toloframework/ker/mod/webgl.math.js

Javascript/HTML/CSS compiler for Firefox OS or nodewebkit apps using modules in the nodejs style.

"use strict";

module.exports = {
  m4: {
    identity: identity4,
    matrix: mat4,
    vector: vec4,
    projection: projection4,
    translation: translation4,
    rotationX: rotationX4,
    rotationY: rotationY4,
    rotationZ: rotationZ4,
    scaling: scaling4,
    copy: copy,
    normalize: normalize,
    cameraPolar: cameraPolar4,
    perspective: perspective4,
    mul: mul
  },
  m3: {
    identity: identity3,
    matrix: mat3,
    projection: projection3,
    translation: translation3,
    rotation: rotation3,
    scaling: scaling3
  }
};


function copy( arr ) {
  return new Float32Array( arr );
}

function normalize( arr ) {
  var n = copy( arr );
  var len = 0,
    v, k;
  for ( k = 0; k < n.length; k++ ) {
    v = n[ k ];
    len += v * v;
  }
  if ( len > 0 ) {
    var coeff = 1 / Math.sqrt( len );
    for ( k = 0; k < n.length; k++ ) {
      n[ k ] *= coeff;
    }
  }
  return n;
}

function cameraPolar4( targetX, targetY, targetZ, dis, lat, lng, result ) {
  result = result || new Float32Array( 16 );
  var cosLat = Math.cos( lat );
  var sinLat = Math.sin( lat );
  var cosLng = - Math.cos( lng + Math.PI * .5 );
  var sinLng = - Math.sin( lng + Math.PI * .5 );
  // Vecteur Z de la caméra.
  var Zx = cosLng * cosLat;
  var Zy = sinLng * cosLat;
  var Zz = sinLat; // V2/2
  // Le vecteur X se déduit par un produit vectoriel de (0,0,1) avec Z.
  var Xx = -Zy;
  var Xy = Zx;
  var Xz = 0;
  // Comme (0,0,1) n'est pas orthogonal à Z, il faut normaliser X.
  var len = Math.sqrt( Xx * Xx + Xy * Xy + Xz * Xz );
  Xx /= len;
  Xy /= len;
  Xz /= len;
  // Y peut alors se déduire par le produit vectoriel de Z par X.
  // Et il n'y aura pas besoin de le normaliser.
  var Yx = Zy * Xz - Zz * Xy;
  var Yy = Xx * Zz - Xz * Zx;
  var Yz = Zx * Xy - Zy * Xx;
  // Translation.
  var Tx = -( Zx * dis + targetX );
  var Ty = -( Zy * dis + targetY );
  var Tz = -( Zz * dis + targetZ );

  // Le résultat est la multiplication de la projection avec la translation.
  result[ 0 ] = Xx;
  result[ 4 ] = Xy;
  result[ 8 ] = Xz;
  result[ 12 ] = Tx * Xx + Ty * Xy + Tz * Xz;

  result[ 1 ] = Yx;
  result[ 5 ] = Yy;
  result[ 9 ] = Yz;
  result[ 13 ] = Tx * Yx + Ty * Yy + Tz * Yz;

  result[ 2 ] = Zx;
  result[ 6 ] = Zy;
  result[ 10 ] = Zz;
  result[ 14 ] = Tx * Zx + Ty * Zy + Tz * Zz;

  result[ 3 ] = 0;
  result[ 7 ] = 0;
  result[ 11 ] = 0;
  result[ 15 ] = 1;

  return result;
}

/**
 * Define the `frustum`.
 * @param {number} fieldAngle - View angle in radians. Maximum is PI.
 * @param {number} aspect - (width / height) of the canvas.
 * @param {number} near - Clip every Z lower than `near`.
 * @param {number} far - Clip every Z greater than `far`.
 */
function perspective4( fieldAngle, aspect, near, far, result ) {
  result = result || new Float32Array( 16 );
  var f = Math.tan( Math.PI * 0.5 - 0.5 * fieldAngle );
  var rangeInv = 1.0 / ( near - far );

  result[ 0 ] = f / aspect;
  result[ 1 ] = 0;
  result[ 2 ] = 0;
  result[ 3 ] = 0;

  result[ 4 ] = 0;
  result[ 5 ] = f;
  result[ 6 ] = 0;
  result[ 7 ] = 0;

  result[ 8 ] = 0;
  result[ 9 ] = 0;
  result[ 10 ] = ( near + far ) * rangeInv;
  result[ 11 ] = -1;

  result[ 12 ] = 0;
  result[ 13 ] = 0;
  result[ 14 ] = near * far * rangeInv * 2;
  result[ 15 ] = 0;

  return result;
}

function identity3() {
  return mat3( 1, 0, 0, 0, 1, 0, 0, 0, 1 );
}

function identity4() {
  return mat4( 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 );
}

