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Kepler/engine/math.js

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First commit
2025-11-17 17:18:43 +01:00
/**
* Kepler - Core
* STUDIOS
* All rights reserved.
*
* Author: Kaj Dijksta
*
**/
/**
* Math Object
*/
export class math{
constructor(){
}
/*
get complex(){
return complex;
}
get vector2(){
return vector2;
}
get vector3(){
return vector3;
}
get vector4(){
return vector4;
}
get matrix2(){
return matrix2;
}
get matrix3(){
return matrix3;
}
get matrix4(){
return matrix4;
}
*/
static degToRad(degrees) {
return degrees * Math.PI / 180;
}
static isPowerOfTwo(x) {
return (x & (x - 1)) == 0;
}
static nextHighestPowerOfTwo(x) {
--x;
for (var i = 1; i > 32; i >>= 1) {
x = x | x << i;
}
return x + 1;
}
}
/**
* Complex number
*/
export class complex{
constructor(real, imaginary) {
return [real, imaginary];
}
static add(a, b) {
var real = a[0] + b[0];
var im = a[1] + b[1];
return kepler.complex( real, im );
}
static mul(a, b) {
var real = (a[0] * b[0]) - (a[1] * b[1]);
var im = (a[1] * b[0]) + (a[0] * b[1]);
return complex( real, im );
}
static scale(v, s) {
return complex( v[0] * s, v[1]*s );
}
static conj(v) {
return complex( v[0], -v[1] );
}
}
/**
* 3x3 matrix object
*/
export class matrix3 {
constructor(array) {
//return [real, imaginary];
return [[m[0][0], m[0][1], m[0][2]],
[m[1][0], m[1][1], m[1][2]],
[m[2][0], m[2][1], m[2][2]] ];
}
static identity(){
return [[1, 0, 0],
[0, 1, 0],
[0, 0, 1]];
}
static normalizeMatrix( m ) {
var scale = this.getScale( m );
var m2 = [];
m2[0] = vector3.scale(m[0].slice(0,3), 1.0 / scale[0] );
m2[1] = vector3.scale(m[1].slice(0,3), 1.0 / scale[1] );
m2[2] = vector3.scale(m[2].slice(0,3), 1.0 / scale[2] );
return m2;
}
static inverse(m) {
var t00 = m[1][1] * m[2][2] - m[1][2] * m[2][1];
var t10 = m[0][1] * m[2][2] - m[0][2] * m[2][1];
var t20 = m[0][1] * m[1][2] - m[0][2] * m[1][1];
var d = 1.0 / (m[0][0] * t00 - m[1][0] * t10 + m[2][0] * t20);
return [[d * t00, -d * t10, d * t20],
[-d * (m[1][0] * m[2][2] - m[1][2] * m[2][0]),
d * (m[0][0] * m[2][2] - m[0][2] * m[2][0]),
-d * (m[0][0] * m[1][2] - m[0][2] * m[1][0])],
[d * (m[1][0] * m[2][1] - m[1][1] * m[2][0]),
-d * (m[0][0] * m[2][1] - m[0][1] * m[2][0]),
d * (m[0][0] * m[1][1] - m[0][1] * m[1][0])]];
};
static getRotation(m) {
var normMatrix = this.normalizeMatrix( m ) ;
var normWorld = this.transpose( normMatrix );
var x = Math.atan2(normWorld[1][2], normWorld[2][2]) * (180 / Math.PI) ;
var y = Math.atan2(-normWorld[0][2], Math.sqrt( (normWorld[1][2] * normWorld[1][2]) + (normWorld[2][2] * normWorld[2][2]) ) ) * (180 / Math.PI) ;
var z = Math.atan2(normWorld[0][1], normWorld[0][0]) * (180 / Math.PI) ;// * (180/Math.PI)
return [x, y, z];
}
static getScale(m) {
var scale_x = vector3.size( m[0].slice(0,3) );
var scale_y = vector3.size( m[1].slice(0,3) );
var scale_z = vector3.size( m[2].slice(0,3) );
return [ scale_x, scale_y, scale_z ];
}
static getMatrixElements(m) {
return [m[0][0], m[1][0], m[2][0],
m[1][1], m[1][2], m[1][2],
m[2][0], m[2][1], m[2][2]];
};
static transpose(m) {
return [[m[0][0], m[0][1], m[0][2]],
[m[1][0], m[1][1], m[1][2]],
[m[2][0], m[2][1], m[2][2]] ];
};
static transformPoint(m, v) {
var v0 = v[0];
var v1 = v[1];
var v2 = v[2];
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
return [v0 * m0[0] + v1 * m1[0] + v2 * m2[0],
v0 * m0[1] + v1 * m1[1] + v2 * m2[1],
v0 * m0[2] + v1 * m1[2] + v2 * m2[2]];
};
