import {Mat3} from "./Mat3";
import {Quat} from "./Quat";
import {Vec3} from "./Vec3";
import {Vec4} from "./Vec4";
export type NumberArray16 = [
number, number, number, number,
number, number, number, number,
number, number, number, number,
number, number, number, number
];
/**
* Class represents a 4x4 matrix.
* @class
*/
export class Mat4 {
/**
* A 4x4 matrix, index-able as a column-major order array.
* @public
* @type {Array.<number>}
*/
public _m: NumberArray16 = [
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0
];
constructor() {
}
/**
* Returns identity matrix instance.
* @static
* @returns {Mat4} -
*/
static identity(): Mat4 {
let res = new Mat4();
res._m[0] = 1;
res._m[1] = 0;
res._m[2] = 0;
res._m[3] = 0;
res._m[4] = 0;
res._m[5] = 1;
res._m[6] = 0;
res._m[7] = 0;
res._m[8] = 0;
res._m[9] = 0;
res._m[10] = 1;
res._m[11] = 0;
res._m[12] = 0;
res._m[13] = 0;
res._m[14] = 0;
res._m[15] = 1;
return res;
}
/**
* Sets column-major order array matrix.
* @public
* @param {Array.<number>} m - Matrix array.
* @returns {Mat4} -
*/
public set(m: NumberArray16): Mat4 {
this._m[0] = m[0];
this._m[1] = m[1];
this._m[2] = m[2];
this._m[3] = m[3];
this._m[4] = m[4];
this._m[5] = m[5];
this._m[6] = m[6];
this._m[7] = m[7];
this._m[8] = m[8];
this._m[9] = m[9];
this._m[10] = m[10];
this._m[11] = m[11];
this._m[12] = m[12];
this._m[13] = m[13];
this._m[14] = m[14];
this._m[15] = m[15];
return this;
}
/**
* Duplicates a Matrix3 instance.
* @public
* @returns {Mat4} -
*/
public clone(): Mat4 {
let res = new Mat4();
res.set(this._m);
return res;
}
/**
* Copy matrix.
* @public
* @param {Mat4} a - Matrix to copy.
* @return {Mat4}
*/
public copy(a: Mat4): Mat4 {
return this.set(a._m);
}
/**
* Converts to 3x3 matrix.
* @public
* @returns {Mat3} -
*/
public toMatrix3(): Mat3 {
let res = new Mat3();
let a = this._m,
b = res._m;
b[0] = a[0];
b[1] = a[1];
b[2] = a[2];
b[3] = a[4];
b[4] = a[5];
b[5] = a[6];
b[6] = a[8];
b[7] = a[9];
b[8] = a[10];
return res;
}
/**
* Multiply to 3d vector.
* @public
* @param {Vec3} p - 3d vector.
* @returns {Vec3} -
*/
public mulVec3(p: Vec3): Vec3 {
let d = p.x,
e = p.y,
g = p.z;
return new Vec3(
this._m[0] * d + this._m[4] * e + this._m[8] * g + this._m[12],
this._m[1] * d + this._m[5] * e + this._m[9] * g + this._m[13],
this._m[2] * d + this._m[6] * e + this._m[10] * g + this._m[14]
);
}
/**
* Multiply to 4d vector.
* @public
* @param {Vec4} p - 4d vector.
* @returns {Vec4} -
*/
public mulVec4(p: Vec4): Vec4 {
let d = p.x,
e = p.y,
g = p.z,
f = p.w;
return new Vec4(
this._m[0] * d + this._m[4] * e + this._m[8] * g + this._m[12] * f,
this._m[1] * d + this._m[5] * e + this._m[9] * g + this._m[13] * f,
this._m[2] * d + this._m[6] * e + this._m[10] * g + this._m[14] * f,
this._m[3] * d + this._m[7] * e + this._m[11] * g + this._m[15] * f
);
}
/**
* Creates an inverse 3x3 matrix of the current.
