/
matrix.js
276 lines (253 loc) · 8.11 KB
/
matrix.js
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export const matrix3 = {
multiply: (a, b, ...rest) => {
const multiplication = [
a[0]*b[0] + a[3]*b[1] + a[6]*b[2], /**/ a[1]*b[0] + a[4]*b[1] + a[7]*b[2], /**/ a[2]*b[0] + a[5]*b[1] + a[8]*b[2],
a[0]*b[3] + a[3]*b[4] + a[6]*b[5], /**/ a[1]*b[3] + a[4]*b[4] + a[7]*b[5], /**/ a[2]*b[3] + a[5]*b[4] + a[8]*b[5],
a[0]*b[6] + a[3]*b[7] + a[6]*b[8], /**/ a[1]*b[6] + a[4]*b[7] + a[7]*b[8], /**/ a[2]*b[6] + a[5]*b[7] + a[8]*b[8],
];
if (rest.length === 0) return multiplication;
return matrix3.multiply(multiplication, ...rest);
},
identity: () => ([
1, 0, 0,
0, 1, 0,
0, 0, 1,
]),
translate: (x, y) => ([
1, 0, 0,
0, 1, 0,
x, y, 1,
]),
scale: (sx, sy) => ([
sx, 0, 0,
0, sy, 0,
0, 0, 1,
]),
rotate: rad => {
const c = Math.cos(rad), s = Math.sin(rad);
return [
c, s, 0,
-s, c, 0,
0, 0, 1,
]
},
projection: (width, height) => (
matrix3.multiply(
matrix3.translate(-1, 1),
matrix3.scale(2 / width, -2 / height),
)
),
log: matrix => {
console.group();
console.log(matrix.slice(0, 3))
console.log(matrix.slice(3, 6))
console.log(matrix.slice(6, 9))
console.groupEnd();
}
}
export const matrix4 = {
multiply: (a, b, ...rest) => {
const multiplication = [
b[0]*a[0] + b[1]*a[4] + b[2]*a[8] + b[3]*a[12], /**/ b[0]*a[1] + b[1]*a[5] + b[2]*a[9] + b[3]*a[13], /**/ b[0]*a[2] + b[1]*a[6] + b[2]*a[10] + b[3]*a[14], /**/ b[0]*a[3] + b[1]*a[7] + b[2]*a[11] + b[3]*a[15],
b[4]*a[0] + b[5]*a[4] + b[6]*a[8] + b[7]*a[12], /**/ b[4]*a[1] + b[5]*a[5] + b[6]*a[9] + b[7]*a[13], /**/ b[4]*a[2] + b[5]*a[6] + b[6]*a[10] + b[7]*a[14], /**/ b[4]*a[3] + b[5]*a[7] + b[6]*a[11] + b[7]*a[15],
b[8]*a[0] + b[9]*a[4] + b[10]*a[8] + b[11]*a[12], /**/ b[8]*a[1] + b[9]*a[5] + b[10]*a[9] + b[11]*a[13], /**/ b[8]*a[2] + b[9]*a[6] + b[10]*a[10] + b[11]*a[14], /**/ b[8]*a[3] + b[9]*a[7] + b[10]*a[11] + b[11]*a[15],
b[12]*a[0] + b[13]*a[4] + b[14]*a[8] + b[15]*a[12], /**/ b[12]*a[1] + b[13]*a[5] + b[14]*a[9] + b[15]*a[13], /**/ b[12]*a[2] + b[13]*a[6] + b[14]*a[10] + b[15]*a[14], /**/ b[12]*a[3] + b[13]*a[7] + b[14]*a[11] + b[15]*a[15],
];
if (rest.length === 0) return multiplication;
return matrix4.multiply(multiplication, ...rest);
},
identity: () => ([
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1,
]),
projection: (width, height, depth) => ([
2 / width, 0, 0, 0,
0, -2 / height, 0, 0,
0, 0, 2 / depth, 0,
-1, 1, 0, 1,
]),
translate: (tx, ty, tz) => ([
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
tx, ty, tz, 1,
]),
scale: (sx, sy, sz) => ([
sx, 0, 0, 0,
0, sy, 0, 0,
0, 0, sz, 0,
0, 0, 0, 1,
]),
xRotate: angleInRadians => {
const c = Math.cos(angleInRadians);
const s = Math.sin(angleInRadians);
return [
1, 0, 0, 0,
0, c, s, 0,
0, -s, c, 0,
0, 0, 0, 1,
]
},
yRotate: angleInRadians => {
const c = Math.cos(angleInRadians);
const s = Math.sin(angleInRadians);
return [
c, 0, -s, 0,
0, 1, 0, 0,
s, 0, c, 0,
0, 0, 0, 1,
]
},
zRotate: angleInRadians => {
const c = Math.cos(angleInRadians);
const s = Math.sin(angleInRadians);
return [
c, s, 0, 0,
-s, c, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1,
]
},
perspective: (fieldOfView, aspect, near, far) => {
const f = Math.tan(Math.PI / 2 - fieldOfView / 2);
const rangeInv = 1.0 / (near - far);
return [
f / aspect, 0, 0, 0,
0, f, 0, 0,
0, 0, (near + far) * rangeInv, -1,
0, 0, far * near * rangeInv * 2, 0,
]
},
lookAt: (cameraPosition, target, up) => {
const kHat = matrix4.normalize(
matrix4.subtractVectors(cameraPosition, target)
);
const iHat = matrix4.normalize(matrix4.cross(up, kHat));
const jHat = matrix4.normalize(matrix4.cross(kHat, iHat));
return [
iHat[0], iHat[1], iHat[2], 0,
jHat[0], jHat[1], jHat[2], 0,
kHat[0], kHat[1], kHat[2], 0,
cameraPosition[0],
cameraPosition[1],
cameraPosition[2],
1,
];
},
subtractVectors: (a, b) => ([
a[0] - b[0], a[1] - b[1], a[2] - b[2]
]),
cross: (a, b) => ([
a[1] * b[2] - a[2] * b[1],
a[2] * b[0] - a[0] * b[2],
a[0] * b[1] - a[1] * b[0],
]),
normalize: v => {
const length = Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
// make sure we don't divide by 0.