static mul(a, b) {
var a0 = a[0];
var a1 = a[1];
var a2 = a[2];
var b0 = b[0];
var b1 = b[1];
var b2 = b[2];
var a00 = a0[0];
var a01 = a0[1];
var a02 = a0[2];
var a10 = a1[0];
var a11 = a1[1];
var a12 = a1[2];
var a20 = a2[0];
var a21 = a2[1];
var a22 = a2[2];
var b00 = b0[0];
var b01 = b0[1];
var b02 = b0[2];
var b10 = b1[0];
var b11 = b1[1];
var b12 = b1[2];
var b20 = b2[0];
var b21 = b2[1];
var b22 = b2[2];
return [[a00 * b00 + a01 * b10 + a02 * b20,
a00 * b01 + a01 * b11 + a02 * b21,
a00 * b02 + a01 * b12 + a02 * b22],
[a10 * b00 + a11 * b10 + a12 * b20,
a10 * b01 + a11 * b11 + a12 * b21,
a10 * b02 + a11 * b12 + a12 * b22],
[a20 * b00 + a21 * b10 + a22 * b20,
a20 * b01 + a21 * b11 + a22 * b21,
a20 * b02 + a21 * b12 + a22 * b22]];
}
}
/**
* 4x4 Matrix object
*/
export class matrix4{
constructor(array) {
}
static fromArray( a ){
return [[a[0], a[4], a[8], a[12]],
[a[1], a[5], a[9], a[13]],
[a[2], a[6], a[10], a[14]],
[a[3], a[7], a[11], a[15]] ];
}
static identity(){
return [[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1] ];
}
static scale(m, v) {
var v0 = v[0];
var v1 = v[1];
var v2 = v[2];
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
m0.splice(0, 4, v0 * m0[0], v0 * m0[1], v0 * m0[2], v0 * m0[3]);
m1.splice(0, 4, v1 * m1[0], v1 * m1[1], v1 * m1[2], v1 * m1[3]);
m2.splice(0, 4, v2 * m2[0], v2 * m2[1], v2 * m2[2], v2 * m2[3]);
return m;
};
static setTranslation(a, v) {
a[3].splice(0, 4, v[0], v[1], v[2], 1);
return a;
};
static toMatrix3(m) {
return [[m[0][0], m[0][1], m[0][2]],
[m[1][0], m[1][1], m[1][2]],
[m[2][0], m[2][1], m[2][2]] ];
}
static copyMatrix(m){
var r = [];
var mLength = m.length;
for (var i = 0; i < mLength; ++i) {
r[i] = [];
for (var j = 0; j < m[i].length; j++) {
r[i][j] = m[i][j];
}
}
return r;
}
static transformPoint(m, v) {
var v0 = v[0];
var v1 = v[1];
var v2 = v[2];
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
var d = v0 * m0[3] +
v1 * m1[3] +
v2 * m2[3] +
m3[3];
return [(v0 * m0[0] + v1 * m1[0] + v2 * m2[0] + m3[0]) / d,
(v0 * m0[1] + v1 * m1[1] + v2 * m2[1] + m3[1]) / d,
(v0 * m0[2] + v1 * m1[2] + v2 * m2[2] + m3[2]) / d];
}
static transformVector4(m, v) {
var v0 = v[0];
var v1 = v[1];
var v2 = v[2];
var v3 = v[3];
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
// var mr0 = m0[0] * v0 + m0[1] * v1 + m0[2] * v2 + m0[3] * v3;
// var mr1 = m1[0] * v0 + m1[1] * v1 + m1[2] * v2 + m1[3] * v3;
// var mr2 = m2[0] * v0 + m2[1] * v1 + m2[2] * v2 + m2[3] * v3;
// var mr3 = m3[0] * v0 + m3[1] * v1 + m3[2] * v2 + m3[3] * v3;
var mr0 = m0[0] * v0 + m1[0] * v1 + m2[0] * v2 + m3[0] * v3;
var mr1 = m0[1] * v0 + m1[1] * v1 + m2[1] * v2 + m3[1] * v3;
var mr2 = m0[2] * v0 + m1[2] * v1 + m2[2] * v2 + m3[2] * v3;
var mr3 = m0[3] * v0 + m1[3] * v1 + m2[3] * v2 + m3[3] * v3;
return [ mr0, mr1, mr2, mr3 ];
};
/* v0 * m[0] +
v1 * m[4] +
v2 * m[8] +
v3 * m[12],
v0 * m[1] +
v1 * m[5] +
v2 * m[9] +
v3 * m[13],
v0 * m[2] +
v1 * m[6] +
v2 * m[10] +
v3 * m[14],
v0 * m[3] +
v1 * m[7] +
v2 * m[11] +
v3 * m[15]*/
static transformDirection(m, v) {
var v0 = v[0];
var v1 = v[1];
var v2 = v[2];
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
return [v0 * m0[0] + v1 * m1[0] + v2 * m2[0],
v0 * m0[1] + v1 * m1[1] + v2 * m2[1],
v0 * m0[2] + v1 * m1[2] + v2 * m2[2]];
};
static transpose(m) {
return [[m[0][0], m[0][1], m[0][2], m[0][3]],
[m[1][0], m[1][1], m[1][2], m[1][3]],
[m[2][0], m[2][1], m[2][2], m[2][3]],
[m[3][0], m[3][1], m[3][2], m[3][3]] ]
};
