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mat4.js
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// Matrix shape:
// aa ab ac ad
// ba bb bc bd
// ca cb cc cd
// da db dc dd
export class Mat4 {
constructor() {
this.setIdentity();
}
setIdentity() {
this.aa = 1; this.ab = 0; this.ac = 0; this.ad = 0;
this.ba = 0; this.bb = 1; this.bc = 0; this.bd = 0;
this.ca = 0; this.cb = 0; this.cc = 1; this.cd = 0;
this.da = 0; this.db = 0; this.dc = 0; this.dd = 1;
return this;
}
setComponents(aa, ab, ac, ad, ba, bb, bc, bd, ca, cb, cc, cd, da, db, dc, dd) {
this.aa = aa; this.ab = ab; this.ac = ac; this.ad = ad;
this.ba = ba; this.bb = bb; this.bc = bc; this.bd = bd;
this.ca = ca; this.cb = cb; this.cc = cc; this.cd = cd;
this.da = da; this.db = db; this.dc = dc; this.dd = dd;
return this;
}
set(m) {
this.aa = m.aa; this.ab = m.ab; this.ac = m.ac; this.ad = m.ad;
this.ba = m.ba; this.bb = m.bb; this.bc = m.bc; this.bd = m.bd;
this.ca = m.ca; this.cb = m.cb; this.cc = m.cc; this.cd = m.cd;
this.da = m.da; this.db = m.db; this.dd = m.dd; this.dd = m.dd;
return this;
}
setMultiply(ma, mb) {
return this.setComponents(
/*aa*/ ma.aa * mb.aa + ma.ab * mb.ba + ma.ac * mb.ca + ma.ad * mb.da,
/*ab*/ ma.aa * mb.ab + ma.ab * mb.bb + ma.ac * mb.cb + ma.ad * mb.db,
/*ac*/ ma.aa * mb.ac + ma.ab * mb.bc + ma.ac * mb.cc + ma.ad * mb.dc,
/*ad*/ ma.aa * mb.ad + ma.ab * mb.bd + ma.ac * mb.cd + ma.ad * mb.dd,
/*ba*/ ma.ba * mb.aa + ma.bb * mb.ba + ma.bc * mb.ca + ma.bd * mb.da,
/*bb*/ ma.ba * mb.ab + ma.bb * mb.bb + ma.bc * mb.cb + ma.bd * mb.db,
/*bc*/ ma.ba * mb.ac + ma.bb * mb.bc + ma.bc * mb.cc + ma.bd * mb.dc,
/*bd*/ ma.ba * mb.ad + ma.bb * mb.bd + ma.bc * mb.cd + ma.bd * mb.dd,
/*ca*/ ma.ca * mb.aa + ma.cb * mb.ba + ma.cc * mb.ca + ma.cd * mb.da,
/*cb*/ ma.ca * mb.ab + ma.cb * mb.bb + ma.cc * mb.cb + ma.cd * mb.db,
/*cc*/ ma.ca * mb.ac + ma.cb * mb.bc + ma.cc * mb.cc + ma.cd * mb.dc,
/*cd*/ ma.ca * mb.ad + ma.cb * mb.bd + ma.cc * mb.cd + ma.cd * mb.dd,
/*da*/ ma.da * mb.aa + ma.db * mb.ba + ma.dc * mb.ca + ma.dd * mb.da,
/*db*/ ma.da * mb.ab + ma.db * mb.bb + ma.dc * mb.cb + ma.dd * mb.db,
/*dc*/ ma.da * mb.ac + ma.db * mb.bc + ma.dc * mb.cc + ma.dd * mb.dc,
/*dd*/ ma.da * mb.ad + ma.db * mb.bd + ma.dc * mb.cd + ma.dd * mb.dd,
);
}
setTranslateXyz(x, y, z) {
return this.setComponents(
1, 0, 0, x,
0, 1, 0, y,
0, 0, 1, z,
0, 0, 0, 1,
);
}
setTranslateVec3(v) {
return this.setTranslateXyz(v.x, v.y, v.z);
}
setScale(k) {
return this.setComponents(
k, 0, 0, 0,
0, k, 0, 0,
0, 0, k, 0,
0, 0, 0, 1,
);
}
setRotateRotor(r) {
const {rr: a, yz: b, zx: c, xy: d} = r;
// (arr - byz - czx - dxy) * (ex + fy + gz) * (arr + byz + czx + dxy)
//
// = (arr - byz - czx - dxy) * (
// eaxrr + ebxyz + ecxzx + edxxy +
// fayrr + fbyyz + fcyzx + fdyxy +
// gazrr + gbzyz + gczzx + gdzxy +
// )
//
// = (arr - byz - czx - dxy) * (
// eax + ebxyz + -ecz + edy +
// fay + fbz + fcxyz + -fdx +
// gaz + -gby + gcx + gdxyz +
// )
//
// = (arr - byz - czx - dxy) * (
// (ea + -fd + gc)x +
// (ed + fa + -gb)y +
// (-ec + fb + ga)z +
// (eb + fc + gd)xyz +
