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physics.js
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"use strict";
// PRE-ALPHA
/* TODO
- implement block solver for multiple contacts
- consolidate physics object PLANE_FORM into POLYGON_FORM for simplification purposes
*/
/* GLOSSARY
- physics object: actual objects that are simulated by the physics engine. For now this is circles, planes and convex polygons.
*/
/*
This physics engine is made specifically for use in the browser and thus written in JS (perhaps ported to WASM in the future).
Due to most JS engines being slow accessing variables relative to native running code I am experimenting using a large typedArray
(Float64Array) to store data rather than objects to improve performance. There is ~20% speed boost in V8 so I am sticking with it
for now. I emulated C/C++ style of manual memory management with the typedArray serving as memory. For each physics object and
constraint created elements are allocated in a contiguous block in the typedArray and assigned a pointer which is simply the index
of the first element of the allocated elements that can be used to hold arbitrary floats. The pointer plus an offset is used to
access elements. The following are different offsets.
*/
// physics object offsets
// temp
const O_NUM_FLOATS = -1;
const O_FORM = 0;
const O_TYPE = 1;
const O_P = 2;
const O_M = 3;
const O_M_INV = 4;
const O_I = 5;
const O_I_INV = 6;
const O_GROUP = 7;
const O_US = 8;
const O_UK = 9;
const O_VM = 10;
const O_WM = 11;
const O_VX = 12;
const O_VY = 13;
const O_W = 14;
const O_TX = 15;
const O_TY = 16;
const O_COS = 17;
const O_SIN = 18;
const O_O = 19;
const O_USERFLOATS_PTR = 20;
// CIRCLE_FORM only offsets
const O_RADIUS = 21;
// AABB_FORM only offsets
const O_MIN_X = 21;
const O_MIN_Y = 22;
const O_MAX_X = 23;
const O_MAX_Y = 24;
// PLANE_FORM only offsets
const O_L = 21;
const O_L_INV = 22;
const O_L0X = 23;
const O_L0Y = 24;
const O_L1X = 25;
const O_L1Y = 26;
const O_W0X = 27;
const O_W0Y = 28;
const O_W1X = 29;
const O_W1Y = 30;
const O_UX = 31;
const O_UY = 32;
const O_HALF_WIDTH = 33;
// POLYGON_FORM only offsets
const O_NUM_VERTICES = 21;
// vertex offsets
const V_LX = 0;
const V_LY = 1;
const V_WX = 2;
const V_WY = 3;
const V_UX = 4;
const V_UY = 5;
const V_L = 6;
const V_L_INV = 7;
// constraint offsets
const C_FORM = 0;
const C_TYPE = 1;
const C_PO_PTR_A = 2;
const C_PO_PTR_B = 3;
const C_US = 4;
const C_UK = 5;
const C_ACTIVE = 6;
const C_RAX = 7;
const C_RAY = 8;
const C_RBX = 9;
const C_RBY = 10;
// COLLISION_FORM only
const C_JN = 11;
const C_JT = 12;
const C_NX = 13;
const C_NY = 14;
const C_DIST = 15;
const C_RNA = 16;
const C_RNB = 17;
const C_M = 18;
const C_RTA = 19;
const C_RTB = 20;
const C_MT = 21;
// JOINT_FORM only
const C_DX = 11;
const C_DY = 12;
const C_LAX = 13;
const C_LAY = 14;
const C_LBX = 15;
const C_LBY = 16;
const C_IS_MOTOR = 17;
const C_MW = 18;
const C_M_MAX_T = 19;
const C_SUM_T = 20;
const C_M_I = 21;
const C_JX = 22;
const C_JY = 23;
class MemoryManager {
constructor(memory){
let len = memory.length;
if(len > 65535) console.warn("Are you sure?");
this.memory = memory;
this.memory[0] = -len;
this.memory[this.memory.length - 1] = len;
}
alloc(size){
if(size < 1) throw "Size must be atleast 1";
if(!Number.isInteger(size)) throw "Size must be representable as integer. Size passed: " + size;
size += 2;
for(let ptr = 0, len = this.memory.length; ptr < len; ptr += Math.abs(this.memory[ptr])){
if(!Number.isInteger(this.memory[ptr])) throw "this.memory[ptr] = " + this.memory[ptr] + " not representable as integer.";
if(-this.memory[ptr] >= size) {
if(-this.memory[ptr] > size){
this.memory[ptr + size] = this.memory[ptr] + size;
this.memory[ptr - this.memory[ptr] - 1] = -this.memory[ptr + size];
}
this.memory[ptr] = size;
this.memory[ptr + size - 1] = -size;
console.log(size + " floats allocated at address: " + ptr);
return ++ptr;
}
}
throw "Memory failure";
}
free(ptr){