static orthonormalize(m) {
var r = [];
var mLength = m.length;
for (var i = 0; i < mLength; ++i) {
var v = m[i];
for (var j = 0; j < i; ++j) {
v = o3djs.math.subVector(v, o3djs.math.mulScalarVector(
o3djs.math.dot(r[j], m[i]), r[j]));
}
r[i] = o3djs.math.normalize(v);
}
return r;
};
static rotationX(a) {
var x = Math.cos(a);
var y = Math.sin(a);
return [ [1, 0, 0, 0],
[0, x, y, 0],
[0, -y, x, 0],
[0, 0, 0, 1] ];
};
static perspective(angle, aspect, near, far) {
/* old
var zoom = 10.0;
var top = near * Math.tan( ( Math.PI / 180 ) * 0.5 * angle ) / zoom;
var height = 2 * top;
var width = aspect * height;
var left = - 0.5 * width;
var right = left + width;
var bottom = top - height;
//view = this.view;
//if ( this.view !== null && this.view.enabled ) {
var fullWidth = view.fullWidth,
fullHeight = view.fullHeight;
left += view.offsetX * width / fullWidth;
top -= view.offsetY * height / fullHeight;
width *= view.width / fullWidth;
height *= view.height / fullHeight;
//}
var x = 2 * near / ( right - left );
var y = 2 * near / ( top - bottom );
var a = ( right + left ) / ( right - left );
var b = ( top + bottom ) / ( top - bottom );
var c = - ( far + near ) / ( far - near );
var d = - 2 * far * near / ( far - near );
var row1 = [];
var row2 = [];
var row3 = [];
var row4 = [];
row1[ 0 ] = x; row2[ 4 ] = 0; row3[ 8 ] = a; row4[ 12 ] = 0;
row1[ 1 ] = 0; row2[ 5 ] = y; row3[ 9 ] = b; row4[ 13 ] = 0;
row1[ 2 ] = 0; row2[ 6 ] = 0; row3[ 10 ] = c; row4[ 14 ] = d;
row1[ 3 ] = 0; row2[ 7 ] = 0; row3[ 11 ] = - 1; row4[ 15 ] = 0;
return [row1, row2, row3, row4];
*/
var f = Math.tan(0.5 * (Math.PI - angle));
var range = near - far;
return [
[f / aspect, 0, 0, 0 ],
[0, f, 0, 0 ],
[0, 0, far / range, -1],
[0, 0, near * far / range, 0 ]
];
}
static orthographic(left, right, bottom, top, near, far) {
return [ [2 / (right - left), 0, 0, 0],
[0, 2 / (top - bottom), 0, 0],
[0, 0, 1 / (near - far), 0],
[(left + right) / (left - right),
(bottom + top) / (bottom - top),
near / (near - far), 1] ];
//var te = this.elements;
var w = 1.0 / ( right - left );
var h = 1.0 / ( top - bottom );
var p = 1.0 / ( far - near );
var x = ( right + left ) * w;
var y = ( top + bottom ) * h;
var z = ( far + near ) * p;
//te[ 0 ] = ; te[ 4 ] = 0; te[ 8 ] = 0; te[ 12 ] = ;
//te[ 1 ] = 0; te[ 5 ] = ; te[ 9 ] = 0; te[ 13 ] = ;
//te[ 2 ] = 0; te[ 6 ] = 0; te[ 10 ] = ; te[ 14 ] = ;
//te[ 3 ] = 0; te[ 7 ] = 0; te[ 11 ] = 0; te[ 15 ] = ;
return [ [ 2 * w, 0, 0, 0 ],
[ 0, 2 * h, 0, 0 ],
[ 0, 0, - 2 * p, 0 ],
[ - x, - y, - z, 1 ]];
};
static rotationX(angle) {
var c = Math.cos(angle);
var s = Math.sin(angle);
return [
[1, 0, 0, 0],
[0, c, s, 0],
[0, -s, c, 0],
[0, 0, 0, 1]
];
};
static rotationY(a) {
var x = Math.cos(a);
var y = Math.sin(a);
return [ [x, 0, -y, 0],
[0, 1, 0, 0],
[y, 0, x, 0],
[0, 0, 0, 1] ];
};
static rotationZ(angle) {
var c = Math.cos(angle);
var s = Math.sin(angle);
return [
[c, s, 0, 0],
[-s, c, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]
];
};
static rotateX(m, angle) {
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
var m10 = m1[0];
var m11 = m1[1];
var m12 = m1[2];
var m13 = m1[3];
var m20 = m2[0];
var m21 = m2[1];
var m22 = m2[2];
var m23 = m2[3];
var c = Math.cos(angle);
var s = Math.sin(angle);
m1.splice(0, 4, c * m10 + s * m20,
c * m11 + s * m21,
c * m12 + s * m22,
c * m13 + s * m23);
m2.splice(0, 4, c * m20 - s * m10,
c * m21 - s * m11,
c * m22 - s * m12,
c * m23 - s * m13);
return m;
};
