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phaser/v3/src/math/Matrix4.js
Richard Davey 6aae306aa0 Added Mat4.makeRotationAxis.
2017-09-20 16:51:06 +01:00

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// Adapted from [gl-matrix](https://github.com/toji/gl-matrix) by toji
// and [vecmath](https://github.com/mattdesl/vecmath) by mattdesl
var Class = require('../utils/Class');
var EPSILON = 0.000001;
var Matrix4 = new Class({
initialize:
function Matrix4 (m)
{
this.val = new Float32Array(16);
if (m)
{
// Assume Matrix4 with val:
this.copy(m);
}
else
{
// Default to identity
this.identity();
}
},
clone: function ()
{
return new Matrix4(this);
},
set: function (src)
{
return this.copy(src);
},
copy: function (src)
{
var out = this.val;
var a = src.val;
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
out[3] = a[3];
out[4] = a[4];
out[5] = a[5];
out[6] = a[6];
out[7] = a[7];
out[8] = a[8];
out[9] = a[9];
out[10] = a[10];
out[11] = a[11];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
return this;
},
fromArray: function (a)
{
var out = this.val;
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
out[3] = a[3];
out[4] = a[4];
out[5] = a[5];
out[6] = a[6];
out[7] = a[7];
out[8] = a[8];
out[9] = a[9];
out[10] = a[10];
out[11] = a[11];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
return this;
},
identity: function ()
{
var out = this.val;
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = 1;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 1;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return this;
},
transpose: function ()
{
var a = this.val;
var a01 = a[1];
var a02 = a[2];
var a03 = a[3];
var a12 = a[6];
var a13 = a[7];
var a23 = a[11];
a[1] = a[4];
a[2] = a[8];
a[3] = a[12];
a[4] = a01;
a[6] = a[9];
a[7] = a[13];
a[8] = a02;
a[9] = a12;
a[11] = a[14];
a[12] = a03;
a[13] = a13;
a[14] = a23;
return this;
},
invert: function ()
{
var a = this.val;
var a00 = a[0];
var a01 = a[1];
var a02 = a[2];
var a03 = a[3];
var a10 = a[4];
var a11 = a[5];
var a12 = a[6];
var a13 = a[7];
var a20 = a[8];
var a21 = a[9];
var a22 = a[10];
var a23 = a[11];
var a30 = a[12];
var a31 = a[13];
var a32 = a[14];
var a33 = a[15];
var b00 = a00 * a11 - a01 * a10;
var b01 = a00 * a12 - a02 * a10;
var b02 = a00 * a13 - a03 * a10;
var b03 = a01 * a12 - a02 * a11;
var b04 = a01 * a13 - a03 * a11;
var b05 = a02 * a13 - a03 * a12;
var b06 = a20 * a31 - a21 * a30;
var b07 = a20 * a32 - a22 * a30;
var b08 = a20 * a33 - a23 * a30;
var b09 = a21 * a32 - a22 * a31;
var b10 = a21 * a33 - a23 * a31;
var b11 = a22 * a33 - a23 * a32;
// Calculate the determinant
var det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
if (!det)
{
return null;
}
det = 1 / det;
a[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
a[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
a[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
a[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
a[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
a[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
a[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
a[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
a[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
a[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
a[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
a[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
a[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
a[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
a[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
a[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;
return this;
},
adjoint: function ()
{
var a = this.val;
var a00 = a[0];
var a01 = a[1];
var a02 = a[2];
var a03 = a[3];
var a10 = a[4];
var a11 = a[5];
var a12 = a[6];
var a13 = a[7];
var a20 = a[8];
var a21 = a[9];
var a22 = a[10];
var a23 = a[11];
var a30 = a[12];
var a31 = a[13];
var a32 = a[14];
var a33 = a[15];
a[0] = (a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22));
a[1] = -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22));
a[2] = (a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12));