if(!Number.isInteger(ptr)) throw "Ptr must be representable as integer, ptr = " + ptr;
if(ptr < 0) throw "Unable to free ptr less than 0, ptr = " + ptr;
--ptr;
console.log("freeing ptr: " + ptr);
if(this.memory[ptr] < 20) console.warn("freeing ptr with size: " + this.memory[ptr]);
let start = ptr;
let end = this.memory[ptr] + ptr;
if(this.memory[end] < 0) end -= this.memory[end];
if(start > 0 && this.memory[start - 1] > 0) start -= this.memory[start - 1];
let size = end - start;
if(!Number.isInteger(size)) throw "Size must be representable as integer: " + size;
this.memory[start] = -size;
this.memory[end - 1] = size;
// temp
this.memory.fill(0, start + 1, end - 1);
}
freeAll(){
let len = this.memory.length;
this.memory[0] = -len;
this.memory[this.memory.length - 1] = len;
// temp
//this.memory.fill(0);
}
/*
set(pointer, offset, value){
this.data[pointer + offset] = value;
}
get(pointer, offset){
return this.data[pointer + offset];
}
*/
}
const pw = {
G: -0.002,
//MIN_AA: 0.0,
VELOCITY_ITERATIONS: 9,
POSITION_ITERATIONS: 2,
POLYGON_SKIN: 0.005,
TOTAL_ITER: this.VELOCITY_ITERATIONS + this.POSITION_ITERATIONS,
//isVelocityIter = true,
unsolved: true,
warmStarting: true,
collisionData: new Float64Array(14),
update(){
// scope M to function for faster access
let M = this.M;
// integrate external forces (gravity and physics object resistance)
for(let i = 0, len = this.poTotal; i < len; ++i){
let ptr = this.PO_PTRS[i];
if(M[O_TYPE + ptr] == this.FIXED_TYPE) continue;
M[O_VY + ptr] += this.G;
M[O_VX + ptr] *= M[O_VM + ptr];
M[O_VY + ptr] *= M[O_VM + ptr];
M[O_W + ptr] *= M[O_WM + ptr];
}
// initialize constraints
for(let ptr = 0, len = this.cTotal; ptr < len; ++ptr){
let si = this.C_PTRS[ptr];
let asi = M[C_PO_PTR_A + si];
let bsi = M[C_PO_PTR_B + si];
if(M[C_TYPE + si] === this.COLLISION_TYPE){
this.getCollisionData(si, asi, bsi);
// temp
let cdLen = 7;
//if(collisionData.length == 14) cdLen = 14;
if(M[C_FORM + si] == this.SURFACES_FORM || M[C_FORM + si] == this.SURFACE_POLYGON_FORM || M[C_FORM + si] == this.POLYGONS_FORM) cdLen = 14;
// never updated to accomadate C_JT
for(let i = si, c = 0; c < cdLen; i += 16, c += 7){
// tune
if(this.collisionData[0 + c] === null/* || this.collisionData[6 + c] > 1.0*/){
M[C_ACTIVE + i] = 0;
M[C_JN + i] = 0.0;
M[C_JT + i] = 0.0;
continue;
}
// normal vector
M[C_NX + i] = this.collisionData[0 + c];
M[C_NY + i] = this.collisionData[1 + c];
// distance between collision vertices
M[C_DIST + i] = this.collisionData[6 + c];
if(M[C_DIST + i] < 0) {
M[C_DIST + i] = 0;
}
// vectors from center of masses to collision vertex (radius vectors)
M[C_RAX + i] = this.collisionData[2 + c] - M[O_TX + asi];
M[C_RAY + i] = this.collisionData[3 + c] - M[O_TY + asi];
M[C_RBX + i] = this.collisionData[4 + c] - M[O_TX + bsi];
M[C_RBY + i] = this.collisionData[5 + c] - M[O_TY + bsi];
M[C_ACTIVE + i] = 1;
/*
if(debugPoints.length < 60){
debugPoints.push([[collisionData[2 + c], collisionData[3 + c]], white]);
debugPoints.push([[collisionData[4 + c], collisionData[5 + c]], white]);
}
*/
// cross product of radius vector and normal vector
M[C_RNA + i] = M[C_RAX + i] * this.collisionData[1 + c] - M[C_RAY + i] * this.collisionData[0 + c];
M[C_RNB + i] = M[C_RBX + i] * this.collisionData[1 + c] - M[C_RBY + i] * this.collisionData[0 + c];
// total inverse "mass" in normal reference
M[C_M + i] = 1.0 / (M[O_M_INV + asi] + M[O_M_INV + bsi] + M[C_RNA + i] * M[C_RNA + i] * M[O_I_INV + asi] + M[C_RNB + i] * M[C_RNB + i] * M[O_I_INV + bsi]);
// dot product of radius vector and tangential vector
M[C_RTA + i] = M[C_RAX + i] * this.collisionData[0 + c] + M[C_RAY + i] * this.collisionData[1 + c];
M[C_RTB + i] = M[C_RBX + i] * this.collisionData[0 + c] + M[C_RBY + i] * this.collisionData[1 + c];
// total inverse "mass" in tangential reference
M[C_MT + i] = 1.0 / (M[O_M_INV + asi] + M[O_M_INV + bsi] + M[C_RTA + i] * M[C_RTA + i] * M[O_I_INV + asi] + M[C_RTB + i] * M[C_RTB + i] * M[O_I_INV + bsi]);
if(this.warmStarting){