function inverse4( m, dst ) {
  dst = dst || mat4( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 );
  var m00 = m[ 0 ];
  var m01 = m[ 1 ];
  var m02 = m[ 2 ];
  var m03 = m[ 3 ];
  var m10 = m[ 4 ];
  var m12 = m[ 5 ];
  var m11 = m[ 6 ];
  var m13 = m[ 7 ];
  var m20 = m[ 8 ];
  var m21 = m[ 9 ];
  var m22 = m[ 10 ];
  var m23 = m[ 11 ];
  var m30 = m[ 12 ];
  var m31 = m[ 13 ];
  var m32 = m[ 14 ];
  var m33 = m[ 15 ];
  var tmp_0 = m22 * m33;
  var tmp_1 = m32 * m23;
  var tmp_2 = m12 * m33;
  var tmp_3 = m32 * m13;
  var tmp_4 = m12 * m23;
  var tmp_5 = m22 * m13;
  var tmp_6 = m02 * m33;
  var tmp_7 = m32 * m03;
  var tmp_8 = m02 * m23;
  var tmp_9 = m22 * m03;
  var tmp_10 = m02 * m13;
  var tmp_11 = m12 * m03;
  var tmp_12 = m20 * m31;
  var tmp_13 = m30 * m21;
  var tmp_14 = m10 * m31;
  var tmp_15 = m30 * m11;
  var tmp_16 = m10 * m21;
  var tmp_17 = m20 * m11;
  var tmp_18 = m00 * m31;
  var tmp_19 = m30 * m01;
  var tmp_20 = m00 * m21;
  var tmp_21 = m20 * m01;
  var tmp_22 = m00 * m11;
  var tmp_23 = m10 * m01;

  var t0 = ( tmp_0 * m11 + tmp_3 * m21 + tmp_4 * m31 ) -
    ( tmp_1 * m11 + tmp_2 * m21 + tmp_5 * m31 );
  var t1 = ( tmp_1 * m01 + tmp_6 * m21 + tmp_9 * m31 ) -
    ( tmp_0 * m01 + tmp_7 * m21 + tmp_8 * m31 );
  var t2 = ( tmp_2 * m01 + tmp_7 * m11 + tmp_10 * m31 ) -
    ( tmp_3 * m01 + tmp_6 * m11 + tmp_11 * m31 );
  var t3 = ( tmp_5 * m01 + tmp_8 * m11 + tmp_11 * m21 ) -
    ( tmp_4 * m01 + tmp_9 * m11 + tmp_10 * m21 );

  var d = 1.0 / ( m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3 );

  dst[ 0 ] = d * t0;
  dst[ 1 ] = d * t1;
  dst[ 2 ] = d * t2;
  dst[ 3 ] = d * t3;
  dst[ 4 ] = d * ( ( tmp_1 * m10 + tmp_2 * m20 + tmp_5 * m30 ) -
    ( tmp_0 * m10 + tmp_3 * m20 + tmp_4 * m30 ) );
  dst[ 5 ] = d * ( ( tmp_0 * m00 + tmp_7 * m20 + tmp_8 * m30 ) -
    ( tmp_1 * m00 + tmp_6 * m20 + tmp_9 * m30 ) );
  dst[ 6 ] = d * ( ( tmp_3 * m00 + tmp_6 * m10 + tmp_11 * m30 ) -
    ( tmp_2 * m00 + tmp_7 * m10 + tmp_10 * m30 ) );
  dst[ 7 ] = d * ( ( tmp_4 * m00 + tmp_9 * m10 + tmp_10 * m20 ) -
    ( tmp_5 * m00 + tmp_8 * m10 + tmp_11 * m20 ) );
  dst[ 8 ] = d * ( ( tmp_12 * m13 + tmp_15 * m23 + tmp_16 * m33 ) -
    ( tmp_13 * m13 + tmp_14 * m23 + tmp_17 * m33 ) );
  dst[ 9 ] = d * ( ( tmp_13 * m03 + tmp_18 * m23 + tmp_21 * m33 ) -
    ( tmp_12 * m03 + tmp_19 * m23 + tmp_20 * m33 ) );
  dst[ 10 ] = d * ( ( tmp_14 * m03 + tmp_19 * m13 + tmp_22 * m33 ) -
    ( tmp_15 * m03 + tmp_18 * m13 + tmp_23 * m33 ) );
  dst[ 11 ] = d * ( ( tmp_17 * m03 + tmp_20 * m13 + tmp_23 * m23 ) -
    ( tmp_16 * m03 + tmp_21 * m13 + tmp_22 * m23 ) );
  dst[ 12 ] = d * ( ( tmp_14 * m22 + tmp_17 * m32 + tmp_13 * m12 ) -
    ( tmp_16 * m32 + tmp_12 * m12 + tmp_15 * m22 ) );
  dst[ 13 ] = d * ( ( tmp_20 * m32 + tmp_12 * m02 + tmp_19 * m22 ) -
    ( tmp_18 * m22 + tmp_21 * m32 + tmp_13 * m02 ) );
  dst[ 14 ] = d * ( ( tmp_18 * m12 + tmp_23 * m32 + tmp_15 * m02 ) -
    ( tmp_22 * m32 + tmp_14 * m02 + tmp_19 * m12 ) );
  dst[ 15 ] = d * ( ( tmp_22 * m22 + tmp_16 * m02 + tmp_21 * m12 ) -
    ( tmp_20 * m12 + tmp_23 * m22 + tmp_17 * m02 ) );