a[3] = -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12));
a[4] = -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22));
a[5] = (a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22));
a[6] = -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12));
a[7] = (a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12));
a[8] = (a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21));
a[9] = -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21));
a[10] = (a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11));
a[11] = -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11));
a[12] = -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21));
a[13] = (a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21));
a[14] = -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11));
a[15] = (a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11));
return this;
},
determinant: function ()
{
var a = this.val;
var a00 = a[0];
var a01 = a[1];
var a02 = a[2];
var a03 = a[3];
var a10 = a[4];
var a11 = a[5];
var a12 = a[6];
var a13 = a[7];
var a20 = a[8];
var a21 = a[9];
var a22 = a[10];
var a23 = a[11];
var a30 = a[12];
var a31 = a[13];
var a32 = a[14];
var a33 = a[15];
var b00 = a00 * a11 - a01 * a10;
var b01 = a00 * a12 - a02 * a10;
var b02 = a00 * a13 - a03 * a10;
var b03 = a01 * a12 - a02 * a11;
var b04 = a01 * a13 - a03 * a11;
var b05 = a02 * a13 - a03 * a12;
var b06 = a20 * a31 - a21 * a30;
var b07 = a20 * a32 - a22 * a30;
var b08 = a20 * a33 - a23 * a30;
var b09 = a21 * a32 - a22 * a31;
var b10 = a21 * a33 - a23 * a31;
var b11 = a22 * a33 - a23 * a32;
// Calculate the determinant
return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
},
multiply: function (src)
{
var a = this.val;
var a00 = a[0];
var a01 = a[1];
var a02 = a[2];
var a03 = a[3];
var a10 = a[4];
var a11 = a[5];
var a12 = a[6];
var a13 = a[7];
var a20 = a[8];
var a21 = a[9];
var a22 = a[10];
var a23 = a[11];
var a30 = a[12];
var a31 = a[13];
var a32 = a[14];
var a33 = a[15];
var b = src.val;
// Cache only the current line of the second matrix
var b0 = b[0];
var b1 = b[1];
var b2 = b[2];
var b3 = b[3];
a[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
a[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
a[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
a[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[4];
b1 = b[5];
b2 = b[6];
b3 = b[7];
a[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
a[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
a[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
a[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[8];
b1 = b[9];
b2 = b[10];
b3 = b[11];
a[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
a[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
a[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
a[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[12];
b1 = b[13];
b2 = b[14];
b3 = b[15];
a[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
a[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
a[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
a[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
return this;
},
translate: function (v)
{
var x = v.x;
var y = v.y;
var z = v.z;
var a = this.val;
a[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
a[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
a[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
a[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
return this;
},
scale: function (v)
{
var x = v.x;
var y = v.y;
var z = v.z;
var a = this.val;
a[0] = a[0] * x;
a[1] = a[1] * x;
a[2] = a[2] * x;
a[3] = a[3] * x;
a[4] = a[4] * y;
a[5] = a[5] * y;
a[6] = a[6] * y;
a[7] = a[7] * y;
a[8] = a[8] * z;
a[9] = a[9] * z;
a[10] = a[10] * z;
a[11] = a[11] * z;
return this;
},
// Axis = vec3, angle = radians
makeRotationAxis: function (axis, angle)
{
// Based on http://www.gamedev.net/reference/articles/article1199.asp
var c = Math.cos(angle);
var s = Math.sin(angle);
var t = 1 - c;
var x = axis.x;
var y = axis.y;
var z = axis.z;
var tx = t * x;
var ty = t * y;
this.set(
tx * x + c, tx * y - s * z, tx * z + s * y, 0,
tx * y + s * z, ty * y + c, ty * z - s * x, 0,
