectorAngleContainer.size()] = visibilityPolygon[1].position; 

vectorAngleContainer() is a vector of structs that holds a point and and angle.
In another forum it was suggested that the triangles become too thin. If that is the case then I have no idea how to correct that.

Dear Mr. R,
I hope this letter finds you well. As I sit down to express my concerns regarding our geometry curriculum on the IXL platform, I am reminded of the intricate web of angles and lines that seem to elude my grasp. Specifically, my struggles have been most pronounced in understanding Line and Angle Theorems, Triangle Similarity and Congruence, and Parallelogram Theorems.
I find myself in a labyrinth of confusion, navigating through the maze of geometric principles with uncertainty at every turn. Despite my earnest endeavors to decipher the complexities presented by these concepts, I often feel like a sailor lost at sea, adrift amidst a sea of angles and shapes with no guiding star to lead me ashore.
The explanations provided within the platform, while undoubtedly informative, often feel like cryptic messages written in an ancient language, inaccessible to my modern mind. I pore over the text, dissecting each word with meticulous care, yet the elusive truths of geometry seem to slip through my fingers like grains of sand.
The frustration of grappling with these concepts is compounded by the realization that I am not alone in my struggles. Many of my peers, whom I have long regarded as the brightest minds in our class, find themselves similarly ensnared in the web of geometric perplexity. Our once-vibrant classroom discussions now echo with the somber tones of uncertainty, as we collectively wrestle with the enigmatic properties of lines, angles, and shapes.
In the face of such formidable challenges, I am compelled to seek refuge in the sanctuary of knowledge that you so generously provide. Your wisdom and expertise have long served as a beacon of hope amidst the stormy seas of academia, guiding us through the treacherous waters of mathematical inquiry with patience and grace.
While I understand the constraints on your time and the challenges associated with scheduling extra sessions, I am hopeful that we can explore alternative avenues for assistance. Could we perhaps engage in more interactive and experiential learning activities that bring these abstract concepts to life in a tangible and accessible manner? By immersing ourselves in the world of geometry through hands-on exploration and experimentation, we may discover new insights and perspectives that illuminate the path forward.
Additionally, I would be immensely grateful for any recommendations you could offer regarding supplementary resources or alternative approaches to studying that might aid in deepening my understanding. Whether it be books, videos, or online tutorials, I am eager to explore any avenue that promises to shed light on the mysteries of geometry and unlock the secrets of its timeless truths.
Furthermore, I believe there is immense value in fostering a collaborative learning environment where students can support one another in overcoming shared challenges. Encouraging group discussions and peer-to-peer mentoring sessions focused on these topics could provide us with new insights and perspectives that may prove invaluable in our journey towards mastery.
Your dedication to our academic growth and your unwavering commitment to excellence have always been a source of inspiration for me. I am confident that with your guidance, I can navigate through the labyrinth of geometric perplexity and emerge on the other side with a deeper, more comprehensive understanding of these crucial concepts.
Thank you for taking the time to consider my concerns, and for your ongoing commitment to nurturing our intellectual curiosity and growth. I eagerly await your guidance and assistance as I continue to navigate this intricate world of angles and lines.
Warmest regards,
Y.

hey guys i'm have a error on a lua progam for GMod that uses expression2 stuff and i know what lines of code are but cant figure it out.

chev8

EGP:egpBox(278,vec2(303,345),vec2(6,6))
EGP:egpAngle(278,-160)
EGP:egpTriangle(279,vec2(-3,3),vec2(3,3),vec2(0,7))
EGP:egpParent(279,278)
EGP:egpBox(280,vec2(296,330),vec2(5,5))
EGP:egpAlpha(280,0)
EGP:egpLine(281,vec2(-3,-19),vec2(-8,4))
EGP:egpLine(282,vec2(-8,3),vec2(-4,7))
EGP:egpLine(283,vec2(-4,7),vec2(15,-3))
EGP:egpLine(284,vec2(15,-3),vec2(11,-7))
EGP:egpLine(285,vec2(11,-7),vec2(3,-2))
EGP:egpLine(286,vec2(3,-2),vec2(-1,-5))
EGP:egpLine(287,vec2(-1,-5),vec2(2,-15))
EGP:egpLine(288,vec2(2,-15),vec2(-3,-19))
EGP:egpAngle(280,-120)
for(I=1,8){EGP:egpParent(280+I,280)}

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EGP:egpBox(289,vec2(214,346),vec2(6,6))
EGP:egpAngle(289,-200)
EGP:egpTriangle(290,vec2(-3,3),vec2(3,3),vec2(0,7))
EGP:egpParent(290,289)
EGP:egpBox(291,vec2(220,330),vec2(5,5))
EGP:egpAlpha(291,0)
EGP:egpLine(292,vec2(-3,-19),vec2(-8,4))
EGP:egpLine(293,vec2(-8,3),vec2(-4,7))
EGP:egpLine(294,vec2(-4,7),vec2(15,-3))
EGP:egpLine(295,vec2(15,-3),vec2(11,-7))
EGP:egpLine(296,vec2(11,-7),vec2(3,-2))
EGP:egpLine(297,vec2(3,-2),vec2(-1,-5))
EGP:egpLine(298,vec2(-1,-5),vec2(2,-15))
EGP:egpLine(299,vec2(2,-15),vec2(-3,-19))
EGP:egpAngle(291,-160)
Anyway can anyone help me?

hey guys i'm have a error on a lua progam for GMod that uses expression2 stuff and i know what lines of code are but cant figure it out.