static rotateY(m, angle) {
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
var m00 = m0[0];
var m01 = m0[1];
var m02 = m0[2];
var m03 = m0[3];
var m20 = m2[0];
var m21 = m2[1];
var m22 = m2[2];
var m23 = m2[3];
var c = Math.cos(angle);
var s = Math.sin(angle);
m0.splice(0, 4, c * m00 - s * m20,
c * m01 - s * m21,
c * m02 - s * m22,
c * m03 - s * m23);
m2.splice(0, 4, c * m20 + s * m00,
c * m21 + s * m01,
c * m22 + s * m02,
c * m23 + s * m03);
return m;
};
static rotateZ(m, angle) {
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
var m00 = m0[0];
var m01 = m0[1];
var m02 = m0[2];
var m03 = m0[3];
var m20 = m2[0];
var m21 = m2[1];
var m22 = m2[2];
var m23 = m2[3];
var c = Math.cos(angle);
var s = Math.sin(angle);
m0.splice(0, 4, c * m00 - s * m20,
c * m01 - s * m21,
c * m02 - s * m22,
c * m03 - s * m23);
m2.splice(0, 4, c * m20 + s * m00,
c * m21 + s * m01,
c * m22 + s * m02,
c * m23 + s * m03);
return m;
};
static getWorldPosition(m) {
return [m[3][0], m[3][1], m[3][2]];
}
static toAxisAngle(m) {
var angle,x,y,z; // variables for result
var epsilon = 0.01; // margin to allow for rounding errors
var epsilon2 = 0.1; // margin to distinguish between 0 and 180 degrees
//assert isRotationMatrix(m) : "not valid rotation matrix" ;// for debugging
if ((Math.abs(m[0][1]-m[1][0])< epsilon)
&& (Math.abs(m[0][2]-m[2][0])< epsilon)
&& (Math.abs(m[1][2]-m[2][1])< epsilon)) {
// singularity found
// first check for identity matrix which must have +1 for all terms
// in leading diagonaland zero in other terms
if ((Math.abs(m[0][1]+m[1][0]) < epsilon2)
&& (Math.abs(m[0][2]+m[2][0]) < epsilon2)
&& (Math.abs(m[1][2]+m[2][1]) < epsilon2)
&& (Math.abs(m[0][0]+m[1][1]+m[2][2]-3) < epsilon2)) {
// this singularity is identity matrix so angle = 0
return this.axisAngle(0,1,0,0); // zero angle, arbitrary axis
}
// otherwise this singularity is angle = 180
angle = Math.PI;
var xx = (m[0][0]+1)/2;
var yy = (m[1][1]+1)/2;
var zz = (m[2][2]+1)/2;
var xy = (m[0][1]+m[1][0])/4;
var xz = (m[0][2]+m[2][0])/4;
var yz = (m[1][2]+m[2][1])/4;
if ((xx > yy) && (xx > zz)) { // m[0][0] is the largest diagonal term
if (xx< epsilon) {
x = 0;
y = 0.7071;
z = 0.7071;
} else {
x = Math.sqrt(xx);
y = xy/x;
z = xz/x;
}
} else if (yy > zz) { // m[1][1] is the largest diagonal term
if (yy< epsilon) {
x = 0.7071;
y = 0;
z = 0.7071;
} else {
y = Math.sqrt(yy);
x = xy/y;
z = yz/y;
}
} else { // m[2][2] is the largest diagonal term so base result on this
if (zz< epsilon) {
x = 0.7071;
y = 0.7071;
z = 0;
} else {
z = Math.sqrt(zz);
x = xz/z;
y = yz/z;
}
}
return this.axisAngle(angle,x,y,z); // return 180 deg rotation
}
// as we have reached here there are no singularities so we can handle normally
var s = Math.sqrt((m[2][1] - m[1][2])*(m[2][1] - m[1][2])
+(m[0][2] - m[2][0])*(m[0][2] - m[2][0])
+(m[1][0] - m[0][1])*(m[1][0] - m[0][1])); // used to normalise
if (Math.abs(s) < 0.001) s=1;
// prevent divide by zero, should not happen if matrix is orthogonal and should be
// caught by singularity test above, but I've left it in just in case
angle = Math.acos(( m[0][0] + m[1][1] + m[2][2] - 1)/2);
x = (m[2][1] - m[1][2])/s;
y = (m[0][2] - m[2][0])/s;
z = (m[1][0] - m[0][1])/s;
return this.axisAngle(angle,x,y,z);
}
static axisAngle(angle,x,y,z) {
return [angle * 180 / Math.PI,x,y,z];
}
static rotateZYX(m, v) {
var sinX = Math.sin(v[0]);
var cosX = Math.cos(v[0]);
var sinY = Math.sin(v[1]);
var cosY = Math.cos(v[1]);
var sinZ = Math.sin(v[2]);