if (length > 0.00001) {
return [v[0] / length, v[1] / length, v[2] / length];
} else {
return [0, 0, 0];
}
},
inverse: m => {
const m00 = m[0 * 4 + 0];
const m01 = m[0 * 4 + 1];
const m02 = m[0 * 4 + 2];
const m03 = m[0 * 4 + 3];
const m10 = m[1 * 4 + 0];
const m11 = m[1 * 4 + 1];
const m12 = m[1 * 4 + 2];
const m13 = m[1 * 4 + 3];
const m20 = m[2 * 4 + 0];
const m21 = m[2 * 4 + 1];
const m22 = m[2 * 4 + 2];
const m23 = m[2 * 4 + 3];
const m30 = m[3 * 4 + 0];
const m31 = m[3 * 4 + 1];
const m32 = m[3 * 4 + 2];
const m33 = m[3 * 4 + 3];
const tmp_0 = m22 * m33;
const tmp_1 = m32 * m23;
const tmp_2 = m12 * m33;
const tmp_3 = m32 * m13;
const tmp_4 = m12 * m23;
const tmp_5 = m22 * m13;
const tmp_6 = m02 * m33;
const tmp_7 = m32 * m03;
const tmp_8 = m02 * m23;
const tmp_9 = m22 * m03;
const tmp_10 = m02 * m13;
const tmp_11 = m12 * m03;
const tmp_12 = m20 * m31;
const tmp_13 = m30 * m21;
const tmp_14 = m10 * m31;
const tmp_15 = m30 * m11;
const tmp_16 = m10 * m21;
const tmp_17 = m20 * m11;
const tmp_18 = m00 * m31;
const tmp_19 = m30 * m01;
const tmp_20 = m00 * m21;
const tmp_21 = m20 * m01;
const tmp_22 = m00 * m11;
const tmp_23 = m10 * m01;
const t0 = (tmp_0 * m11 + tmp_3 * m21 + tmp_4 * m31) -
(tmp_1 * m11 + tmp_2 * m21 + tmp_5 * m31);
const t1 = (tmp_1 * m01 + tmp_6 * m21 + tmp_9 * m31) -
(tmp_0 * m01 + tmp_7 * m21 + tmp_8 * m31);
const t2 = (tmp_2 * m01 + tmp_7 * m11 + tmp_10 * m31) -
(tmp_3 * m01 + tmp_6 * m11 + tmp_11 * m31);
const t3 = (tmp_5 * m01 + tmp_8 * m11 + tmp_11 * m21) -
(tmp_4 * m01 + tmp_9 * m11 + tmp_10 * m21);
const d = 1.0 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);
return [
d * t0,
d * t1,
d * t2,
d * t3,
d * ((tmp_1 * m10 + tmp_2 * m20 + tmp_5 * m30) -
(tmp_0 * m10 + tmp_3 * m20 + tmp_4 * m30)),
d * ((tmp_0 * m00 + tmp_7 * m20 + tmp_8 * m30) -
(tmp_1 * m00 + tmp_6 * m20 + tmp_9 * m30)),
d * ((tmp_3 * m00 + tmp_6 * m10 + tmp_11 * m30) -
(tmp_2 * m00 + tmp_7 * m10 + tmp_10 * m30)),
d * ((tmp_4 * m00 + tmp_9 * m10 + tmp_10 * m20) -
(tmp_5 * m00 + tmp_8 * m10 + tmp_11 * m20)),
d * ((tmp_12 * m13 + tmp_15 * m23 + tmp_16 * m33) -
(tmp_13 * m13 + tmp_14 * m23 + tmp_17 * m33)),
d * ((tmp_13 * m03 + tmp_18 * m23 + tmp_21 * m33) -
(tmp_12 * m03 + tmp_19 * m23 + tmp_20 * m33)),
d * ((tmp_14 * m03 + tmp_19 * m13 + tmp_22 * m33) -
(tmp_15 * m03 + tmp_18 * m13 + tmp_23 * m33)),
d * ((tmp_17 * m03 + tmp_20 * m13 + tmp_23 * m23) -
(tmp_16 * m03 + tmp_21 * m13 + tmp_22 * m23)),
d * ((tmp_14 * m22 + tmp_17 * m32 + tmp_13 * m12) -
(tmp_16 * m32 + tmp_12 * m12 + tmp_15 * m22)),
d * ((tmp_20 * m32 + tmp_12 * m02 + tmp_19 * m22) -
(tmp_18 * m22 + tmp_21 * m32 + tmp_13 * m02)),
d * ((tmp_18 * m12 + tmp_23 * m32 + tmp_15 * m02) -
(tmp_22 * m32 + tmp_14 * m02 + tmp_19 * m12)),
d * ((tmp_22 * m22 + tmp_16 * m02 + tmp_21 * m12) -
(tmp_20 * m12 + tmp_23 * m22 + tmp_17 * m02)),
];
},
transpose: m => {
return [
m[0], m[4], m[8], m[12],
m[1], m[5], m[9], m[13],
m[2], m[6], m[10], m[14],
m[3], m[7], m[11], m[15],
];
},
log: matrix => {
console.group();
console.log(matrix.slice(0, 4))
console.log(matrix.slice(4, 8))
console.log(matrix.slice(8, 12))
console.log(matrix.slice(12))
console.groupEnd();
},
}