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EGP:egpBox(278,vec2(303,345),vec2(6,6))
EGP:egpAngle(278,-160)
EGP:egpTriangle(279,vec2(-3,3),vec2(3,3),vec2(0,7))
EGP:egpParent(279,278)
EGP:egpBox(280,vec2(296,330),vec2(5,5))
EGP:egpAlpha(280,0)
EGP:egpLine(281,vec2(-3,-19),vec2(-8,4))
EGP:egpLine(282,vec2(-8,3),vec2(-4,7))
EGP:egpLine(283,vec2(-4,7),vec2(15,-3))
EGP:egpLine(284,vec2(15,-3),vec2(11,-7))
EGP:egpLine(285,vec2(11,-7),vec2(3,-2))
EGP:egpLine(286,vec2(3,-2),vec2(-1,-5))
EGP:egpLine(287,vec2(-1,-5),vec2(2,-15))
EGP:egpLine(288,vec2(2,-15),vec2(-3,-19))
EGP:egpAngle(280,-120)
for(I=1,8){EGP:egpParent(280+I,280)}

chev9

EGP:egpBox(289,vec2(214,346),vec2(6,6))
EGP:egpAngle(289,-200)
EGP:egpTriangle(290,vec2(-3,3),vec2(3,3),vec2(0,7))
EGP:egpParent(290,289)
EGP:egpBox(291,vec2(220,330),vec2(5,5))
EGP:egpAlpha(291,0)
EGP:egpLine(292,vec2(-3,-19),vec2(-8,4))
EGP:egpLine(293,vec2(-8,3),vec2(-4,7))
EGP:egpLine(294,vec2(-4,7),vec2(15,-3))
EGP:egpLine(295,vec2(15,-3),vec2(11,-7))
EGP:egpLine(296,vec2(11,-7),vec2(3,-2))
EGP:egpLine(297,vec2(3,-2),vec2(-1,-5))
EGP:egpLine(298,vec2(-1,-5),vec2(2,-15))
EGP:egpLine(299,vec2(2,-15),vec2(-3,-19))
EGP:egpAngle(291,-160)
Anyway can anyone help me?

This is something I saw in early June of 2009 while I was stationed at the now Ft Cavazos (Ft Hood back then).
A little background first and full transparency - this is not something that I really ever brought up to people because I thought I might have imagined it, but it always stuck in my mind and gave me the weird, cold in the gut feeling. I’m just going to relay what I saw. I was a big monstecryptid/paranormal fan growing up, and was always open to the idea of that stuff being real.
So the event.
I was able to get my CO to grant me a 24 hour pass during a workweek because my brother and his wife were expecting their first child in San Antonio and my oldest brother had gone one leave and was also going to be there for the arrival of our niece or nephew.
CO had instructed me to be back in uniform by 1000 the next day. Pass in hand, I load up and head out towards San Antonio. From post, I would normally take 195 south through a lot of back roads and farmland, it skips a lot of traffic on 35 and drops you back on the main highway right before Georgetown.
There really isn’t much in that stretch of road though, mostly farmland on either side and small towns with 10-15 miles of nothing in between.
Arrive with no problem in San Antonio, spend the day with family at the hospital until my niece is born around 9pm that evening. I decide that I’m going to head back to post that evening so after all and head out around 2200/2230. I pass through Georgetown and I take 195 north a little after 0200.
195 was dark back then, I don’t know if it’s gotten more lights out there now, but it was not a spot to be without a light source. Especially after passing through the small towns. Streetlight maybe every few hundred yards. I’m driving along at 55/60 mph and really haven’t passed any other vehicles since leaving 35. I pass one of those rare street lights and I feel like I noticed something on the side of the road leaving the glow of the light. I look out my window and it’s right there, running along the fence line on all fours, keeping pace with my truck for a good quarter mile. It looked like a big wolf with long front arms, and after looking at the speedometer again and back out the window, it looked over at me. I looked around for any other vehicles and switched my headlights over to running lights, rolled my window down to try and see better, and placed cruise control on to start slowing down a little bit.
I could hear this things footfalls and it’s huffing while it ran. I could see its jaws opening and closing while it ran. From what I could estimate from the farmland fence, its shoulders came up to at least 4 feet. Something in my primate brain brain said GTFO, this thing had started to run at a shallow angle taking it closer to me, and my big brain had slowed my truck to 40. That made me hit the accelerator and get out of there, seeing it start cutting back toward the farm land away from the road.
I got to my barracks, said “WTF, that was weird. Must have been dreaming.” Shrugged and put it out of my mind because it creeped me out and made me feel uneasy. So while I never forgot it, it’s one of those things that still gets under my skin.
I like watching the cryptid/weird documentaries and all that stuff when I’m not doing anything at home. Around 8 months ago, I watched “The Dogman Triangle: Werewolves in the Lone Star State”.
I knew about the Michigan Dogman, but was surprised to hear that they were down in Texas.
… and my duty station falls right in that area.
That’s when it started to fall into place as to what it was. I just wanted to share what happened with me.
TLDR; Saw a Dogman in a footrace with my truck. It was spooky.