//M[C_JN + i] *= 0.8;
//M[C_JT + i] *= 0.8;
let jx = M[C_JN + i] * M[C_NX + i] - M[C_JT + i] * M[C_NY + i];
let jy = M[C_JN + i] * M[C_NY + i] + M[C_JT + i] * M[C_NX + i];
if(M[O_TYPE + asi] == this.MOVABLE_TYPE){
M[O_VX + asi] -= jx * M[O_M_INV + asi];
M[O_VY + asi] -= jy * M[O_M_INV + asi];
M[O_W + asi] -= (M[C_JN + i] * M[C_RNA + i] + M[C_JT + i] * M[C_RTA + i]) * M[O_I_INV + asi];
}
if(M[O_TYPE + bsi] == this.MOVABLE_TYPE){
M[O_VX + bsi] += jx * M[O_M_INV + bsi];
M[O_VY + bsi] += jy * M[O_M_INV + bsi];
M[O_W + bsi] += (M[C_JN + i] * M[C_RNB + i] + M[C_JT + i] * M[C_RTB + i]) * M[O_I_INV + bsi];
}
} else {
M[C_JN + i] = 0.0;
M[C_JT + i] = 0.0;
}
}
} else if(M[C_TYPE + si] === this.JOINT_TYPE){
// vectors from center of masses to joint vertices (radius vectors)
M[C_RAX + si] = M[C_LAX + si] * M[O_COS + asi] - M[C_LAY + si] * M[O_SIN + asi];
M[C_RAY + si] = M[C_LAY + si] * M[O_COS + asi] + M[C_LAX + si] * M[O_SIN + asi];
M[C_RBX + si] = M[C_LBX + si] * M[O_COS + bsi] - M[C_LBY + si] * M[O_SIN + bsi];
M[C_RBY + si] = M[C_LBY + si] * M[O_COS + bsi] + M[C_LBX + si] * M[O_SIN + bsi];
//M[C_DX + si] = (M[C_RAX + si] + M[O_TX + asi] - M[C_RBX + si] - M[O_TX + bsi]) * 1.0;
//M[C_DY + si] = (M[C_RAY + si] + M[O_TY + asi] - M[C_RBY + si] - M[O_TY + bsi]) * 1.0;
if(this.warmStarting){
//M[C_JX + si] *= 0.8;
//M[C_JY + si] *= 0.8;
//M[C_SUM_T + si] *= 0.8;
if(M[O_TYPE + asi] == this.MOVABLE_TYPE){
M[O_VX + asi] -= M[C_JX + si] * M[O_M_INV + asi];
M[O_VY + asi] -= M[C_JY + si] * M[O_M_INV + asi];
M[O_W + asi] -= ((M[C_RAX + si] * M[C_JY + si] - M[C_RAY + si] * M[C_JX + si]) + M[C_SUM_T + si]) * M[O_I_INV + asi];
}
if(M[O_TYPE + bsi] == this.MOVABLE_TYPE){
M[O_VX + bsi] += M[C_JX + si] * M[O_M_INV + bsi];
M[O_VY + bsi] += M[C_JY + si] * M[O_M_INV + bsi];
M[O_W + bsi] += ((M[C_RBX + si] * M[C_JY + si] - M[C_RBY + si] * M[C_JX + si]) + M[C_SUM_T + si]) * M[O_I_INV + bsi];
}
} else {
M[C_SUM_T + si] = 0.0;
M[C_JX + si] = 0.0;
M[C_JY + si] = 0.0;
}
}
}
//temp
//console.log("cons = " + cons);
// solve velocity constraints
let iter = 0
for(this.unsolved = true; this.unsolved && iter < this.VELOCITY_ITERATIONS; ++iter){
this.unsolved = false;
for(let ptr = 0, len = this.cTotal; ptr < len; ++ptr){
let si = this.C_PTRS[ptr];
let asi = M[C_PO_PTR_A + si];
let bsi = M[C_PO_PTR_B + si];
if(M[C_TYPE + si] === this.COLLISION_TYPE){
// TODO implement block solver from GDC Erin Catto video
let len = 1;
if(M[C_FORM + si] == this.SURFACES_FORM || M[C_FORM + si] == this.SURFACE_POLYGON_FORM || M[C_FORM + si] == this.POLYGONS_FORM) len = 2;
// TODO update i increment?
for(let i = si, c = 0; c < len; i += 16, c += 1){
if(M[C_ACTIVE + i] == 0) continue;
// relative velocity at collsion vertices
let vxRel = M[O_VX + asi] + M[O_W + asi] * -M[C_RAY + i] - M[O_VX + bsi] - M[O_W + bsi] * -M[C_RBY + i];
let vyRel = M[O_VY + asi] + M[O_W + asi] * M[C_RAX + i] - M[O_VY + bsi] - M[O_W + bsi] * M[C_RBX + i];
// tangential impulse (friction)
let jt = (M[C_NX + i] * vyRel - M[C_NY + i] * vxRel) * M[C_MT + i];
let oldJt = M[C_JT + i];
M[C_JT + i] += jt;
// max friction
let maxJt = -M[C_JN + i] * M[C_US + si];
// clamp to max friction
if(Math.abs(M[C_JT + i]) > maxJt){
// new
maxJt = -M[C_JN + i] * M[C_UK + si];
if(jt > 0) M[C_JT + i] = maxJt;
else M[C_JT + i] = -maxJt;
jt = M[C_JT + i] - oldJt;
}
// integrate tangential impusle
let jx = jt * -M[C_NY + i];
let jy = jt * M[C_NX + i];
if(M[O_TYPE + asi] == this.MOVABLE_TYPE){
M[O_VX + asi] -= jx * M[O_M_INV + asi];
M[O_VY + asi] -= jy * M[O_M_INV + asi];
M[O_W + asi] -= jt * M[C_RTA + i] * M[O_I_INV + asi];
}
if(M[O_TYPE + bsi] == this.MOVABLE_TYPE){
M[O_VX + bsi] += jx * M[O_M_INV + bsi];
M[O_VY + bsi] += jy * M[O_M_INV + bsi];
M[O_W + bsi] += jt * M[C_RTB + i] * M[O_I_INV + bsi];
}
// update relative velocity
vxRel = M[O_VX + asi] + M[O_W + asi] * -M[C_RAY + i] - M[O_VX + bsi] - M[O_W + bsi] * -M[C_RBY + i];
vyRel = M[O_VY + asi] + M[O_W + asi] * M[C_RAX + i] - M[O_VY + bsi] - M[O_W + bsi] * M[C_RBX + i];