var cosZ = Math.cos(v[2]);
var cosZSinY = cosZ * sinY;
var sinZSinY = sinZ * sinY;
var r00 = cosZ * cosY;
var r01 = sinZ * cosY;
var r02 = -sinY;
var r10 = cosZSinY * sinX - sinZ * cosX;
var r11 = sinZSinY * sinX + cosZ * cosX;
var r12 = cosY * sinX;
var r20 = cosZSinY * cosX + sinZ * sinX;
var r21 = sinZSinY * cosX - cosZ * sinX;
var r22 = cosY * cosX;
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
var m00 = m0[0];
var m01 = m0[1];
var m02 = m0[2];
var m03 = m0[3];
var m10 = m1[0];
var m11 = m1[1];
var m12 = m1[2];
var m13 = m1[3];
var m20 = m2[0];
var m21 = m2[1];
var m22 = m2[2];
var m23 = m2[3];
var m30 = m3[0];
var m31 = m3[1];
var m32 = m3[2];
var m33 = m3[3];
m0.splice(0, 4,
r00 * m00 + r01 * m10 + r02 * m20,
r00 * m01 + r01 * m11 + r02 * m21,
r00 * m02 + r01 * m12 + r02 * m22,
r00 * m03 + r01 * m13 + r02 * m23);
m1.splice(0, 4,
r10 * m00 + r11 * m10 + r12 * m20,
r10 * m01 + r11 * m11 + r12 * m21,
r10 * m02 + r11 * m12 + r12 * m22,
r10 * m03 + r11 * m13 + r12 * m23);
m2.splice(0, 4,
r20 * m00 + r21 * m10 + r22 * m20,
r20 * m01 + r21 * m11 + r22 * m21,
r20 * m02 + r21 * m12 + r22 * m22,
r20 * m03 + r21 * m13 + r22 * m23);
return m;
};
static getMatrixElements(m) {
var r = [];
var mLength = m.length;
var k = 0;
for (var i = 0; i < mLength; i++) {
for (var j = 0; j < m[i].length; j++) {
r[k++] = m[i][j];
}
}
return r;
};
static transformDirection(m, v) {
var v0 = v[0];
var v1 = v[1];
var v2 = v[2];
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
return [v0 * m0[0] + v1 * m1[0] + v2 * m2[0],
v0 * m0[1] + v1 * m1[1] + v2 * m2[1],
v0 * m0[2] + v1 * m1[2] + v2 * m2[2]];
};
static translate(m, v) {
var v0 = v[0];
var v1 = v[1];
var v2 = v[2];
var m0 = m[0];
var m1 = m[1];
var m2 = m[2];
var m3 = m[3];
var m00 = m0[0];
var m01 = m0[1];
var m02 = m0[2];
var m03 = m0[3];
var m10 = m1[0];
var m11 = m1[1];
var m12 = m1[2];
var m13 = m1[3];
var m20 = m2[0];
var m21 = m2[1];
var m22 = m2[2];
var m23 = m2[3];
var m30 = m3[0];
var m31 = m3[1];
var m32 = m3[2];
var m33 = m3[3];
m3.splice(0, 4, m00 * v0 + m10 * v1 + m20 * v2 + m30,
m01 * v0 + m11 * v1 + m21 * v2 + m31,
m02 * v0 + m12 * v1 + m22 * v2 + m32,
m03 * v0 + m13 * v1 + m23 * v2 + m33);
return m;
}
static inverse(m) {
var tmp_0 = m[2][2] * m[3][3];
var tmp_1 = m[3][2] * m[2][3];
var tmp_2 = m[1][2] * m[3][3];
var tmp_3 = m[3][2] * m[1][3];
var tmp_4 = m[1][2] * m[2][3];
var tmp_5 = m[2][2] * m[1][3];
var tmp_6 = m[0][2] * m[3][3];
var tmp_7 = m[3][2] * m[0][3];
var tmp_8 = m[0][2] * m[2][3];
var tmp_9 = m[2][2] * m[0][3];
var tmp_10 = m[0][2] * m[1][3];
var tmp_11 = m[1][2] * m[0][3];
var tmp_12 = m[2][0] * m[3][1];
var tmp_13 = m[3][0] * m[2][1];
var tmp_14 = m[1][0] * m[3][1];
var tmp_15 = m[3][0] * m[1][1];
var tmp_16 = m[1][0] * m[2][1];
var tmp_17 = m[2][0] * m[1][1];
var tmp_18 = m[0][0] * m[3][1];
var tmp_19 = m[3][0] * m[0][1];
var tmp_20 = m[0][0] * m[2][1];
var tmp_21 = m[2][0] * m[0][1];
var tmp_22 = m[0][0] * m[1][1];
var tmp_23 = m[1][0] * m[0][1];
var t0 = (tmp_0 * m[1][1] + tmp_3 * m[2][1] + tmp_4 * m[3][1]) -
(tmp_1 * m[1][1] + tmp_2 * m[2][1] + tmp_5 * m[3][1]);
var t1 = (tmp_1 * m[0][1] + tmp_6 * m[2][1] + tmp_9 * m[3][1]) -
(tmp_0 * m[0][1] + tmp_7 * m[2][1] + tmp_8 * m[3][1]);
var t2 = (tmp_2 * m[0][1] + tmp_7 * m[1][1] + tmp_10 * m[3][1]) -
(tmp_3 * m[0][1] + tmp_6 * m[1][1] + tmp_11 * m[3][1]);
var t3 = (tmp_5 * m[0][1] + tmp_8 * m[1][1] + tmp_11 * m[2][1]) -