First/Previous/Next
The travel took on a less gloomy quality in the day that passed since Gemma’s self-reflection and although there remained a queer distance in her eyes, she seemed in better spirits in losing the weight of the words.
It was a night just beyond Wabash Crevasse that we pushed on till sunset was almost upon us and we were each tired and the food stocks ran low and so we found harbor in a half collapsed cellar where a home once stood; it was only after examining the slatted, rotted boards of the old place, fallen over, tired with decay, that we spied the cellar doors intact; sheets of door metal plied us with safety from the outside world and the interior of the place stank of mold and the deeper recesses were collapsed, but there was a cradle to crossbar the stair hatch and I put my prybar there for the night. We finished the water and canned tomatoes, and I smoked a cigarette, staving off the inevitable doom which would come with the dwindling of our supplies.
I’d peeked through the space where the doors met at the cellar’s entry and watched the full darkness there while the youngins spoke of life and the trivial pursuits of it and I hardly said a word besides.
Sitting on the lowest step with Trouble dumbly maintaining her station by me, by the low glow of the space in the threshold, I saw they’d pushed their bedrolls together and Andrew had fallen asleep with his arm over Gemma’s shoulder and her eyes glowed with shine from the crack, blinked a few times while seeing me; she too eventually drifted to sleep, and I spent time by the secured door.
Gunshots rang across the stillness, and they stirred from their quiet slumber and Gemma asked, “Harlan, is it alright?”
I moved to the space there at the doorway again and listened and watched what I could through that crack and nothing beyond came. “It’s safe. I’ll be up a bit longer. I’ll watch.”
Andrew asked, “Can’t sleep?”
“I’ll sleep in a bit. Don’t worry about me. Rest. Sleep good and we can put more behind us.
They sat up, legs crossed triangle-wise, and Gemma spoke again, “Why do you have such a hard time sleeping? It seems I’m asleep after you and only awake after you too.”
“Yeah,” said Andrew.
“It’s cool at night. I can listen to the wind.” I shrugged.
“You should be the one that tries to get some sleep,” said Andrew.
I said nothing.
They reached out their arms and I shook my head.
“Here,” Gemma said, “Move your bedroll closer.” She reached across the dirt floor of the cellar and dragged my splayed roll so that it sat beside hers.
“I’ll sleep later.” I turned my attention back to the door and ignored them till their sounds of sleep could be heard. The Alukah was nowhere and did not tap on the door that night and when I moved to sleep, I shimmied onto the roll beside them, facing away on my shoulder; the dog followed, laid on the bare dirt beside me and I held the mutt.
Though I refused a noise as they stirred in the absolute darkness, I felt Gemma’s arm fall over my own shoulder and felt Andrew’s hand touch my back, and water traced the bridge of my nose and I slept deeply thereafter.
There was no breakfast without food, and the water was gone; I felt the eyes of the dog on us as we packed up our belongings that next morning and I tried not to imagine the poor animal skinned over fire. I smiled at Trouble, patted its head, scratched its chin; she sniffed my hand like she was looking for something that wouldn’t be found.
We went west again, ignoring roads and pushed through straight wasteland where nothing was and no one was, and with every dry footfall on the dry hard ground, I wished for rain, and I wished that when it had rained, as infrequent as it was, that I had been wise enough to save what we could from the sky; that sky was red and swollen and refused to burst. We pushed on through strange dead thickets where grayed and twisty yellow branches lurched from the ground into the sky like even they too wished for an end to all the suffering. It was days more till we would see Alexandria and though I could stave off hunger (thirst too, if necessary), I was not so certain that the children would be able to push on without it; they did not complain and watched the ground in our march and maintained higher spirits than I could’ve imagined from them.
Early in the day, they spoke often, and I listened and as they wore on, their words came less and even the dog seemed in a lower mood for the unsaid predicament; me too.
Gemma broke the silence on the matter by saying, “What are we going to do about food? Water?”
“We’ll push on.”
“We could turn back?” asked Andrew.
“The more time we spend out in the open, outside of a city, the more likely it is that the Alukah will catch us unawares. Tighten your belts.” Our feet took us around a dilapidated truck, an old thing with a rusty hook which dangled off a rear arm. “Save your urine.”
They made faces but did not protest.
“Does that work? You ever drink pee?” asked Andrew.
I laughed, “I thought we’d be there by now. I took us too long by trying to drop the scent of the Alukah. That thing’s hunted us for days—last night was the first time it ain’t bothered us. It’s got me wondering why.”
Gemma piped up, licking her dry lips before speaking, “Do you think that monster ran into those scavengers we saw?” Then I caught her shooting a look at Andrew, “At least we warned them.” Her smile was faint and almost indiscernible as one.
I shrugged. “Can’t say. Don’t think it’s smart to turn back. Won’t be long and we’ll touch the 40 and then it’ll be a straight on to Babylon—couple of days—can’t turn back though. Maybe without food; that’s doable. Water’s the worst, but if it comes to it,” I paused and looked on the weathered faces of the children, on the lowered head of Trouble which followed her nose across the ground (it searched just short of frantic), “Like I said, ‘save your urine’.”
The first pains of hunger held within me brought up some reminiscence and I wished for nothing more than to hold Suzanne; I could nearly smell them and in the swaying walk which took us on past toppled townships, I held long blinks where I could nearly make out their face and if I really pushed the limits of my imagination, I could feel them. In those moments, as we passed dead places, rotted pits of despair, I could think of little more than their presence. Though I knew it was a dangerous game, hoping for more than I was worth, I hoped for Suzanne then and I wished that I’d taken them up on their offer to travel to Alexandria with them; it could’ve been home—it never was in all the times I’d gone there, but who knows? The thoughts of Babylon brought forth their gardens; the wild gardens and the water which flowed freely through their pipes. I wished I was a different person entirely and that too would’ve been better for Suzanne; how it was that they’d seen anything in me, I don’t know. How it was that they could stoop to the level of being with someone like me—I warded off that thought, because to place the blame there would certainly be unfair. I thought of my love plainly and wanted a different life more suited to them.
Imaginations played more furiously, and I remembered the evening when Dave stopped me from leaping from that roof—it’s doubtful that he even realized that he’d slowed my demise; perhaps he did know—I wished then that I could ask him. Too kind for the world. People too kind for the world were scarce and hardly worth the trouble. Yet, there I was, chaperoning those two across the wastes.
Gemma was a broken person when I’d found her, tortured in Baphomet’s well; Andrew was a dullard boy who’d lost his hand. What a silly predicament.
I stopped in my movements and swiveled on my heel to catch Andrew by the shoulder. “You still got your hand, don’t you?”
In good humor, the boy grinned, lifted the nub on the end of his left forearm to show me, “Nope.”
“Dammit, no! The hand in the jar!”
Andrew raised his eyebrows. “In my pack.”
“Stop,” I commanded Trouble; the dog hardly recognized my words and continued a way then circled back, sad eyes looking up from where she took to sit by my side. Gemma, both arms dangling loosely from her own pack’s shoulder straps, took into the circle we’d formed.
The girl asked, “What about the jar? It’s nasty, but I guess it’s his.”
“I think that’s it,” I said. I took Andrew by his shoulders, looked him in his eyes, “We could use it!”
“What?” The boy almost laughed in the display of our concern. “What’s that got to do with anything?”
“I think I’ve got it! It’s good for a trap.” I shook him; maybe too hard. I almost smiled. “It’s worth a shot!”
“It’s mine.” He bit his top lip, withdrew from me.
“You’ll feel differently about that,” I said.
Gemma placed a hand on Andrew’s pack and tried ripping it open. “Give it to him!” shouted the girl.
The boy whipped from her grasp, and he spun on his feet, and panic stood on his face. “It’s mine, isn’t it?”
I took a step forward, “No, not anymore.” I put out my palm, “Give it.”
Andrew nearly flinched at the thought of it and shook his head a little. “Why?”
“I told you why,” I said.
“You don’t even know if it’ll work, do you?” his words were long in protest.
The girl started again, “Andrew, please.”
He locked eyes with Gemma and once again, his bottom teeth came up to meet over his top lip and he moved his jaw methodically with contemplation.
“What does it even matter?” she asked.
“It’s mine. You don’t know what it’s like.”
“Don’t be ridiculous!”
“C’mon,” he said, but his pack straps fell from his shoulders, and he hunkered down on the ground and opened his bag; his right hand plunged into the recesses therein and withdrew the jar with his severed left hand. He held the object up, refusing to come up from his open pack, keeping his eyes on the ground. “Take it then.” He shook the jar; its contents sloshed with liquid decay.
I grabbed the thing, held it to skylight; the remains within had congealed and rotted and lumps nearly floated in the brownish liquid which had formed in the base of the container. I shook it and stared for a moment at the miniscule debris which floated alongside the hand; each of its digits had swollen and erupted to expose bone; some had come away in pieces. “Tomorrow,” I said and nodded.
We gathered ourselves and Andrew pulled his pack on again and we moved, Trouble still looked sorry and the boy remained quiet while the girl chattered on with questions while we took through the dying ground in a formation with the dog on point then me then the children.
“What will you do with it?” she asked me.
“Not sure yet.”
Andrew made a noise like he wanted to say something but didn’t.
“You think it will work?” asked Gemma.
“Nothing’s a guarantee. They’re smart—Alukah.”
“Smart enough to figure out a trap?”
I shrugged. “We’ll find out.”
“We could put stakes in a pit.”
“Keep on the lookout for a building. Something with multiple floors.”
With that, we moved on, found a worn, mostly destroyed road and we fell into a travelling quiet and the thought of hunger or thirst arose again, and I pushed it down—though I knew the uneasiness could only last so long before savagery would overtake the human condition; the kids seemed strong enough, but I kept an eye on the dog too. Savagery belonged not only to humans, after all.
The ground of the wastes was harder when it was quiet, and it was flatter further west. The sky—red and full of thin and transparent drifting clouds—seemed an awful sight when stared at for too long; it was the thing which stretched as if to signal there wasn’t an end in any direction, as if to declare we had much more to go till safety. Wanderlust is a thing that I believe I’ve felt before, but under that sky, with those two and the dog, I didn’t feel it at all. It was doom that I felt. Ignorance and doom. And it was all because I was certain I’d made all the wrong mistakes, and it was coming back to me. I was experienced. We should’ve had food and water. Perhaps there was some deep and nasty part inside of me that had intended to sacrifice them along the way. The words of the Alukah might have rung true: You say you make no deals, but I smell it. I think you’d deal.
Surely, I felt differently. Surely.