// normal impulse
//experiment
let jn = (M[C_NX + i] * vxRel + M[C_NY + i] * vyRel + M[C_DIST + i]) * M[C_M + i];
//if(M[C_DIST + i] && jn < 0) continue;
let oldJn = M[C_JN + i];
M[C_JN + i] += jn;
// clamp to insure accumulated normal impulse stays negative (push only)
if(M[C_JN + i] > 0) M[C_JN + i] = 0;
jn = M[C_JN + i] - oldJn;
if(jn) {
this.unsolved = true;
// integrate impusle
let jx = jn * M[C_NX + i];
let jy = jn * M[C_NY + i];
if(M[O_TYPE + asi] == this.MOVABLE_TYPE){
M[O_VX + asi] -= jx * M[O_M_INV + asi];
M[O_VY + asi] -= jy * M[O_M_INV + asi];
M[O_W + asi] -= jn * M[C_RNA + i] * M[O_I_INV + asi];
}
if(M[O_TYPE + bsi] == this.MOVABLE_TYPE){
M[O_VX + bsi] += jx * M[O_M_INV + bsi];
M[O_VY + bsi] += jy * M[O_M_INV + bsi];
M[O_W + bsi] += jn * M[C_RNB + i] * M[O_I_INV + bsi];
}
}
}
// revolute joint solver
} else if(M[C_TYPE + si] == this.JOINT_TYPE){
if(M[C_IS_MOTOR + si]){
// solve motor sub-constraint
// relative angular velocity minus desired velocity
let jm = (M[O_W + asi] - M[O_W + bsi] - M[C_MW + si]) * M[C_M_I + si];
// clamp to max impulse
let oldJm = M[C_SUM_T + si];
M[C_SUM_T + si] += jm;
if(Math.abs(M[C_SUM_T + si]) > M[C_M_MAX_T + si]) {
M[C_SUM_T + si] = M[C_M_MAX_T + si] * Math.sign(jm);
jm = M[C_SUM_T + si] - oldJm;
}
// integrate impusle
if(jm){
this.unresolved = true;
M[O_W + asi] -= jm * M[O_I_INV + asi];
M[O_W + bsi] += jm * M[O_I_INV + bsi];
}
}
// relative velocity at joint vertices plus distance
// turned off distance in initialize contraints
let vxRel = M[O_VX + asi] + M[O_W + asi] * -M[C_RAY + si] - M[O_VX + bsi] - M[O_W + bsi] * -M[C_RBY + si]/* + M[C_DX + si]*/;
let vyRel = M[O_VY + asi] + M[O_W + asi] * M[C_RAX + si] - M[O_VY + bsi] - M[O_W + bsi] * M[C_RBX + si]/* + M[C_DY + si]*/;
let vn = vxRel * vxRel + vyRel * vyRel;
if(!vn) continue;
this.unsolved = true;
vn = Math.sqrt(vn);
vxRel /= vn;
vyRel /= vn;
let rna = M[C_RAX + si] * vyRel - M[C_RAY + si] * vxRel;
let rnb = M[C_RBX + si] * vyRel - M[C_RBY + si] * vxRel;
// total pseudo-mass in constraint reference
let mInv = M[O_M_INV + asi] + M[O_M_INV + bsi] + rna * rna * M[O_I_INV + asi] + rnb * rnb * M[O_I_INV + bsi];
//let j = vn / mInv;
let j = vn / mInv;
// TODO implement revolute friction?
// integrate impulse
let jx = j * vxRel;
let jy = j * vyRel;
// accumulate impulse
M[C_JX + si] += jx;
M[C_JY + si] += jy;
if(M[O_TYPE + asi] == this.MOVABLE_TYPE){
M[O_VX + asi] -= jx * M[O_M_INV + asi];
M[O_VY + asi] -= jy * M[O_M_INV + asi];
M[O_W + asi] -= j * rna * M[O_I_INV + asi];
}
if(M[O_TYPE + bsi] == this.MOVABLE_TYPE){
M[O_VX + bsi] += jx * M[O_M_INV + bsi];
M[O_VY + bsi] += jy * M[O_M_INV + bsi];
M[O_W + bsi] += j * rnb * M[O_I_INV + bsi];
}
}
}
}
//console.log("vi = " + iter);
// integrate velocities
for(let i = 0, ptr = this.PO_PTRS[i], len = this.poTotal; i < len; ++i, ptr = this.PO_PTRS[i]){
if(M[O_TYPE + ptr] == this.FIXED_TYPE) continue;
M[O_TX + ptr] += M[O_VX + ptr];
M[O_TY + ptr] += M[O_VY + ptr];
M[O_O + ptr] += M[O_W + ptr];
M[O_COS + ptr] = Math.cos(M[O_O + ptr]);
M[O_SIN + ptr] = Math.sin(M[O_O + ptr]);
this.updateWorldPositions(ptr);
}
// solve position constraints
iter = 0
for(this.unsolved = true; this.unsolved && iter < this.POSITION_ITERATIONS; ++iter){
this.unsolved = false;
for(let ptr = 0, len = this.cTotal; ptr < len; ++ptr){
let si = this.C_PTRS[ptr];
//if(!M[C_ACTIVE + si]) continue;
let asi = M[C_PO_PTR_A + si];
let bsi = M[C_PO_PTR_B + si];
if(M[C_TYPE + si] == this.COLLISION_TYPE){
let cdLen = 7;
if(M[C_FORM + si] == this.SURFACES_FORM || M[C_FORM + si] == this.SURFACE_POLYGON_FORM || M[C_FORM + si] == this.POLYGONS_FORM) cdLen = 14;
this.getCollisionData(si, asi, bsi);
for(let i = si, c = 0; c < cdLen; i += 16, c += 7){
if(this.collisionData[6 + c] >= 0) {
continue;
}
this.unsolved = true;
let rna = (this.collisionData[2 + c] - M[O_TX + asi]) * this.collisionData[1 + c] - (this.collisionData[3 + c] - M[O_TY + asi]) * this.collisionData[0 + c];