// )
//
// = a(ea + -fd + gc)x +
// a(ed + fa + -gb)y +
// a(-ec + fb + ga)z +
// a(eb + fc + gd)xyz +
// -b(ea + -fd + gc)yzx +
// -b(ed + fa + -gb)yzy +
// -b(-ec + fb + ga)yzz +
// -b(eb + fc + gd)yzxyz +
// -c(ea + -fd + gc)zxx +
// -c(ed + fa + -gb)zxy +
// -c(-ec + fb + ga)zxz +
// -c(eb + fc + gd)zxxyz +
// -d(ea + -fd + gc)xyx +
// -d(ed + fa + -gb)xyy +
// -d(-ec + fb + ga)xyz +
// -d(eb + fc + gd)xyxyz +
//
// = a(ea + -fd + gc)x +
// a(ed + fa + -gb)y +
// a(-ec + fb + ga)z +
// a(eb + fc + gd)xyz +
// -b(ea + -fd + gc)xyz +
// b(ed + fa + -gb)z +
// -b(-ec + fb + ga)y +
// b(eb + fc + gd)x +
// -c(ea + -fd + gc)z +
// -c(ed + fa + -gb)xyz +
// c(-ec + fb + ga)x +
// c(eb + fc + gd)y +
// d(ea + -fd + gc)y +
// -d(ed + fa + -gb)x +
// -d(-ec + fb + ga)xyz +
// d(eb + fc + gd)z +
//
// = (
// a(ea + -fd + gc) +
// b(eb + fc + gd) +
// c(-ec + fb + ga) +
// -d(ed + fa + -gb) +
// )x +
// (
// a(ed + fa + -gb) +
// -b(-ec + fb + ga) +
// c(eb + fc + gd) +
// d(ea + -fd + gc) +
// )y +
// (
// a(-ec + fb + ga) +
// b(ed + fa + -gb) +
// -c(ea + -fd + gc) +
// d(eb + fc + gd) +
// )z +
// (
// a(eb + fc + gd) +
// -b(ea + -fd + gc) +
// -c(ed + fa + -gb) +
// -d(-ec + fb + ga) +
// )xyz +
//
// = (
// aea + -afd + agc +
// beb + bfc + bgd +
// -cec + cfb + cga +
// -ded + -dfa + dgb +
// )x +
// (
// aed + afa + -agb +
// bec + -bfb + -bga +
// ceb + cfc + cgd +
// dea + -dfd + dgc +
// )y +
// (
// -aec + afb + aga +
// bed + bfa + -bgb +
// -cea + cfd + -cgc +
// deb + dfc + dgd +
// )z +
// (
// aeb + afc + agd +
// -bea + bfd + -bgc +
// -ced + -cfa + cgb +
// dec + -dfb + -dga +
// )xyz +
//
// = (
// (-cc + -dd + aa + bb)e +
// (-ad + -da + bc + cb)f +
// (ac + bd + ca + db)g +
// )x +
// (
// (ad + bc + cb + da)e +
// (-bb + -dd + aa + cc)f +
// (-ab + -ba + cd + dc)g +
// )y +
// (
// (-ac + -ca + bd + db)e +
// (ab + ba + cd + dc)f +
// (-bb + -cc + aa + dd)g +
// )z +
// (
// (-ba + -cd + ab + dc)e +
// (-ca + -db + ac + bd)f +
// (-bc + -da + ad + cb)g +
// )xyz +
return this.setComponents(
-c * c + -d * d + a * a + b * b,
-a * d + -d * a + b * c + c * b,
a * c + b * d + c * a + d * b,
0,
a * d + b * c + c * b + d * a,
-b * b + -d * d + a * a + c * c,
-a * b + -b * a + c * d + d * c,
0,
-a * c + -c * a + b * d + d * b,
a * b + b * a + c * d + d * c,
-b * b + -c * c + a * a + d * d,
0,
0, 0, 0, 1,
);
}
inplaceMultiplyLeft(m) { return this.setMultiply(m, this); }
inplaceMultiplyRight(m) { return this.setMultiply(this, m); }
exportToArrayBuffer(float32ArrayBuffer) {
float32ArrayBuffer[0] = this.aa;
float32ArrayBuffer[1] = this.ba;
float32ArrayBuffer[2] = this.ca;
float32ArrayBuffer[3] = this.da;
float32ArrayBuffer[4] = this.ab;
float32ArrayBuffer[5] = this.bb;
float32ArrayBuffer[6] = this.cb;
float32ArrayBuffer[7] = this.db;
float32ArrayBuffer[8] = this.ac;
float32ArrayBuffer[9] = this.bc;
float32ArrayBuffer[10] = this.cc;
float32ArrayBuffer[11] = this.dc;
float32ArrayBuffer[12] = this.ad;
float32ArrayBuffer[13] = this.bd;
float32ArrayBuffer[14] = this.cd;
float32ArrayBuffer[15] = this.dd;
}
}