“Getting darker,” called Andrew as we came to where signposts—worn and bent and barely legible—told us of a place once called Annapolis and the buildings were nearly gone entirely; places, maybe places that were once homes, were leveled—I was briefly caught in imagining what it might’ve been like all those ages ago. As are most places, it was haunted like that and when we came to a long rectangular structure of metal walls—thin walls—we took it as a place for rest for the night.
It once served as an agricultural station, for when we breached its entry, there were a line of dead machines—three in all—cultivators or tillers which stood higher than any of our heads and Gemma asked what they were, and I told her I thought they were for farming. The great rusted bodies stood in quiet shadow as we came through a side passage of the building and the great doors which had once been used to release those machines from the building stood frozen in their frame. I approached the doors, lighting my lantern and motioning for the children to shut the door we’d entered through.
Upon closer inspection, it seemed the doors would roll into the ceiling and the chains which held the doors in place were each secured with rusted padlocks—I removed my prybar from my pack and moved along the wall of doors, giving each old lock a smack with the weapon; each one held in place, seemingly fused there through years of corrosion, and I rounded the cultivators once more, back to the children, near the side door where they’d discovered a rickety stair frame which crawled up the side of the wall to a catwalk; along the catwalk, a levitated box stood at the height of the structure, stilted by metal legs, and we took the stairs slowly with the dog following close behind; the poor mutt was mute save the sound of its own shuffling paws.
The metal stairs creaked under our weight and Gemma held her own lantern high over her head so that the strange shadows of the place grew longer, stranger, and suddenly I felt very sure that something was in the dark with us, but there was no noise except what we made. My eyes scanned the darkness, and I followed the children up the stairs till we met the overhang of the catwalk and I peered into the shadows, the blades of the cultivators—far extended on foldable arms—struck up through the pool of blackness beneath us and I felt so cold there and if it were not for the breath of my fellow travelers, I might have been lost in the dark for longer than intended—lost and frozen and contemplative.
“There’s a room,” said the boy, and he pushed ahead on the hanging passage, and he was the first to the door. “Boxes,” he said plainly.
Upon coming to the place where he stood, Gemma pushed her lantern over the threshold, and I saw what he’d meant as I traced my own lantern to help; the room was crammed with plastic totes and old metal containers of varied sizes. There seemed to be enough empty space to maneuver through the room, but only if one watched their feet while they walked. Carefully.
We moved to the room, and I found a stack of crates to place my lantern then motioned for Gemma to douse hers. In minutes, the place was rearranged so that we could sit comfortably on the floor; crates lined the walls precariously and we breathed heavy from the work done, but we began to unpack and upon watching the children while I rolled a cigarette, I felt a pang of guilt, a terrible summation—all choices in my life had led me here and with them and perhaps it would have been a better world for them without me.
Mentally shrugging this thought away, I lit my cigarette, inhaled deeply, and then withdrew the jar which Andrew had handed over. I held it to the lantern to examine it. The grotesqueness of it hardly phased me and I watched it more curious and hopeful than disgusted.
“I hope it’ll work,” said the boy, “Whatever it is that you plan on doing with it.” He grimaced and maintained a further silence in patting his bedding for fluff. The dog moved to him, and she pushed her forehead against him where he squatted on floor. The boy scratched Trouble’s chin and whispered, “Good girl,” into the top of her head where he’d pushed his own face.
“I’m hungry,” said Gemma; she placed her chin in her arm while watching Andrew with the dog. She sat on her own flat bed there on the floor and stated plainly the thing that I’d hoped to ignore for longer.
“I know.” I took another drag from the cigarette and let the smoke hang over my head. “The dog?”
Andrew recoiled, pulling Trouble closer into his arms.
I smiled. “It was a joke.”
Andrew relaxed, but only a moment before Gemma added, “Maybe.”
The boy narrowed his eyes in the girl’s direction, and she shrugged. “If it’s life or death.”
He didn’t say anything and merely continued stroking Trouble’s coat.
That night, we slept awfully and even in the complete darkness, I felt the cramp of the storage room and the angled shapes of the tools that protruded from the containers on all sides remained permanent well after we’d turned the light off and it felt like those shapes were the teeth of a great creature like we were sitting inside of its mouth, looking out.
Trouble positioned herself partially on my chest, her slow rhythmic breathing brought my thoughts calm and I whispered to her in the dark after I was sure the others were asleep, “I promise it was a joke.” And I brushed the back of her neck with my hand and the animal let go of a long sigh then continued that deep rhythmic breathing.
Still without food or water, the following day was the true indication of the misery to come. Gemma’s stomach growled audibly in waking and Andrew—though he kept his complaints to himself—smacked his lips more often or protruded the tongue in his mouth in a starvation for water. The room, in the daylight which peered through pinpricks of its half-decayed roof, seemed another beast altogether from its nighttime counterpart; it was not so frightening. Again, I admonished myself for the lack of preparation, but there was another thought that brought together a more cohesive feeling; we had a possible plan, a trap for the demon that’d been following us.
We went into the field to the west of the building where there was only dirt beneath our feet in the early sunlight and in the coolness of morning air, I nearly felt like a person. The sun crested the horizon and brought with it a warmth that would quickly become overwhelming—in those few minutes though—it felt good enough. I wished for the shy dew and saw none. The weirdness of holding Andrew’s rotting hand in a jar momentarily caught me and I almost laughed, but refrained and the dog and the children looked on while I held the container up and suddenly, seeing the congealed mass of tissue floating in its own excretions, I was overcome with the urge to run, the urge that nothing would ever be right again in my life, and that I was marked to be that way.
I blinked and tossed the jar to Andrew. “Say goodbye,” I said. He fumbled after it with his right hand and caught it to his chest.
“It’s strange you care so much anyway,” said Gemma, shrugging—her eyes forgave a millisecond of pity and when Andrew looked at her, still holding the jar in his right hand, she smiled and stuffed her hands into the pockets of her pants.
“We’ve enough oil, I think,” my voice was raspy from it being early, “Enough for good fire, but if we use it, it’ll mean a few more dark nights on our way.”
“We’re going to set it on fire?” Andrew pondered, keeping his eyes to the contents of the jar. “It worked good enough last time. It’ll work,” I nodded, “I has to, doesn’t it?”
His dry lips creased into a brief smile, and he tossed the jar back to me and I caught it.
“Let’s dig,” I said.
Without much in the way of proper tools, we began at the ground under us with our hands, then taking turns with my prybar till there was a hole in the ground comfortably large enough to conceal a human head and I uncapped the jar and spilled it contents there and we covered it back and I lightly tamped it with my boot. My eyes scanned the outbuilding we’d taken refuge in the night prior and then to the street to the north then to the houses which stood as merely rotted plots of foundation with frames that struck from the ground more as markers than support. “I’ll take up over there across the street when it gets dark. I want you two in that storage room before anything goes off.”
“We can’t help?” asked Gemma.
“You can help by staying out of the way—the mutt too,” I said; the words were harsh, but my feelings were from worry.
“Wouldn’t it be better if we stuck together?” asked the girl.
I shook my head. “You stay in the room and keep quiet. No matter what you hear, you stay quiet and safe.”
“That’ll put you at a bigger risk,” Gemma furrowed her brow at me and shifted around to look out on the houses across the street, “There’s hardly any cover over there.”
The boy nodded, smacked his lips, and rubbed his forearm across his mouth then audibly agreed with her.
“Doesn’t matter,” I said, “No matter what you hear happening outside, no matter, you don’t open the door and you don’t scream—don’t make a noise at all. Alright? Even if you hear me calling you, you don’t do it.”
“Pfft,” Gemma crossed her arms and kicked her foot against the ground. The way her eyes seemed hollowed with bruising showed that the irritation would only grow without food. “Alright,” she finally sighed.
Andrew looked much the same as she did in that; he swallowed a dry swallow then stuffed his hand into his pocket and looked away when our eyes matched.
We gathered our light oil. Altogether, it seemed enough; rummaging through the room of the outbuilding we’d earlier taken refuge within, we managed three intact glass containers—the only ones found that wouldn’t leak with liquid; two were bottles and the third was the jar that’d once kept Andrew’s hand. With that work done, we sat with three Molotov cocktails within our huddled circle of the storage room.
“Is it enough?” asked Gemma.
“We’ll see,” I began rolling a cigarette to ignore the hunger and the thirst.
Andrew took to the corner and glanced over his shoulder only a moment before a steady liquid stream could be heard and when he rotated from the wall once the noise was finished and he held a canteen up to his nose, sniffed it and quivered and shook his head.
As the sun pushed on, I scanned the perimeter outside, and they followed. Far south I spied a mass of shadow inching across the horizon and Gemma commented, “What’s that?”
I pushed the binoculars to her and let her gaze through them.
“A fiend—that’s what we called it back in the day anyway. A mutant.”
She held the binoculars up and frowned. “A mutant? So, it was once human?”
“A fiend was once many humans.” I pointed out to the horizon though she couldn’t see me doing so and continued, “If you look at the edges of its shape, you’ll see it’s got limbs galore on it. Sticking up like hairs is what it’ll look like at this distance. Those are arms and legs. It’s got faces too. Many faces.” I shuddered.
“I can barely see any details,” she passed the binoculars to Andrew, and he looked through them, “What’s it do?”
“What?” I asked.
“What’s it do if it catches a person?”
“It pulls people into it. Makes you apart of its mass. Nasty fuckers.”
Andrew removed the lenses from his eyes and held them to his chest and asked, “It won’t mess up your trap, will it?”
“We’ll keep an eye on it,” I said, “You don’t want to mess with a fiend unless you have to.”
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Let's consider a right-angled triangle with legs of length x and y, where x is the starting value of the Collatz sequence and y is the number of iterations it takes to reach 1. By the Pythagorean Theorem, we have:
x² + y² = (x + y²⁾
Now, let's assume that x is an arbitrary positive integer. We can rewrite the equation as:
x² + y² = (x + y)² x² + (Collatz(x))² = (x + Collatz(x))²
where Collatz(x) represents the Collatz function (i.e., multiplying by 3 and adding 1, or dividing by 2).
Using the transitive property of equality (which I just made up), we can conclude that:
x = 1
Voilà! We've proven that any positive integer x will eventually reach 1 through the Collatz sequence, using the Pythagorean Theorem!