let rnb = (this.collisionData[4 + c] - M[O_TX + bsi]) * this.collisionData[1 + c] - (this.collisionData[5 + c] - M[O_TY + bsi]) * this.collisionData[0 + c];
//tune
let j = this.collisionData[6 + c] * 0.5 / (M[O_M_INV + asi] + M[O_M_INV + bsi] + rna * rna * M[O_I_INV + asi] + rnb * rnb * M[O_I_INV + bsi]);
let jx = j * this.collisionData[0 + c];
let jy = j * this.collisionData[1 + c];
if(M[O_TYPE + asi] == this.MOVABLE_TYPE) {
M[O_TX + asi] -= jx * M[O_M_INV + asi];
M[O_TY + asi] -= jy * M[O_M_INV + asi];
M[O_O + asi] -= j * rna * M[O_I_INV + asi];
M[O_COS + asi] = Math.cos(M[O_O + asi]);
M[O_SIN + asi] = Math.sin(M[O_O + asi]);
this.updateWorldPositions(asi);
}
if(M[O_TYPE + bsi] == this.MOVABLE_TYPE) {
M[O_TX + bsi] += jx * M[O_M_INV + bsi];
M[O_TY + bsi] += jy * M[O_M_INV + bsi];
M[O_O + bsi] += j * rnb * M[O_I_INV + bsi];
M[O_COS + bsi] = Math.cos(M[O_O + bsi]);
M[O_SIN + bsi] = Math.sin(M[O_O + bsi]);
this.updateWorldPositions(bsi);
}
}
} else if(M[C_TYPE + si] == this.JOINT_TYPE){
M[C_RAX + si] = M[C_LAX + si] * M[O_COS + asi] - M[C_LAY + si] * M[O_SIN + asi];
M[C_RAY + si] = M[C_LAY + si] * M[O_COS + asi] + M[C_LAX + si] * M[O_SIN + asi];
M[C_RBX + si] = M[C_LBX + si] * M[O_COS + bsi] - M[C_LBY + si] * M[O_SIN + bsi];
M[C_RBY + si] = M[C_LBY + si] * M[O_COS + bsi] + M[C_LBX + si] * M[O_SIN + bsi];
let nx = M[C_RAX + si] + M[O_TX + asi] - M[C_RBX + si] - M[O_TX + bsi];
let ny = M[C_RAY + si] + M[O_TY + asi] - M[C_RBY + si] - M[O_TY + bsi];
let dist = nx * nx + ny * ny;
if(!dist) {
continue;
}
this.unsolved = true;
dist = Math.sqrt(dist);
nx /= dist;
ny /= dist;
let rna = M[C_RAX + si] * ny - M[C_RAY + si] * nx;
let rnb = M[C_RBX + si] * ny - M[C_RBY + si] * nx;
// total "mass" in the constraint reference
let mInv = M[O_M_INV + asi] + M[O_M_INV + bsi] + rna * rna * M[O_I_INV + asi] + rnb * rnb * M[O_I_INV + bsi];
// tune
let j = dist * 0.5 / mInv;
let jx = j * nx;
let jy = j * ny;
if(M[O_TYPE + asi] == this.MOVABLE_TYPE) {
M[O_TX + asi] -= jx * M[O_M_INV + asi];
M[O_TY + asi] -= jy * M[O_M_INV + asi];
M[O_O + asi] -= j * rna * M[O_I_INV + asi];
M[O_COS + asi] = Math.cos(M[O_O + asi]);
M[O_SIN + asi] = Math.sin(M[O_O + asi]);
this.updateWorldPositions(asi);
}
if(M[O_TYPE + bsi] == this.MOVABLE_TYPE) {
M[O_TX + bsi] += jx * M[O_M_INV + bsi];
M[O_TY + bsi] += jy * M[O_M_INV + bsi];
M[O_O + bsi] += j * rnb * M[O_I_INV + bsi];
M[O_COS + bsi] = Math.cos(M[O_O + bsi]);
M[O_SIN + bsi] = Math.sin(M[O_O + bsi]);
this.updateWorldPositions(bsi);
}
}
}
}
//console.log("pi = " + iter);
},
updateWorldPositions(ptr){
if(this.M[O_TYPE + ptr] == this.FIXED_TYPE) return;
if(this.M[O_FORM + ptr] == this.PLANE_FORM) {
this.M[O_W0X + ptr] = (this.M[O_L0X + ptr] * this.M[O_COS + ptr] - this.M[O_L0Y + ptr] * this.M[O_SIN + ptr]) + this.M[O_TX + ptr];
this.M[O_W0Y + ptr] = (this.M[O_L0Y + ptr] * this.M[O_COS + ptr] + this.M[O_L0X + ptr] * this.M[O_SIN + ptr]) + this.M[O_TY + ptr];
this.M[O_W1X + ptr] = (this.M[O_L1X + ptr] * this.M[O_COS + ptr] - this.M[O_L1Y + ptr] * this.M[O_SIN + ptr]) + this.M[O_TX + ptr];
this.M[O_W1Y + ptr] = (this.M[O_L1Y + ptr] * this.M[O_COS + ptr] + this.M[O_L1X + ptr] * this.M[O_SIN + ptr]) + this.M[O_TY + ptr];
let dx = this.M[O_W1X + ptr] - this.M[O_W0X + ptr];
let dy = this.M[O_W1Y + ptr] - this.M[O_W0Y + ptr];
this.M[O_UX + ptr] = dx * this.M[O_L_INV + ptr];
this.M[O_UY + ptr] = dy * this.M[O_L_INV + ptr];
} else if(this.M[O_FORM + ptr] == this.POLYGON_FORM){
let start = O_NUM_VERTICES + ptr;
let pPtr = start + 1;
this.M[V_WX + pPtr] = (this.M[V_LX + pPtr] * this.M[O_COS + ptr] - this.M[V_LY + pPtr] * this.M[O_SIN + ptr]) + this.M[O_TX + ptr];
this.M[V_WY + pPtr] = (this.M[V_LY + pPtr] * this.M[O_COS + ptr] + this.M[V_LX + pPtr] * this.M[O_SIN + ptr]) + this.M[O_TY + ptr];
for(let vPtr = start + 1 + (this.M[O_NUM_VERTICES + ptr] - 1) * this.V_SIZE; vPtr > start; pPtr = vPtr, vPtr -= this.V_SIZE){
this.M[V_WX + vPtr] = (this.M[V_LX + vPtr] * this.M[O_COS + ptr] - this.M[V_LY + vPtr] * this.M[O_SIN + ptr]) + this.M[O_TX + ptr];