tx * z - s * y, ty * z + s * x, t * z * z + c, 0,
0, 0, 0, 1
);
return this;
},
rotate: function (rad, axis)
{
var a = this.val;
var x = axis.x;
var y = axis.y;
var z = axis.z;
var len = Math.sqrt(x * x + y * y + z * z);
if (Math.abs(len) < EPSILON)
{
return null;
}
len = 1 / len;
x *= len;
y *= len;
z *= len;
var s = Math.sin(rad);
var c = Math.cos(rad);
var t = 1 - c;
var a00 = a[0];
var a01 = a[1];
var a02 = a[2];
var a03 = a[3];
var a10 = a[4];
var a11 = a[5];
var a12 = a[6];
var a13 = a[7];
var a20 = a[8];
var a21 = a[9];
var a22 = a[10];
var a23 = a[11];
// Construct the elements of the rotation matrix
var b00 = x * x * t + c;
var b01 = y * x * t + z * s;
var b02 = z * x * t - y * s;
var b10 = x * y * t - z * s;
var b11 = y * y * t + c;
var b12 = z * y * t + x * s;
var b20 = x * z * t + y * s;
var b21 = y * z * t - x * s;
var b22 = z * z * t + c;
// Perform rotation-specific matrix multiplication
a[0] = a00 * b00 + a10 * b01 + a20 * b02;
a[1] = a01 * b00 + a11 * b01 + a21 * b02;
a[2] = a02 * b00 + a12 * b01 + a22 * b02;
a[3] = a03 * b00 + a13 * b01 + a23 * b02;
a[4] = a00 * b10 + a10 * b11 + a20 * b12;
a[5] = a01 * b10 + a11 * b11 + a21 * b12;
a[6] = a02 * b10 + a12 * b11 + a22 * b12;
a[7] = a03 * b10 + a13 * b11 + a23 * b12;
a[8] = a00 * b20 + a10 * b21 + a20 * b22;
a[9] = a01 * b20 + a11 * b21 + a21 * b22;
a[10] = a02 * b20 + a12 * b21 + a22 * b22;
a[11] = a03 * b20 + a13 * b21 + a23 * b22;
return this;
},
rotateX: function (rad)
{
var a = this.val;
var s = Math.sin(rad);
var c = Math.cos(rad);
var a10 = a[4];
var a11 = a[5];
var a12 = a[6];
var a13 = a[7];
var a20 = a[8];
var a21 = a[9];
var a22 = a[10];
var a23 = a[11];
// Perform axis-specific matrix multiplication
a[4] = a10 * c + a20 * s;
a[5] = a11 * c + a21 * s;
a[6] = a12 * c + a22 * s;
a[7] = a13 * c + a23 * s;
a[8] = a20 * c - a10 * s;
a[9] = a21 * c - a11 * s;
a[10] = a22 * c - a12 * s;
a[11] = a23 * c - a13 * s;
return this;
},
rotateY: function (rad)
{
var a = this.val;
var s = Math.sin(rad);
var c = Math.cos(rad);
var a00 = a[0];
var a01 = a[1];
var a02 = a[2];
var a03 = a[3];
var a20 = a[8];
var a21 = a[9];
var a22 = a[10];
var a23 = a[11];
// Perform axis-specific matrix multiplication
a[0] = a00 * c - a20 * s;
a[1] = a01 * c - a21 * s;
a[2] = a02 * c - a22 * s;
a[3] = a03 * c - a23 * s;
a[8] = a00 * s + a20 * c;
a[9] = a01 * s + a21 * c;
a[10] = a02 * s + a22 * c;
a[11] = a03 * s + a23 * c;
return this;
},
rotateZ: function (rad)
{
var a = this.val;
var s = Math.sin(rad);
var c = Math.cos(rad);
var a00 = a[0];
var a01 = a[1];
var a02 = a[2];
var a03 = a[3];
var a10 = a[4];
var a11 = a[5];
var a12 = a[6];
var a13 = a[7];
// Perform axis-specific matrix multiplication
a[0] = a00 * c + a10 * s;
a[1] = a01 * c + a11 * s;
a[2] = a02 * c + a12 * s;
a[3] = a03 * c + a13 * s;
a[4] = a10 * c - a00 * s;
a[5] = a11 * c - a01 * s;
a[6] = a12 * c - a02 * s;
a[7] = a13 * c - a03 * s;
return this;
},
fromRotationTranslation: function (q, v)
{
// Quaternion math
var out = this.val;
var x = q.x;
var y = q.y;
var z = q.z;
var w = q.w;
var x2 = x + x;
var y2 = y + y;
var z2 = z + z;
var xx = x * x2;
var xy = x * y2;
var xz = x * z2;
var yy = y * y2;
var yz = y * z2;
var zz = z * z2;
var wx = w * x2;
var wy = w * y2;
var wz = w * z2;
out[0] = 1 - (yy + zz);
out[1] = xy + wz;
out[2] = xz - wy;
out[3] = 0;
out[4] = xy - wz;
out[5] = 1 - (xx + zz);
out[6] = yz + wx;
out[7] = 0;
out[8] = xz + wy;
out[9] = yz - wx;
out[10] = 1 - (xx + yy);
out[11] = 0;
out[12] = v.x;
out[13] = v.y;
out[14] = v.z;
out[15] = 1;
return this;
},
fromQuat: function (q)
{
var out = this.val;
var x = q.x;
var y = q.y;
var z = q.z;
var w = q.w;
var x2 = x + x;
var y2 = y + y;
var z2 = z + z;
var xx = x * x2;
var xy = x * y2;
var xz = x * z2;
var yy = y * y2;
var yz = y * z2;
var zz = z * z2;
var wx = w * x2;
var wy = w * y2;
var wz = w * z2;
out[0] = 1 - (yy + zz);
out[1] = xy + wz;
out[2] = xz - wy;
out[3] = 0;
out[4] = xy - wz;
out[5] = 1 - (xx + zz);
out[6] = yz + wx;
out[7] = 0;
out[8] = xz + wy;
out[9] = yz - wx;
out[10] = 1 - (xx + yy);
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return this;
},
/**
* Generates a frustum matrix with the given bounds
*