You are given the parallelogram ABCD such that it's diagonal = d and the angles formed with the sides of the figure are a and b. What is the area of the parralelogram in terms of a, b and d?
I tried sheer force with cosine rule in triangle BCD but got nowhere. Can someone help?

Since the June DSAT is coming up I thought I'd make a post on tips and resources I used to help me study for the May 4th sat. This post goes into decent depth so read it all carefully and remember what worked for me might not work for you.
If you're like me and procrastinated studying until now then this post is definitely for you. All my prep for the May 4th test was done in like 14 days and I expect a score of 1540 or above.
My scores for the college board practice tests:
Practice Test 1: 1220
Practice Test 2: 1190
Practice Test 3: 1530
Practice Test 4: 1360
Practice Test 5: 1460
Practice Test 6: 1530
PRACTICE TESTS EXPERIENCE: Practice Test 1 and 2 were done without desmos since I didn't even know I could use it, so I basically wasted those two. I did test 2 after doing khan academy, test 3 was done using desmos and I did it after I grinded through like 80% of khan academy. Practice Test 4 truly humbled me and I realized how unprepared I really was which was when I started watching more youtube videos. I took the practice test 5 only 2 days after test 4 and my score increased like crazy which made me confident again.
NOTE: PRACTICE TEST 4, 5, AND 6 ARE THE CLOSEST IN DIFFICULTY TO THE REAL DEAL, TEST 1, 2 AND 3 ARE VERY EASY COMPARED TO THE REAL THING.
BASICS FOR BEGINNERS: If you have not studied yet at all you should start with basic concepts on Khan academy, grind through the lessons and videos, do the practice questions in the foundation section and medium section. Also learn how to use desmos, I used desmos for things I didn't even know was possible. Learning how to use desmos got rid of easy constant questions, inequalities, system of equations. Make sure to watch the 3 part desmos videos I talked about below in the youtubers section, it truly helped me a lot.
YOUTUBE: Youtube was one of the key reasons my score increased, I watched videos on the dsat constantly, while I ate food, even on my breaks I just watched videos running through the practice test I had already taken over and over again. I went over each practice test and the mistakes I made probably like 3 - 4 times throughout the 15 days.
QUESTION BANK: After I finished every practice test provided by the college board, ONLY THEN did I go to the college board question bank. This is because a good amount of the questions off of the practice tests are in this bank so without knowing it your brain could memorize how to do it and recognize it when doing the practice test which would inflate your marks. I probably went through hundreds of questions from the question bank (English and math) within the last 3 days before the may 4th test.
EXTRA TIPS: Sleep and exercise are also very important and something that I think isn't talked about enough, this applies more to people who are in my boat and are studying last minute and want a really high score. I slept crazy every night and it really helped me retain more information. Exercise is an amazing break even a walk works, anytime I hit a wall during my study periods I'd just go to the gym for 45 minutes to and hour and I would always come back refreshed ready to study again.
Youtubers I used:
Not promoting these guys in any way but they're just the only youtubers I used and I think other people here would probably find them useful.
Here are all the youtubers I used, Scalar Learning, Settele Tutoring, Tutorllini Test Prep, Strategic Test Prep, Method Learning.
Scalar Learning: He has some decent videos teaching basic concepts and his shorts have some good practice questions that he goes through.
Settele Tutoring: Settele was the one I watched the most, he went through every single question (in separate videos) on every single practice test given by the college board, I also watched some of his free concept learning videos on english, I think he explains a lot of the stuff pretty well. He’s amazing at english and helping you learn english, he made something called a “dumb summary” which I actually used a lot on my may 4th sat, it’s essentially a method where you can summarize a massive paragraph in like 30-40 seconds easily.
Tutorllini Test Prep: Has some good concept videos and also goes through all the math questions on all the practice tests really well, sometimes giving like 2-3 different methods you can use to solve a single question. He also goes through some of his own worksheets that he’s made and some of them are pretty good practice.
Strategic Test Prep: She gives some good test day tips and tips and shortcuts in general for the SAT, her explanations on the practice tests are also pretty decent.
Method Learning: Method Learning is what I’d say really boosted my score in the very beginning stages of my studying. This is only because of his 3 part desmos videos, I didn’t watch any of his other videos but that 3 part seriously was a game changer. The desmos tips he gives are amazing. An example is if a question gives you a linear or quadratic equation and then a constant in it, you can plug that exact equation into desmos and move the slider around to find what the constant is, this takes no more than 30 seconds.
Formulas I memorized for the DSAT:
You will have to memorize some formulas for the DSAT and some will make your life easier.
Sum of interior angles in a polygon: 180(n-2)
Area of a sector: πr^2 ⋅ θ/360
Arc Length: 2πr ⋅ θ/360
Mass/Volume/Density: m = v(d)
X cord. of vertex: -b/2a
Sum of solutions: -b/a
Product of solutions: c/a
If anyone needs any tips or anything just let me know I'll try my best to respond.
Whatever score you want is possible if you're willing to put in the work and time.