* @public
* @returns {Mat3} -
*/
public toInverseMatrix3(): Mat3 | undefined {
let a = this._m;
let c = a[0],
d = a[1],
e = a[2],
g = a[4],
f = a[5],
h = a[6],
i = a[8],
j = a[9],
k = a[10],
l = k * f - h * j,
o = -k * g + h * i,
m = j * g - f * i,
n = c * l + d * o + e * m;
if (!n) {
return;
}
n = 1.0 / n;
let res = new Mat3();
res._m[0] = l * n;
res._m[1] = (-k * d + e * j) * n;
res._m[2] = (h * d - e * f) * n;
res._m[3] = o * n;
res._m[4] = (k * c - e * i) * n;
res._m[5] = (-h * c + e * g) * n;
res._m[6] = m * n;
res._m[7] = (-j * c + d * i) * n;
res._m[8] = (f * c - d * g) * n;
return res;
}
/**
* Creates an inverse matrix of the current.
* @public
* @returns {Mat4} -
*/
public inverseTo(res: Mat4 = new Mat4()): Mat4 {
let c = this._m[0],
d = this._m[1],
e = this._m[2],
g = this._m[3],
f = this._m[4],
h = this._m[5],
i = this._m[6],
j = this._m[7],
k = this._m[8],
l = this._m[9],
o = this._m[10],
m = this._m[11],
n = this._m[12],
p = this._m[13],
r = this._m[14],
s = this._m[15],
A = c * h - d * f,
B = c * i - e * f,
t = c * j - g * f,
u = d * i - e * h,
v = d * j - g * h,
w = e * j - g * i,
x = k * p - l * n,
y = k * r - o * n,
z = k * s - m * n,
C = l * r - o * p,
D = l * s - m * p,
E = o * s - m * r,
q = 1 / (A * E - B * D + t * C + u * z - v * y + w * x);
res._m[0] = (h * E - i * D + j * C) * q;
res._m[1] = (-d * E + e * D - g * C) * q;
res._m[2] = (p * w - r * v + s * u) * q;
res._m[3] = (-l * w + o * v - m * u) * q;
res._m[4] = (-f * E + i * z - j * y) * q;
res._m[5] = (c * E - e * z + g * y) * q;
res._m[6] = (-n * w + r * t - s * B) * q;
res._m[7] = (k * w - o * t + m * B) * q;
res._m[8] = (f * D - h * z + j * x) * q;
res._m[9] = (-c * D + d * z - g * x) * q;
res._m[10] = (n * v - p * t + s * A) * q;
res._m[11] = (-k * v + l * t - m * A) * q;
res._m[12] = (-f * C + h * y - i * x) * q;
res._m[13] = (c * C - d * y + e * x) * q;
res._m[14] = (-n * u + p * B - r * A) * q;
res._m[15] = (k * u - l * B + o * A) * q;
return res;
}
/**
* Creates a transposed matrix of the current.
* @public
* @returns {Mat4} -
*/
public transposeTo(): Mat4 {
let res = new Mat4();
res._m[0] = this._m[0];
res._m[1] = this._m[4];
res._m[2] = this._m[8];
res._m[3] = this._m[12];
res._m[4] = this._m[1];
res._m[5] = this._m[5];
res._m[6] = this._m[9];
res._m[7] = this._m[13];
res._m[8] = this._m[2];
res._m[9] = this._m[6];
res._m[10] = this._m[10];
res._m[11] = this._m[14];
res._m[12] = this._m[3];
res._m[13] = this._m[7];
res._m[14] = this._m[11];
res._m[15] = this._m[15];
return res;
}
/**
* Sets matrix to identity.
* @public
* @returns {Mat4} -
*/
public setIdentity(): Mat4 {
this._m[0] = 1;
this._m[1] = 0;
this._m[2] = 0;
this._m[3] = 0;
this._m[4] = 0;
this._m[5] = 1;
this._m[6] = 0;
this._m[7] = 0;
this._m[8] = 0;
this._m[9] = 0;
this._m[10] = 1;
this._m[11] = 0;
this._m[12] = 0;
this._m[13] = 0;
this._m[14] = 0;
this._m[15] = 1;
return this;
}
/**
* Computes the product of two matrices.
* @public
* @param {Mat4} mx - Matrix to multiply.