* @param {Number} left Left bound of the frustum
* @param {Number} right Right bound of the frustum
* @param {Number} bottom Bottom bound of the frustum
* @param {Number} top Top bound of the frustum
* @param {Number} near Near bound of the frustum
* @param {Number} far Far bound of the frustum
* @returns {Matrix4} this for chaining
*/
frustum: function (left, right, bottom, top, near, far)
{
var out = this.val;
var rl = 1 / (right - left);
var tb = 1 / (top - bottom);
var nf = 1 / (near - far);
out[0] = (near * 2) * rl;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = (near * 2) * tb;
out[6] = 0;
out[7] = 0;
out[8] = (right + left) * rl;
out[9] = (top + bottom) * tb;
out[10] = (far + near) * nf;
out[11] = -1;
out[12] = 0;
out[13] = 0;
out[14] = (far * near * 2) * nf;
out[15] = 0;
return this;
},
/**
* Generates a perspective projection matrix with the given bounds
*
* @param {number} fovy Vertical field of view in radians
* @param {number} aspect Aspect ratio. typically viewport width/height
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum
* @returns {Matrix4} this for chaining
*/
perspective: function (fovy, aspect, near, far)
{
var out = this.val;
var f = 1.0 / Math.tan(fovy / 2);
var nf = 1 / (near - far);
out[0] = f / aspect;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = f;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = (far + near) * nf;
out[11] = -1;
out[12] = 0;
out[13] = 0;
out[14] = (2 * far * near) * nf;
out[15] = 0;
return this;
},
/**
* Generates a orthogonal projection matrix with the given bounds
*
* @param {number} left Left bound of the frustum
* @param {number} right Right bound of the frustum
* @param {number} bottom Bottom bound of the frustum
* @param {number} top Top bound of the frustum
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum
* @returns {Matrix4} this for chaining
*/
ortho: function (left, right, bottom, top, near, far)
{
var out = this.val;
var lr = left - right;
var bt = bottom - top;
var nf = near - far;
// Avoid division by zero
lr = (lr === 0) ? lr : 1 / lr;
bt = (bt === 0) ? bt : 1 / bt;
nf = (nf === 0) ? nf : 1 / nf;
out[0] = -2 * lr;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = -2 * bt;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 2 * nf;
out[11] = 0;
out[12] = (left + right) * lr;
out[13] = (top + bottom) * bt;
out[14] = (far + near) * nf;
out[15] = 1;
return this;
},
/**
* Generates a look-at matrix with the given eye position, focal point, and up axis
*
* @param {Vector3} eye Position of the viewer
* @param {Vector3} center Point the viewer is looking at
* @param {Vector3} up vec3 pointing up
* @returns {Matrix4} this for chaining
*/
lookAt: function (eye, center, up)
{
var out = this.val;
var eyex = eye.x;
var eyey = eye.y;
var eyez = eye.z;
var upx = up.x;
var upy = up.y;
var upz = up.z;
var centerx = center.x;
var centery = center.y;
var centerz = center.z;
if (Math.abs(eyex - centerx) < EPSILON &&
Math.abs(eyey - centery) < EPSILON &&
Math.abs(eyez - centerz) < EPSILON)
{
return this.identity();
}
var z0 = eyex - centerx;
var z1 = eyey - centery;
var z2 = eyez - centerz;
var len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
z0 *= len;
z1 *= len;
z2 *= len;
var x0 = upy * z2 - upz * z1;
var x1 = upz * z0 - upx * z2;
var x2 = upx * z1 - upy * z0;
len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2);
if (!len)
{
x0 = 0;
x1 = 0;
x2 = 0;
}
else
{
len = 1 / len;
x0 *= len;
x1 *= len;
x2 *= len;
}
var y0 = z1 * x2 - z2 * x1;
var y1 = z2 * x0 - z0 * x2;
var y2 = z0 * x1 - z1 * x0;
len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2);
if (!len)
{
y0 = 0;
y1 = 0;
y2 = 0;
}
else
{
len = 1 / len;
y0 *= len;
y1 *= len;
y2 *= len;
}
out[0] = x0;
out[1] = y0;
out[2] = z0;
out[3] = 0;
out[4] = x1;
out[5] = y1;
out[6] = z1;
out[7] = 0;
out[8] = x2;
out[9] = y2;
out[10] = z2;
out[11] = 0;
out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
out[15] = 1;
return this;
}
});
Matrix4.prototype.mul = Matrix4.prototype.multiply;
Matrix4.prototype.idt = Matrix4.prototype.identity;
Matrix4.prototype.reset = Matrix4.prototype.idt;
module.exports = Matrix4;
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