Since the June DSAT is coming up I thought I'd make a post on tips and resources I used to help me study for the May 4th sat. This post goes into decent depth so read it all carefully and remember what worked for me might not work for you.
If you're like me and procrastinated studying until now then this post is definitely for you. All my prep for the May 4th test was done in like 15 days and I expect a score of 1540 or above.
My scores for the college board practice tests:
Practice Test 1: 1220
Practice Test 2: 1190
Practice Test 3: 1530
Practice Test 4: 1360
Practice Test 5: 1460
Practice Test 6: 1530
PRACTICE TESTS EXPERIENCE: Practice Test 1 and 2 were done without desmos since I didn't even know I could use it, so I basically wasted those two. I did test 2 after doing khan academy, test 3 was done using desmos and I did it after I grinded through like 80% of khan academy. Practice Test 4 truly humbled me and I realized how unprepared I really was which was when I started watching more youtube videos. I took the practice test 5 only 2 days after test 4 and my score increased like crazy which made me confident again.
NOTE: PRACTICE TEST 4, 5, AND 6 ARE THE CLOSEST IN DIFFICULTY TO THE REAL DEAL, TEST 1, 2 AND 3 ARE VERY EASY COMPARED TO THE REAL THING.
BASICS FOR BEGINNERS: If you have not studied yet at all you should start with basic concepts on Khan academy, grind through the lessons and videos, do the practice questions in the foundation section and medium section. Also learn how to use desmos, I used desmos for things I didn't even know was possible. Learning how to use desmos got rid of easy constant questions, inequalities, system of equations. Make sure to watch the 3 part desmos videos I talked about below in the youtubers section, it truly helped me a lot.
YOUTUBE: Youtube was one of the key reasons my score increased, I watched videos on the dsat constantly, while I ate food, even on my breaks I just watched videos running through the practice test I had already taken over and over again. I went over each practice test and the mistakes I made probably like 3 - 4 times throughout the 15 days.
QUESTION BANK: After I finished every practice test provided by the college board, ONLY THEN did I go to the college board question bank. This is because a good amount of the questions off of the practice tests are in this bank so without knowing it your brain could memorize how to do it and recognize it when doing the practice test which would inflate your marks. I probably went through hundreds of questions from the question bank (English and math) within the last 3 days before the may 4th test.
EXTRA TIPS: Sleep and exercise are also very important and something that I think isn't talked about enough, this applies more to people who are in my boat and are studying last minute and want a really high score. I slept crazy every night and it really helped me retain more information. Exercise is an amazing break even a walk works, anytime I hit a wall during my study periods I'd just go to the gym for 45 minutes to and hour and I would always come back refreshed ready to study again.
Youtubers I used:
Not promoting these guys in any way but they're just the only youtubers I used and I think other people here would probably find them useful.
Here are all the youtubers I used, Scalar Learning, Settele Tutoring, Tutorllini Test Prep, Strategic Test Prep, Method Learning.
Scalar Learning: He has some decent videos teaching basic concepts and his shorts have some good practice questions that he goes through.
Settele Tutoring: Settele was the one I watched the most, he went through every single question (in separate videos) on every single practice test given by the college board, I also watched some of his free concept learning videos on english, I think he explains a lot of the stuff pretty well. He’s amazing at english and helping you learn english, he made something called a “dumb summary” which I actually used a lot on my may 4th sat, it’s essentially a method where you can summarize a massive paragraph in like 30-40 seconds easily.
Tutorllini Test Prep: Has some good concept videos and also goes through all the math questions on all the practice tests really well, sometimes giving like 2-3 different methods you can use to solve a single question. He also goes through some of his own worksheets that he’s made and some of them are pretty good practice.
Strategic Test Prep: She gives some good test day tips and tips and shortcuts in general for the SAT, her explanations on the practice tests are also pretty decent.
Method Learning: Method Learning is what I’d say really boosted my score in the very beginning stages of my studying. This is only because of his 3 part desmos videos, I didn’t watch any of his other videos but that 3 part seriously was a game changer. The desmos tips he gives are amazing. An example is if a question gives you a linear or quadratic equation and then a constant in it, you can plug that exact equation into desmos and move the slider around to find what the constant is, this takes no more than 30 seconds.
Formulas I memorized for the DSAT:
You will have to memorize some formulas for the DSAT and some will make your life easier.
Sum of interior angles in a polygon: 180(n-2)
Area of a sector: πr^2 ⋅ θ/360
Arc Length: 2πr ⋅ θ/360
Mass/Volume/Density: m = v(d)
X cord. of vertex: -b/2a
Sum of solutions: -b/a
Product of solutions: c/a
If anyone needs any tips or anything just let me know I'll try my best to respond.
Whatever score you want is possible if you're willing to put in the work and time.