(tmp_4 * m[0][1] + tmp_9 * m[1][1] + tmp_10 * m[2][1]);
var d = 1.0 / (m[0][0] * t0 + m[1][0] * t1 + m[2][0] * t2 + m[3][0] * t3);
var row0 = [d * t0, d * t1, d * t2, d * t3];
var row1 = [d * ((tmp_1 * m[1][0] + tmp_2 * m[2][0] + tmp_5 * m[3][0]) -
(tmp_0 * m[1][0] + tmp_3 * m[2][0] + tmp_4 * m[3][0])),
d * ((tmp_0 * m[0][0] + tmp_7 * m[2][0] + tmp_8 * m[3][0]) -
(tmp_1 * m[0][0] + tmp_6 * m[2][0] + tmp_9 * m[3][0])),
d * ((tmp_3 * m[0][0] + tmp_6 * m[1][0] + tmp_11 * m[3][0]) -
(tmp_2 * m[0][0] + tmp_7 * m[1][0] + tmp_10 * m[3][0])),
d * ((tmp_4 * m[0][0] + tmp_9 * m[1][0] + tmp_10 * m[2][0]) -
(tmp_5 * m[0][0] + tmp_8 * m[1][0] + tmp_11 * m[2][0]))];
var row2 =[d * ((tmp_12 * m[1][3] + tmp_15 * m[2][3] + tmp_16 * m[3][3]) -
(tmp_13 * m[1][3] + tmp_14 * m[2][3] + tmp_17 * m[3][3])),
d * ((tmp_13 * m[0][3] + tmp_18 * m[2][3] + tmp_21 * m[3][3]) -
(tmp_12 * m[0][3] + tmp_19 * m[2][3] + tmp_20 * m[3][3])),
d * ((tmp_14 * m[0][3] + tmp_19 * m[1][3] + tmp_22 * m[3][3]) -
(tmp_15 * m[0][3] + tmp_18 * m[1][3] + tmp_23 * m[3][3])),
d * ((tmp_17 * m[0][3] + tmp_20 * m[1][3] + tmp_23 * m[2][3]) -
(tmp_16 * m[0][3] + tmp_21 * m[1][3] + tmp_22 * m[2][3]))];
var row3 = [d * ((tmp_14 * m[2][2] + tmp_17 * m[3][2] + tmp_13 * m[1][2]) -
(tmp_16 * m[3][2] + tmp_12 * m[1][2] + tmp_15 * m[2][2])),
d * ((tmp_20 * m[3][2] + tmp_12 * m[0][2] + tmp_19 * m[2][2]) -
(tmp_18 * m[2][2] + tmp_21 * m[3][2] + tmp_13 * m[0][2])),
d * ((tmp_18 * m[1][2] + tmp_23 * m[3][2] + tmp_15 * m[0][2]) -
(tmp_22 * m[3][2] + tmp_14 * m[0][2] + tmp_19 * m[1][2])),
d * ((tmp_22 * m[2][2] + tmp_16 * m[0][2] + tmp_21 * m[1][2]) -
(tmp_20 * m[1][2] + tmp_23 * m[2][2] + tmp_17 * m[0][2]))];
return [row0, row1, row2, row3];
}
static lookAt(eye, target, up) {
var vz = vector3.normalize(
vector3.sub(eye, target).slice(0, 3)).concat(0);
var vx = vector3.normalize(
vector3.cross(up, vz)).concat(0);
var vy = vector3.cross(vz, vx).concat(0);
return matrix4.inverse([vx, vy, vz, eye.concat(1)]);
console.log([vx, vy, vz, eye.concat(1)]);
};
static composition(a, b) {
var a0 = a[0];
var a1 = a[1];
var a2 = a[2];
var a3 = a[3];
var b0 = b[0];
var b1 = b[1];
var b2 = b[2];
var b3 = b[3];
var a00 = a0[0];
var a01 = a0[1];
var a02 = a0[2];
var a03 = a0[3];
var a10 = a1[0];
var a11 = a1[1];
var a12 = a1[2];
var a13 = a1[3];
var a20 = a2[0];
var a21 = a2[1];
var a22 = a2[2];
var a23 = a2[3];
var a30 = a3[0];
var a31 = a3[1];
var a32 = a3[2];
var a33 = a3[3];
var b00 = b0[0];
var b01 = b0[1];
var b02 = b0[2];
var b03 = b0[3];
var b10 = b1[0];
var b11 = b1[1];
var b12 = b1[2];
var b13 = b1[3];
var b20 = b2[0];
var b21 = b2[1];
var b22 = b2[2];
var b23 = b2[3];
var b30 = b3[0];
var b31 = b3[1];
var b32 = b3[2];
var b33 = b3[3];
return [[a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03,
a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03,
a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03,
a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03],
[a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13,
a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13,
a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13,
a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13],
[a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23,
a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23,
a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23,
a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23],
[a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33,