* @returns {Mat4} -
*/
public mul(mx: Mat4): Mat4 {
let d = this._m[0],
e = this._m[1],
g = this._m[2],
f = this._m[3],
h = this._m[4],
i = this._m[5],
j = this._m[6],
k = this._m[7],
l = this._m[8],
o = this._m[9],
m = this._m[10],
n = this._m[11],
p = this._m[12],
r = this._m[13],
s = this._m[14],
a = this._m[15];
let A = mx._m[0],
B = mx._m[1],
t = mx._m[2],
u = mx._m[3],
v = mx._m[4],
w = mx._m[5],
x = mx._m[6],
y = mx._m[7],
z = mx._m[8],
C = mx._m[9],
D = mx._m[10],
E = mx._m[11],
q = mx._m[12],
F = mx._m[13],
G = mx._m[14],
b = mx._m[15];
let res = new Mat4();
res._m[0] = A * d + B * h + t * l + u * p;
res._m[1] = A * e + B * i + t * o + u * r;
res._m[2] = A * g + B * j + t * m + u * s;
res._m[3] = A * f + B * k + t * n + u * a;
res._m[4] = v * d + w * h + x * l + y * p;
res._m[5] = v * e + w * i + x * o + y * r;
res._m[6] = v * g + w * j + x * m + y * s;
res._m[7] = v * f + w * k + x * n + y * a;
res._m[8] = z * d + C * h + D * l + E * p;
res._m[9] = z * e + C * i + D * o + E * r;
res._m[10] = z * g + C * j + D * m + E * s;
res._m[11] = z * f + C * k + D * n + E * a;
res._m[12] = q * d + F * h + G * l + b * p;
res._m[13] = q * e + F * i + G * o + b * r;
res._m[14] = q * g + F * j + G * m + b * s;
res._m[15] = q * f + F * k + G * n + b * a;
return res;
}
/**
* Add translation vector to the current matrix.
* @public
* @param {Vec3} v - Translate vector.
* @returns {Mat4} -
*/
public translate(v: Vec3): Mat4 {
let d = v.x,
e = v.y,
b = v.z;
let a = this._m;
a[12] = a[0] * d + a[4] * e + a[8] * b + a[12];
a[13] = a[1] * d + a[5] * e + a[9] * b + a[13];
a[14] = a[2] * d + a[6] * e + a[10] * b + a[14];
a[15] = a[3] * d + a[7] * e + a[11] * b + a[15];
return this;
}
/**
* Sets translation matrix to the position.
* @public
* @param {Vec3} v - Translate to position.
* @returns {Mat4} -
*/
public translateToPosition(v: Vec3): Mat4 {
let a = this._m;
a[12] = v.x;
a[13] = v.y;
a[14] = v.z;
return this;
}
/**
* Rotate current matrix around the aligned axis and angle.
* @public
* @param {Vec3} u - Aligned axis.
* @param {number} angle - Aligned axis angle in radians.
* @returns {Mat4} -
*/
public rotate(u: Vec3, angle: number): Mat4 {
let c = Math.cos(angle),
s = Math.sin(angle);
let rot = new Mat4();
let mx = rot._m;
mx[0] = c + (1 - c) * u.x * u.x;
mx[1] = (1 - c) * u.y * u.x - s * u.z;
mx[2] = (1 - c) * u.z * u.x + s * u.y;
mx[3] = 0;
mx[4] = (1 - c) * u.x * u.y + s * u.z;
mx[5] = c + (1 - c) * u.y * u.y;
mx[6] = (1 - c) * u.z * u.y - s * u.x;
mx[7] = 0;
mx[8] = (1 - c) * u.x * u.z - s * u.y;
mx[9] = (1 - c) * u.y * u.z + s * u.x;
mx[10] = c + (1 - c) * u.z * u.z;
mx[11] = 0;
mx[12] = 0;
mx[13] = 0;
mx[14] = 0;
mx[15] = 1;
return this.mul(rot);
}
/**
* Sets current rotation matrix around the aligned axis and angle.
* @public
* @param {Vec3} u - Aligned axis.
* @param {number} angle - Aligned axis angle in radians.
* @returns {Mat4} -
*/
public setRotation(u: Vec3, angle: number): Mat4 {
let c = Math.cos(angle),
s = Math.sin(angle);
let mx = this._m;
mx[0] = c + (1 - c) * u.x * u.x;
mx[1] = (1 - c) * u.y * u.x - s * u.z;
mx[2] = (1 - c) * u.z * u.x + s * u.y;
mx[3] = 0;
mx[4] = (1 - c) * u.x * u.y + s * u.z;
mx[5] = c + (1 - c) * u.y * u.y;
mx[6] = (1 - c) * u.z * u.y - s * u.x;
mx[7] = 0;
mx[8] = (1 - c) * u.x * u.z - s * u.y;
mx[9] = (1 - c) * u.y * u.z + s * u.x;
mx[10] = c + (1 - c) * u.z * u.z;
mx[11] = 0;
mx[12] = 0;
mx[13] = 0;
mx[14] = 0;
mx[15] = 1;
return this;
}
/**
* Gets the rotation matrix from one vector to another.