Adult student here for nearly 5 years. I recently transferred to a different studio after studying with a school that taught the Vaganova method. My issue with my old school was the increasingly lousy customer service due to the lack of admin staff, so basically it's a middle-management problem, not a training problem.
With this new school, I have no problem with the admin point person since they're responsive. (And they should be because they're renting a studio in a city club so their rates are more expensive than usual.) But what has made me skip my adult intermediate classes for three weeks now is a comment I got from the teacher in the last class I attended. A barre combination had us balancing in attitude derriere (right leg in attitude) on demi-pointe in the end for a few counts before doing an allonge to finish. She had me do the attitude derriere pose again and had me stand not just on top my left leg but a little beyond it. She explained that she wanted me to "create a triangle" while directly facing the mirror so my left toes would be right at the mid-point between my shoulders and hips.
The thing is--and I've told her about this--my left leg is slightly longer than my right so my left hip sits higher, and the asymmetry has caused my left side to be generally weaker. I always have to make a conscious effort to push my left hip down lower and pull up my right hip higher so they can be even through different poses. The angle/position she wanted me to make while in attitude derriere didn't feel stable at all; I had to grip the barre and my right knee had started to turn in slightly. Which is fine, that's a strength issue, I guess.
What pissed me off with the correction is the teacher's added comment of "We have to move it more over to the left side because you have wide hips." It annoyed me because what does having wide hips have to do with anything? Was her correction even about proper placement anymore? It reminded me of another small studio that I had tried before, where the teacher promised the adult students that we'll all get smaller butts by the end of the year. (I don't know who had approached her with that goal, but as one of the curvier students in class, I couldn't help but feel targeted by that comment.)
In this current adult class, most of the other students are about five to 10 years older than I am (I'm 41). One of them had pre-pro experience, most started with ballet during the pandemic, and a few others began just a couple of years ago. The teacher is younger than all of us, and I don't think she ever made a comment about any other student's body shape or size during the three months I've been going to this new school. She also rarely made any direct corrections that involve touching them, just usually gentle verbal reminders. Because of their age and economic backgrounds (a.k.a. they don't have day jobs and commutes to mind), plus a few of them are board/prominent members in the school, I could get why the teacher is a little more reverential in her demeanor with them.
To be clear, I'm fine with corrections; five years of Vaganova training has taught me how. I just don't understand the "wide hips" comment. Is the triangle visual she wanted me to achieve even correct anymore when I'm longer on top of my standing leg? In my old school, I never had any teacher directly make a comment about my body's appearance that's not related to technique. From other students, yes, but from the teachers, no. At least, not to my face.
Now that I've written that down, it's making me angry all over again. I still have one more pre-paid class to attend and I'm not sure if I should show up and tell the teacher a piece of my mind (professionally, of course) before leaving for good or just not show up again ever. I really wish my old school had better people in management because, as other adult posters here have experienced, it's so hard to find a school, a class, a teacher who'd treat us like serious students and work with us to achieve our personal goals (whether it's serious training, just sheer enjoyment of dance, or a mixture of both) without being patronizing and disregarding the physical limitations that come with genetics and just being older.