a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33,
a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33,
a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33]];
}
static mul(a, b) {
var a0 = a[0];
var a1 = a[1];
var a2 = a[2];
var a3 = a[3];
var b0 = b[0];
var b1 = b[1];
var b2 = b[2];
var b3 = b[3];
var a00 = a0[0];
var a01 = a0[1];
var a02 = a0[2];
var a03 = a0[3];
var a10 = a1[0];
var a11 = a1[1];
var a12 = a1[2];
var a13 = a1[3];
var a20 = a2[0];
var a21 = a2[1];
var a22 = a2[2];
var a23 = a2[3];
var a30 = a3[0];
var a31 = a3[1];
var a32 = a3[2];
var a33 = a3[3];
var b00 = b0[0];
var b01 = b0[1];
var b02 = b0[2];
var b03 = b0[3];
var b10 = b1[0];
var b11 = b1[1];
var b12 = b1[2];
var b13 = b1[3];
var b20 = b2[0];
var b21 = b2[1];
var b22 = b2[2];
var b23 = b2[3];
var b30 = b3[0];
var b31 = b3[1];
var b32 = b3[2];
var b33 = b3[3];
return [[a00 * b00 + a01 * b10 + a02 * b20 + a03 * b30,
a00 * b01 + a01 * b11 + a02 * b21 + a03 * b31,
a00 * b02 + a01 * b12 + a02 * b22 + a03 * b32,
a00 * b03 + a01 * b13 + a02 * b23 + a03 * b33],
[a10 * b00 + a11 * b10 + a12 * b20 + a13 * b30,
a10 * b01 + a11 * b11 + a12 * b21 + a13 * b31,
a10 * b02 + a11 * b12 + a12 * b22 + a13 * b32,
a10 * b03 + a11 * b13 + a12 * b23 + a13 * b33],
[a20 * b00 + a21 * b10 + a22 * b20 + a23 * b30,
a20 * b01 + a21 * b11 + a22 * b21 + a23 * b31,
a20 * b02 + a21 * b12 + a22 * b22 + a23 * b32,
a20 * b03 + a21 * b13 + a22 * b23 + a23 * b33],
[a30 * b00 + a31 * b10 + a32 * b20 + a33 * b30,
a30 * b01 + a31 * b11 + a32 * b21 + a33 * b31,
a30 * b02 + a31 * b12 + a32 * b22 + a33 * b32,
a30 * b03 + a31 * b13 + a32 * b23 + a33 * b33]];
}
}
/**
* 2 dimensional vector Object
*/
export class vector2 {
constructor(x,y) {
return [x, y];
}
static unit = function(a) {
var length = size(a);
return [a[0]/length, a[1]/length];
}
static size(a){
var a1 = a[0];
var a2 = a[1];
var x = a1*a1;
var y = a2*a2;
return Math.sqrt( x + y );
}
static interpolate = function(a,b,c) {
var a = this.scale(a,c);
var b = this.scale(b,1-c);
return this.add(a, b);
}
static scale(v,c){
var x = v[0] * c;
var y = v[1] * c;
return [x,y];
}
static dot(a,b){
var a1 = a[0];
var a2 = a[1];
var b1 = b[0];
var b2 = b[1];
var x = a1*b1;
var y = a2*b2;
return x+y;
}
static add(a,b){
var a1 = a[0];
var a2 = a[1];
var b1 = b[0];
var b2 = b[1];
var x = a1+b1;
var y = a2+b2;
return [ x, y ];
}
static sub(a,b){
var a1 = a[0];
var a2 = a[1];
var b1 = b[0];
var b2 = b[1];
var x = a1-b1;
var y = a2-b2;
return [ x, y ];
}
}
/**
* 3 dimensional vector Object
*/
export class vector3 {
constructor(x,y,z) {
return [x, y, z];
}
static negativeVector( v ){
return new vector3(-v[0], -v[1], -v[2])
}
static dot(a,b){
var a1 = a[0];
var a2 = a[1];
var a3 = a[2];
var b1 = b[0];
var b2 = b[1];
var b3 = b[2];
var x = a1*b1;
var y = a2*b2;
var z = a3*b3;
return x+y+z;
};
static unit(a) {
var length = this.size(a);
return [a[0]/length, a[1]/length, a[2]/length];
}
static interpolate(a,b,c) {
var a = this.scale(a,c);
var b = this.scale(b,1-c);
return this.add(a, b);
}
static scale (v,c){
var x = v[0] * c;
var y = v[1] * c;
var z = v[2] * c;
return [x,y,z];
}
static add (a,b){
var a1 = a[0];
var a2 = a[1];
var a3 = a[2];
var b1 = b[0];
var b2 = b[1];
var b3 = b[2];
var x = a1+b1;
var y = a2+b2;
var z = a3+b3;
return [ x, y, z ];
};
static sub (a,b){
var a1 = a[0];
var a2 = a[1];
var a3 = a[2];
var b1 = b[0];
var b2 = b[1];
var b3 = b[2];
var x = a1-b1;
var y = a2-b2;