* @public
* @param {Vec3} a - First vector.
* @param {Vec3} b - Second vector.
* @returns {Mat4} -
*/
public rotateBetweenVectors(a: Vec3, b: Vec3): Mat4 {
let q = Quat.getRotationBetweenVectors(a, b);
return q.getMat4();
}
/**
* Scale current matrix to the vector values.
* @public
* @param {Vec3} v - Scale vector.
* @returns {Mat4} -
*/
public scale(v: Vec3): Mat4 {
let mx = this._m;
mx[0] = mx[0] * v.x;
mx[1] = mx[1] * v.x;
mx[2] = mx[2] * v.x;
mx[3] = mx[3] * v.x;
mx[4] = mx[4] * v.y;
mx[5] = mx[5] * v.y;
mx[6] = mx[6] * v.y;
mx[7] = mx[7] * v.y;
mx[8] = mx[8] * v.z;
mx[9] = mx[9] * v.z;
mx[10] = mx[10] * v.z;
mx[11] = mx[11] * v.z;
return this;
}
/**
* Sets perspective projection matrix frustum values.
* @public
* @param {number} left -
* @param {number} right -
* @param {number} bottom -
* @param {number} top -
* @param {number} near -
* @param {number} far -
* @returns {Mat4} -
*/
public setPerspective(left: number, right: number, bottom: number, top: number, near: number, far: number): Mat4 {
let h = right - left,
i = top - bottom,
j = near - far,
n2 = 2 * near;
let mm = this._m;
mm[0] = n2 / h;
mm[1] = 0;
mm[2] = 0;
mm[3] = 0;
mm[4] = 0;
mm[5] = n2 / i;
mm[6] = 0;
mm[7] = 0;
mm[8] = (right + left) / h;
mm[9] = (top + bottom) / i;
mm[10] = (far + near) / j;
mm[11] = -1;
mm[12] = 0;
mm[13] = 0;
mm[14] = (n2 * far) / j;
mm[15] = 0;
return this;
}
/**
* Creates current orthographic projection matrix.
* @public
* @param {number} left -
* @param {number} right -
* @param {number} bottom -
* @param {number} top -
* @param {number} near -
* @param {number} far -
* @return {Mat4} -
*/
public setOrtho(left: number, right: number, bottom: number, top: number, near: number, far: number): Mat4 {
let lr = 1.0 / (left - right),
bt = 1.0 / (bottom - top),
nf = 1.0 / (near - far),
m = this._m;
m[0] = -2.0 * lr;
m[1] = 0;
m[2] = 0;
m[3] = 0;
m[4] = 0;
m[5] = -2.0 * bt;
m[6] = 0;
m[7] = 0;
m[8] = 0;
m[9] = 0;
m[10] = 2.0 * nf;
m[11] = 0;
m[12] = (left + right) * lr;
m[13] = (top + bottom) * bt;
m[14] = (far + near) * nf;
m[15] = 1.0;
return this;
}
/**
* Sets current rotation matrix by euler's angles.
* @public
* @param {number} ax - Rotation angle in radians around X axis.
* @param {number} ay - Rotation angle in radians around Y axis.
* @param {number} az - Rotation angle in radians around Z axis.
* @returns {Mat4} -
*/
public eulerToMatrix(ax: number, ay: number, az: number): Mat4 {
let a = Math.cos(ax),
b = Math.sin(ax),
c = Math.cos(ay),
d = Math.sin(ay),
e = Math.cos(az),
f = Math.sin(az);
let ad = a * d,
bd = b * d;
let mat = this._m;
mat[0] = c * e;
mat[1] = -c * f;
mat[2] = -d;
mat[4] = -bd * e + a * f;
mat[5] = bd * f + a * e;
mat[6] = -b * c;
mat[8] = ad * e + b * f;
mat[9] = -ad * f + b * e;
mat[10] = a * c;
mat[3] = mat[7] = mat[11] = mat[12] = mat[13] = mat[14] = 0;
mat[15] = 1;
return this;
}
}
/**
* Mat4 factory.
* @static
* @returns {Mat4} -
*/
export function mat4(): Mat4 {
return new Mat4();
}