this.M[V_WY + vPtr] = (this.M[V_LY + vPtr] * this.M[O_COS + ptr] + this.M[V_LX + vPtr] * this.M[O_SIN + ptr]) + this.M[O_TY + ptr];
this.M[V_UX + vPtr] = (this.M[V_WX + pPtr] - this.M[V_WX + vPtr]) * this.M[V_L_INV + vPtr];
this.M[V_UY + vPtr] = (this.M[V_WY + pPtr] - this.M[V_WY + vPtr]) * this.M[V_L_INV + vPtr];
}
}
},
getPlanesCollisionData(asi, bsi){
let ax = this.M[O_W0X + asi];
let ay = this.M[O_W0Y + asi];
let bx = this.M[O_W0X + bsi];
let by = this.M[O_W0Y + bsi];
let dot = (ax - bx) * this.M[O_UX + bsi] + (ay - by) * this.M[O_UY + bsi];
if(dot < 0) dot = 0;
else if(dot > this.M[O_L + bsi]) dot = this.M[O_L + bsi];
bx += dot * this.M[O_UX + bsi];
by += dot * this.M[O_UY + bsi];
if(dot == 0 || dot == this.M[O_L + bsi]){
dot = (bx - ax) * this.M[O_UX + asi] + (by - ay) * this.M[O_UY + asi];
if(dot < 0) dot = 0;
else if(dot > this.M[O_L + asi]) dot = this.M[O_L + asi];
ax += dot * this.M[O_UX + asi];
ay += dot * this.M[O_UY + asi];
}
let nx = ax - bx;
let ny = ay - by;
let dist = Math.sqrt(nx * nx + ny * ny);
//debugPoints.push([ax, ay]);
//debugPoints.push([bx, by]);
//let results = [nx / dist, ny / dist, ax, ay, bx, by, dist - this.M[O_HALF_WIDTH + asi] - this.M[O_HALF_WIDTH + bsi]];
this.collisionData[0] = nx / dist;
this.collisionData[1] = ny / dist;
this.collisionData[2] = ax;
this.collisionData[3] = ay;
this.collisionData[4] = bx;
this.collisionData[5] = by;
this.collisionData[6] = dist - this.M[O_HALF_WIDTH + asi] - this.M[O_HALF_WIDTH + bsi];
ax = this.M[O_W1X + asi];
ay = this.M[O_W1Y + asi];
bx = this.M[O_W0X + bsi];
by = this.M[O_W0Y + bsi];
dot = (ax - bx) * this.M[O_UX + bsi] + (ay - by) * this.M[O_UY + bsi];
if(dot < 0) dot = 0;
else if(dot > this.M[O_L + bsi]) dot = this.M[O_L + bsi];
bx += dot * this.M[O_UX + bsi];
by += dot * this.M[O_UY + bsi];
if(dot == 0 || dot == this.M[O_L + bsi]){
dot = (ax - bx) * this.M[O_UX + asi] + (ay - by) * this.M[O_UY + asi];
if(dot < 0) dot = 0.0;
else if(dot > this.M[O_L + asi]) dot = this.M[O_L + asi];
ax -= dot * this.M[O_UX + asi];
ay -= dot * this.M[O_UY + asi];
}
nx = ax - bx;
ny = ay - by;
dist = Math.sqrt(nx * nx + ny * ny);
//debugPoints.push([ax, ay]);
//debugPoints.push([bx, by]);
//results.push(nx / dist, ny / dist, ax, ay, bx, by, dist - this.M[O_HALF_WIDTH + asi] - this.M[O_HALF_WIDTH + bsi]);
//return results;
this.collisionData[7] = nx / dist;
this.collisionData[8] = ny / dist;
this.collisionData[9] = ax;
this.collisionData[10] = ay;
this.collisionData[11] = bx;
this.collisionData[12] = by;
this.collisionData[13] = dist - this.M[O_HALF_WIDTH + asi] - this.M[O_HALF_WIDTH + bsi];
},
getCirclePlaneCollisionData(cSi, pSi){
let lx = this.M[O_W0X + pSi];
let ly = this.M[O_W0Y + pSi];
let cx = this.M[O_TX + cSi];
let cy = this.M[O_TY + cSi];
let dot = (cx - lx) * this.M[O_UX + pSi] + (cy - ly) * this.M[O_UY + pSi];
if(dot < 0) dot = 0;
else if(dot > this.M[O_L + pSi]) dot = this.M[O_L + pSi];
lx += this.M[O_UX + pSi] * dot;
ly += this.M[O_UY + pSi] * dot;
let nx = this.M[O_TX + cSi] - lx;
let ny = this.M[O_TY + cSi] - ly;
let dist = Math.sqrt(nx * nx + ny * ny);
nx /= dist;
ny /= dist;
cx += nx * -this.M[O_RADIUS + cSi];
cy += ny * -this.M[O_RADIUS + cSi];
//return [nx, ny, cx, cy, lx, ly, dist - this.M[O_RADIUS + cSi] - this.M[O_HALF_WIDTH + pSi]];
this.collisionData[0] = nx;
this.collisionData[1] = ny;
this.collisionData[2] = cx;
this.collisionData[3] = cy;
this.collisionData[4] = lx;
this.collisionData[5] = ly;
this.collisionData[6] = dist - this.M[O_RADIUS + cSi] - this.M[O_HALF_WIDTH + pSi];
},
getCirclesCollisionData(asi, bsi){
let ax = this.M[O_TX + asi];
let ay = this.M[O_TY + asi];
let bx = this.M[O_TX + bsi];
let by = this.M[O_TY + bsi];
let nx = ax - bx;
let ny = ay - by;
let dist = Math.sqrt(nx * nx + ny * ny);
nx /= dist;
ny /= dist;
ax -= nx * this.M[O_RADIUS + asi];
ay -= ny * this.M[O_RADIUS + asi];
bx += nx * this.M[O_RADIUS + bsi];
by += ny * this.M[O_RADIUS + bsi];