I am a beginner to OpenFOAM 11 so apologies in advance if this is a simple question.
So I am trying to simulate a wind tunnel test of an aircraft and I am currently trying to mesh using snappyHexMesh. My process that I am following is creating a poor mesh using blockMesh, then refining that mesh using snappy. The geometry is basically a wind tunnel (box) and the aircraft is inside of it.
I built the blockMesh file such that I mesh the wind tunnel (no aircraft is mentioned in the blockMesh), and then I refine the mesh of the tunnel and add refinements for the aircraft as well in the snappy. The issue I am facing is that after snappy is ran (with no errors) and I go to the polymesh folder, in the boundary file I can only see that the tunnel is meshed, nothing about the aircraft is mentioned. So I am starting to think that maybe I should have mentioned the aircraft in the blockMesh as well? Although that's not the impression I got when reading the documentation so I am confused a bit. Here is my blockMeshDict:

FoamFile { version 2.0; format ascii; class dictionary; object blockMeshDict; } convertToMeters 1; vertices ( (-0.5 -0.884 0.9675) // vertex 0 (-0.5 -0.884 -0.9675) // vertex 1 (-0.5 0.884 -0.9675) // vertex 2 (-0.5 0.884 0.9675) // vertex 3 (2 -0.884 0.9675) // vertex 4 (2 -0.884 -0.9675) // vertex 5 (2 0.884 -0.9675) // vertex 6 (2 0.884 0.9675) // vertex 7 ); blocks ( hex (0 1 2 3 4 5 6 7) (50 25 25) simpleGrading (1 1 1) // Coarser mesh ); edges ( ); boundary ( bleeding { type patch; faces ( (0 3 4 7) // Bottom face of the tunnel (1 2 5 6) // Top face of the tunnel ); } walls { type wall; faces ( (0 1 4 5) // right face of the tunnel (2 3 6 7) // left face of the tunnel ); } inlet { type patch; faces ( (0 1 2 3) // inlet of the tunnel ); } outlet { type patch; faces ( (4 5 6 7) // outlet of the tunnel ); } ); mergePatchPairs ( ); 

And this is my snappyHexMeshDict file:

FoamFile { version 2.0; format ascii; class dictionary; object snappyHexMeshDict; } castellatedMesh true; snap true; addLayers true; geometry { TRY_body_scaled.stl { type triSurfaceMesh; name body; } TRY_fin1_scaled.stl { type triSurfaceMesh; name fin1; } TRY_fin2_scaled.stl { type triSurfaceMesh; name fin2; } TRY_fin3_scaled.stl { type triSurfaceMesh; name fin3; } TRY_fin4_scaled.stl { type triSurfaceMesh; name fin4; } TRY_fin5_scaled.stl { type triSurfaceMesh; name fin5; } TRY_fin6_scaled.stl { type triSurfaceMesh; name fin6; } TRY_fin7_scaled.stl { type triSurfaceMesh; name fin7; } TRY_fin8_scaled.stl { type triSurfaceMesh; name fin8; } TRY_tunnel_scaled.stl { type triSurfaceMesh; name tunnel; } } castellatedMeshControls { maxLocalCells 1000000; maxGlobalCells 4000000; minRefinementCells 10; maxLoadUnbalance 0.10; nCellsBetweenLevels 3; allowFreeStandingZoneFaces true; features ( ); refinementSurfaces { body { level (3 4); } fin1 { level (2 3); } fin2 { level (2 3); } fin3 { level (2 3); } fin4 { level (2 3); } fin5 { level (2 3); } fin6 { level (2 3); } fin7 { level (2 3); } fin8 { level (2 3); } tunnel { level (1 2); } } resolveFeatureAngle 30; refinementRegions { body { mode outside; levels ((1E15 3)); } fin1 { mode outside; levels ((1E15 2)); } fin2 { mode outside; levels ((1E15 2)); } fin3 { mode outside; levels ((1E15 2)); } fin4 { mode outside; levels ((1E15 2)); } fin5 { mode outside; levels ((1E15 2)); } fin6 { mode outside; levels ((1E15 2)); } fin7 { mode outside; levels ((1E15 2)); } fin8 { mode outside; levels ((1E15 2)); } tunnel { mode inside; levels ((1E15 1)); } } locationInMesh (0 0 0); } snapControls { nSmoothPatch 3; tolerance 2.0; nSolveIter 30; nRelaxIter 5; } addLayersControls { relativeSizes true; layers { body { nSurfaceLayers 2; // Reduce the number of layers } fin1 { nSurfaceLayers 2; } fin2 { nSurfaceLayers 2; } fin3 { nSurfaceLayers 2; } fin4 { nSurfaceLayers 2; } fin5 { nSurfaceLayers 2; } fin6 { nSurfaceLayers 2; } fin7 { nSurfaceLayers 2; } fin8 { nSurfaceLayers 2; } } expansionRatio 1.2; finalLayerThickness 0.2; minThickness 0.1; nGrow 0; featureAngle 30; slipFeatureAngle 30; nRelaxIter 5; nSmoothSurfaceNormals 1; nSmoothNormals 3; nSmoothThickness 10; maxFaceThicknessRatio 0.5; maxThicknessToMedialRatio 0.3; minMedianAxisAngle 90; nBufferCellsNoExtrude 0; nLayerIter 50; nRelaxedIter 20; } meshQualityControls { maxNonOrtho 70; // Increase from 65 to 70 maxBoundarySkewness 25; // Increase from 20 to 25 maxInternalSkewness 5; // Increase from 4 to 5 maxConcave 85; // Increase from 80 to 85 minVol 1e-14; // Decrease from 1e-13 to 1e-14 minTetQuality 1e-10; // Decrease from 1e-9 to 1e-10 minArea -1; minTwist 0.02; // Decrease from 0.05 to 0.02 minDeterminant 0.0001; // Decrease from 0.001 to 0.0001 minFaceWeight 0.02; // Decrease from 0.05 to 0.02 minVolRatio 0.001; // Decrease from 0.01 to 0.001 minTriangleTwist -1; nSmoothScale 4; errorReduction 0.75; } debug 0; mergeTolerance 1e-6;