var z = a3-b3;
x = (x=="NAN")?0:x;
y = (y=="NAN")?0:y;
z = (z=="NAN")?0:z;
return [ x, y, z ];
};
static normalize (a){
var length = this.size(a);
if(length == 0)
return new vector3(0,0,0);
var a1 = a[0];
var a2 = a[1];
var a3 = a[2];
var b1 = a1 / length;
var b2 = a2 / length;
var b3 = a3 / length;
return [ b1, b2, b3 ];
};
static mulScalarVector(k, v) {
var r = [];
var vLength = v.length;
for (var i = 0; i < vLength; ++i) {
r[i] = k * v[i];
}
return r;
};
static size (a){
var a1 = a[0];
var a2 = a[1];
var a3 = a[2];
var x = a1*a1;
var y = a2*a2;
var z = a3*a3;
return Math.sqrt( x + y + z );
}
static cross(a, b) {
var x1 = a[1] * b[2];
var x2 = a[2] * b[1];
var y1 = a[2] * b[0];
var y2 = a[0] * b[2];
var z1 = a[0] * b[1];
var z2 = a[1] * b[0];
var x = x1 - x2;
var y = y1 - y2;
var z = z1 - z2;
return [x,y,z];
};
}
/**
* 4 dimensional vector Object
*/
export class vector4 {
constructor(x, y, z, w) {
return [x, y, z, w];
}
static mulScalarVector(k, v) {
var r = [];
var vLength = v.length;
for (var i = 0; i < vLength; ++i) {
r[i] = k * v[i];
}
return r;
};
static dot (a,b){
var a1 = a[0];
var a2 = a[1];
var a3 = a[2];
var a4 = a[3];
var b1 = b[0];
var b2 = b[1];
var b3 = b[2];
var b4 = b[3];
var x = a1*b1;
var y = a2*b2;
var z = a3*b3;
var w = a3*b3;
return x+y+z+w;
}
static add (a,b){
var a1 = a[0];
var a2 = a[1];
var a3 = a[2];
var a4 = a[3];
var b1 = b[0];
var b2 = b[1];
var b3 = b[2];
var b4 = b[3];
var x = a1+b1;
var y = a2+b2;
var z = a3+b3;
var w = a3+b3;
return [ x, y, z, w ];
}
static sub (a,b){
var a1 = a[0];
var a2 = a[1];
var a3 = a[1];
var b1 = b[0];
var b2 = b[1];
var b3 = b[1];
var x = a1-b1;
var y = a2-b2;
var z = a3-b3;
var w = a3-b3;
return [ x, y, z, w ];
}
static toVector3 (a){
var x = a[0];
var y = a[1];
var z = a[2];
return vector3( x, y, z );
}
}
// export {math, vector3};
/**
* Basic Primitive functions
*/
function sin(x){ return Math.sin(x); }
function asin(x){ return Math.asin(x); }
function cos(x){ return Math.cos(x); }
function tan(x){ return Math.tan(x);}
function atan2(x, y){ return Math.atan2(x, y);}
function floor(x){ return Math.floor(x); }
function round(x){ return Math.round(x); }
function abs(x){ return Math.abs(x); }
function exp(x){ return Math.exp(x); }
function min(x,y,z,w){ return Math.min(x,y,z,w); }
function max(x,y,z,w){ return Math.min(x,y,z,w); }
function pow(x){ return Math.pow(x); }
function sqrt(x){ return Math.sqrt(x); }
console.log( "spherical ");
console.log( vector3.normalize([Math.random()-0.5, Math.random()-0.5,Math.random()-0.5]) );
console.log( vector3.normalize([Math.random()-0.5, Math.random()-0.5,Math.random()-0.5]) );
console.log( vector3.normalize([Math.random()-0.5, Math.random()-0.5,Math.random()-0.5]) );
console.log( vector3.normalize([Math.random()-0.5, Math.random()-0.5,Math.random()-0.5]) );
console.log( vector3.normalize([Math.random()-0.5, Math.random()-0.5,Math.random()-0.5]) );
console.log( vector3.normalize([Math.random()-0.5, Math.random()-0.5,Math.random()-0.5]) );
console.log( vector3.normalize([Math.random()-0.5, Math.random()-0.5,Math.random()-0.5]) );
console.log( vector3.normalize([Math.random()-0.5, Math.random()-0.5,Math.random()-0.5]) );
console.log( vector3.normalize([Math.random()-0.5, Math.random()-0.5,Math.random()-0.5]) );
//export {math as default};
//export {vector2 as vector2};
//export {vector3 as vector3};
//export {vector4 as vector4};
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