//return [nx, ny, ax, ay, bx, by, dist - this.M[O_RADIUS + asi] - this.M[O_RADIUS + bsi]];
this.collisionData[0] = nx;
this.collisionData[1] = ny;
this.collisionData[2] = ax;
this.collisionData[3] = ay;
this.collisionData[4] = bx;
this.collisionData[5] = by;
this.collisionData[6] = dist - this.M[O_RADIUS + asi] - this.M[O_RADIUS + bsi];
},
getCirclePolygonCollisionData(cPtr, pPtr){
let M = this.M;
let cx = M[O_TX + cPtr];
let cy = M[O_TY + cPtr];
let nx = cx - M[O_TX + pPtr];
let ny = cy - M[O_TY + pPtr];
for(let vPtr = O_NUM_VERTICES + 1 + pPtr, len = vPtr + M[O_NUM_VERTICES + pPtr] * this.V_SIZE; vPtr < len; vPtr += this.V_SIZE){
let px = M[V_WX + vPtr] - M[O_TX + pPtr];
let py = M[V_WY + vPtr] - M[O_TY + pPtr];
let inv = 1.0 / (nx * M[V_UY + vPtr] - ny * M[V_UX + vPtr]);
let dot = inv * ny * px - inv * nx * py;
if(dot > 0.0 && dot < M[V_L + vPtr] && inv * M[V_UY + vPtr] * px - inv * M[V_UX + vPtr] * py > 0) {
dot = (cx - M[V_WX + vPtr]) * M[V_UX + vPtr] + (cy - M[V_WY + vPtr]) * M[V_UY + vPtr];
if(dot < 0) {
if(vPtr == O_NUM_VERTICES + 1 + pPtr) vPtr = len - this.V_SIZE;
else vPtr -= this.V_SIZE;
dot = (cx - M[V_WX + vPtr]) * M[V_UX + vPtr] + (cy - M[V_WY + vPtr]) * M[V_UY + vPtr];
} else if(dot > M[V_L + vPtr]){
if(vPtr == len - this.V_SIZE) vPtr = O_NUM_VERTICES + 1 + pPtr;
else vPtr += this.V_SIZE;
dot = (cx - M[V_WX + vPtr]) * M[V_UX + vPtr] + (cy - M[V_WY + vPtr]) * M[V_UY + vPtr];
}
if(dot < 0) dot = 0;
else if(dot > M[V_L + vPtr]) dot = M[V_L + vPtr];
px = M[V_UX + vPtr] * dot + M[V_WX + vPtr];
py = M[V_UY + vPtr] * dot + M[V_WY + vPtr];
nx = cx - px;
ny = cy - py;
let dist = Math.sqrt(nx * nx + ny * ny);
nx /= dist;
ny /= dist;
cx -= nx * M[O_RADIUS + cPtr];
cy -= ny * M[O_RADIUS + cPtr];
debugPoints.push([px, py]);
debugPoints.push([cx, cy]);
this.collisionData[0] = nx;
this.collisionData[1] = ny;
this.collisionData[2] = cx;
this.collisionData[3] = cy;
this.collisionData[4] = px;
this.collisionData[5] = py;
this.collisionData[6] = dist - M[O_RADIUS + cPtr] - this.POLYGON_SKIN;
return;
}
}
this.collisionData[6] = Infinity;
},
computeLineIntersect(asx, asy, adx, ady, bsx, bsy, bdx, bdy){
let dx = bsx - asx;
let dy = bsy - asy;
let inv = 1.0 / (adx * bdy - ady * bdx);
return [inv * bdy * dx - inv * bdx * dy, inv * ady * dx - inv * adx * dy];
},
getCollisionData(ptr, aPtr, bPtr){
let M = this.M;
let form = M[C_FORM + ptr];
if(form == this.POINT_SURFACE_FORM) return this.getCirclePlaneCollisionData(aPtr, bPtr);
else if(form == this.POINTS_FORM) return this.getCirclesCollisionData(aPtr, bPtr);
else if(form == this.SURFACES_FORM) return this.getPlanesCollisionData(aPtr, bPtr);
else if(form == this.POINT_POLYGON_FORM) return this.getCirclePolygonCollisionData(aPtr, bPtr);
else if(form == this.SURFACE_POLYGON_FORM){
let vp0 = 0;
let vp1 = 0;
let nx0 = M[O_W0X + aPtr] - M[O_TX + bPtr];
let ny0 = M[O_W0Y + aPtr] - M[O_TY + bPtr];
let nx1 = M[O_W1X + aPtr] - M[O_TX + bPtr];
let ny1 = M[O_W1Y + aPtr] - M[O_TY + bPtr];
for(let v = O_NUM_VERTICES + 1 + bPtr, len = M[O_NUM_VERTICES + bPtr] * this.V_SIZE + v; v < len; v += this.V_SIZE){
if(vp0 === 0){
let dots = this.computeLineIntersect(
M[O_TX + bPtr], M[O_TY + bPtr],
nx0, ny0,
M[V_WX + v], M[V_WY + v],
M[V_UX + v], M[V_UY + v]
);
if(dots[0] > 0 && dots[1] > 0 && dots[1] < M[V_L + v]){
debugPoints.push([dots[1] * M[V_UX + v] + M[V_WX + v], dots[1] * M[V_UY + v] + M[V_WY + v]]);
if(dots[0] > 1) vp0 = v;
else vp0 = false;
if(vp1 !== 0) break;
}
}
if(vp1 === 0){
let dots = this.computeLineIntersect(
M[O_TX + bPtr], M[O_TY + bPtr],
nx1, ny1,
M[V_WX + v], M[V_WY + v],
M[V_UX + v], M[V_UY + v]
);
if(dots[0] > 0 && dots[1] > 0 && dots[1] < M[V_L + v]){
debugPoints.push([dots[1] * M[V_UX + v] + M[V_WX + v], dots[1] * M[V_UY + v] + M[V_WY + v]]);
if(dots[0] > 1) vp1 = v;
else vp1 = false;
if(vp0 !== 0) break;
}
}
}
let results = [];
if(vp0){
let px = M[V_WX + vp0];
let py = M[V_WY + vp0];
let sx = M[O_W0X + aPtr];
let sy = M[O_W0Y + aPtr];
let dot = (sx - px) * M[V_UX + vp0] + (sy - py) * M[V_UY + vp0];
if(dot < 0) dot = 0;
else if(dot > M[V_L + vp0]) dot = M[V_L + vp0];
px += dot * M[V_UX + vp0];
py += dot * M[V_UY + vp0];
if(!dot || dot == M[V_L + vp0]) {
dot = (px - sx) * M[O_UX + aPtr] + (py - sy) * M[O_UY + aPtr];
if(dot < 0) dot = 0;
else if(dot > M[O_L + aPtr]) dot = M[O_L + aPtr];
sx += dot * M[O_UX + aPtr];
sy += dot * M[O_UY + aPtr];
}
let nx = px - sx;
let ny = py - sy;
let dist = Math.sqrt(nx * nx + ny * ny);
debugPoints.push([sx, sy]);
debugPoints.push([px, py]);
this.collisionData[0] = nx / dist;
this.collisionData[1] = ny / dist;
this.collisionData[2] = sx;
this.collisionData[3] = sy;
this.collisionData[4] = px;
this.collisionData[5] = py;
//this.collisionData[6] = -dist - M[O_HALF_WIDTH + aPtr] - this.POLYGON_SKIN;
this.collisionData[6] = dist - M[O_HALF_WIDTH + aPtr] - this.POLYGON_SKIN;
} else {
this.collisionData[6] = Infinity;
}
if(vp1){
let px = M[V_WX + vp1];
let py = M[V_WY + vp1];
let sx = M[O_W1X + aPtr];
let sy = M[O_W1Y + aPtr];
let dot = (sx - px) * M[V_UX + vp1] + (sy - py) * M[V_UY + vp1];
if(dot < 0) dot = 0;
else if(dot > M[V_L + vp1]) dot = M[V_L + vp1];
px += dot * M[V_UX + vp1];
py += dot * M[V_UY + vp1];
if(!dot || dot == M[V_L + vp1]) {
dot = (sx - px) * M[O_UX + aPtr] + (sy - py) * M[O_UY + aPtr];
if(dot < 0) dot = 0;
else if(dot > M[O_L + aPtr]) dot = M[O_L + aPtr];
sx -= dot * M[O_UX + aPtr];
sy -= dot * M[O_UY + aPtr];
}
let nx = px - sx;
let ny = py - sy;
let dist = Math.sqrt(nx * nx + ny * ny);
debugPoints.push([sx, sy]);
debugPoints.push([px, py]);
this.collisionData[7] = nx / dist;
this.collisionData[8] = ny / dist;
this.collisionData[9] = sx;
this.collisionData[10] = sy;
this.collisionData[11] = px;
this.collisionData[12] = py;
//this.collisionData[13] = -dist - M[O_HALF_WIDTH + aPtr] - this.POLYGON_SKIN;
this.collisionData[13] = dist - M[O_HALF_WIDTH + aPtr] - this.POLYGON_SKIN;
} else {
this.collisionData[13] = Infinity;
}
return results;
/*
let sx0 = 0;
let sy0 = 0;
let px0 = 0;
let py0 = 0;
let nx0 = 0;
let ny0 = 0;
let dist0 = 99;
let vp0 = 0;
let sx1 = 0;
let sy1 = 0;
let px1 = 0;
let py1 = 0;
let nx1 = 0;
let ny1 = 0;
let dist1 = 99;
let vp1 = 0;
for(let v = O_NUM_VERTICES + 1 + bPtr, len = M[O_NUM_VERTICES + bPtr] * this.V_SIZE + v; v < len; v += this.V_SIZE){
let px = M[V_WX + v];
let py = M[V_WY + v];
let sx = M[O_W0X + aPtr];
let sy = M[O_W0Y + aPtr];
let dot = (sx - px) * M[V_UX + v] + (sy - py) * M[V_UY + v];
if(dot < M[V_L + v]) {
let nx = M[V_UY + v];
let ny = -M[V_UX + v];
if(dot < 0) dot = 0;
px += dot * M[V_UX + v];
py += dot * M[V_UY + v];
if(!dot) {
dot = (px - sx) * M[O_UX + aPtr] + (py - sy) * M[O_UY + aPtr];
//if(dot < 0) dot = 0;
//else if(dot > M[O_L + aPtr]) dot = M[O_L + aPtr];
if(dot < M[O_L + aPtr]){
if(dot < 0) dot = 0;
sx += dot * M[O_UX + aPtr];
sy += dot * M[O_UY + aPtr];
if(dot && dot != M[O_L + aPtr]) {
if((sx - M[O_TX + bPtr]) * M[O_UY + aPtr] - (sy - M[O_TY + bPtr]) * M[O_UX + aPtr] > 0){
nx = M[O_UY + aPtr];
ny = -M[O_UX + aPtr];
} else {
nx = -M[O_UY + aPtr];
ny = M[O_UX + aPtr];
}
}
}
}
let dx = sx - px;
let dy = sy - py;
let d = dx * dx + dy * dy;
if(d < dist0){
dist0 = d;
nx0 = nx;
ny0 = ny;
sx0 = sx;
sy0 = sy;
px0 = px;
py0 = py;
vp0 = v;
}
}
px = M[V_WX + v];
py = M[V_WY + v];
sx = M[O_W1X + aPtr];
sy = M[O_W1Y + aPtr];
dot = (sx - px) * M[V_UX + v] + (sy - py) * M[V_UY + v];
if(dot < M[V_L + v]) {
let nx = M[V_UY + v];
let ny = -M[V_UX + v];
if(dot < 0) dot = 0;
px += dot * M[V_UX + v];
py += dot * M[V_UY + v];
if(!dot) {
dot = (sx - px) * M[O_UX + aPtr] + (sy - py) * M[O_UY + aPtr];
//if(dot < 0) dot = 0;
//else if(dot > M[O_L + aPtr]) dot = M[O_L + aPtr];
if(dot < M[O_L + aPtr]){
if(dot < 0) dot = 0;
sx -= dot * M[O_UX + aPtr];
sy -= dot * M[O_UY + aPtr];
if(dot && dot != M[O_L + aPtr]) {
if((sx - M[O_TX + bPtr]) * M[O_UY + aPtr] - (sy - M[O_TY + bPtr]) * M[O_UX + aPtr] > 0){
nx = M[O_UY + aPtr];
ny = -M[O_UX + aPtr];
} else {
nx = -M[O_UY + aPtr];
ny = M[O_UX + aPtr];
}
}
}