  return dst;
}

function projection3( width, height ) {
  return mat3( 2 / width, 0, 0, 0, -2 / height, 0, 0, 0, 1 );
}

function projection4( width, height, depth ) {
  return mat4( 2 / width, 0, 0, 0, 0, -2 / height, 0, 0, 0, 0, 2 / depth, 0, 0, 0, 0, 1 );
}

function translation3( tx, ty ) {
  return mat3( 1, 0, 0, 0, 1, 0, tx, ty, 1 );
}

function translation4( tx, ty, tz ) {
  return mat4( 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, tx, ty, tz, 1 );
}

function rotation3( rad ) {
  var c = Math.cos( rad );
  var s = Math.sin( rad );
  return mat3( c, -s, 0, s, c, 0, 0, 0, 1 );
}

function rotationX4( rad ) {
  var c = Math.cos( rad );
  var s = Math.sin( rad );
  return mat4( 1, 0, 0, 0, 0, c, s, 0, 0, -s, c, 0, 0, 0, 0, 1 );
}

function rotationY4( rad ) {
  var c = Math.cos( rad );
  var s = Math.sin( rad );
  return mat4( c, 0, -s, 0, 0, 1, 0, 0, s, 0, c, 0, 0, 0, 0, 1 );
}

function rotationZ4( rad ) {
  var c = Math.cos( rad );
  var s = Math.sin( rad );
  return mat4( c, s, 0, 0, -s, c, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 );
}

function scaling3( sx, sy ) {
  return mat3( sx, 0, 0, 0, sy, 0, 0, 0, 1 );
}

function scaling4( sx, sy, sz ) {
  return mat4( sx, 0, 0, 0, 0, sy, 0, 0, 0, 0, sz, 0, 0, 0, 0, 1 );
}

function mat2( v00, v10, v01, v11 ) {
  return Float32Array( [ v00, v10, v01, v11 ] );
}

function mat3( v00, v10, v20, v01, v11, v21, v02, v12, v22 ) {
  return new Float32Array( [ v00, v10, v20, v01, v11, v21, v02, v12, v22 ] );
}

function mat4( v00, v10, v20, v30, v01, v11, v21, v31, v02, v12, v22, v32, v03, v13, v23, v33 ) {
  return new Float32Array( [ v00, v10, v20, v30, v01, v11, v21, v31, v02, v12, v22, v32, v03, v13, v23, v33 ] );
}

function vec2( a, b ) {
  return new Float32Array( [ a, b ] );
}

function vec3( a, b, c ) {
  return new Float32Array( [ a, b, c ] );
}

function vec4( a, b, c, d ) {
  return new Float32Array( [ a, b, c, d ] );
}

var MUL = {
  m4m4: function ( a, b, result ) {
    result = result || new Float32Array( 4 );
    result[ 0 ] = a[ 0 ] * b[ 0 ] + a[ 2 ] * b[ 1 ];
    result[ 1 ] = a[ 1 ] * b[ 0 ] + a[ 3 ] * b[ 1 ];
    result[ 2 ] = a[ 0 ] * b[ 2 ] + a[ 2 ] * b[ 3 ];
    result[ 3 ] = a[ 1 ] * b[ 2 ] + a[ 3 ] * b[ 3 ];
    return result;
  },
  m9m9: function ( a, b, result ) {
    result = result || new Float32Array( 9 );
    result[ 0 ] = a[ 0 ] * b[ 0 ] + a[ 3 ] * b[ 1 ] + a[ 6 ] * b[ 2 ];
    result[ 1 ] = a[ 1 ] * b[ 0 ] + a[ 4 ] * b[ 1 ] + a[ 7 ] * b[ 2 ];
    result[ 2 ] = a[ 2 ] * b[ 0 ] + a[ 5 ] * b[ 1 ] + a[ 8 ] * b[ 2 ];
    result[ 3 ] = a[ 0 ] * b[ 3 ] + a[ 3 ] * b[ 4 ] + a[ 6 ] * b[ 5 ];
    result[ 4 ] = a[ 1 ] * b[ 3 ] + a[ 4 ] * b[ 4 ] + a[ 7 ] * b[ 5 ];
    result[ 5 ] = a[ 2 ] * b[ 3 ] + a[ 5 ] * b[ 4 ] + a[ 8 ] * b[ 5 ];
    result[ 6 ] = a[ 0 ] * b[ 6 ] + a[ 3 ] * b[ 7 ] + a[ 6 ] * b[ 8 ];
    result[ 7 ] = a[ 1 ] * b[ 6 ] + a[ 4 ] * b[ 7 ] + a[ 7 ] * b[ 8 ];
    result[ 8 ] = a[ 2 ] * b[ 6 ] + a[ 5 ] * b[ 7 ] + a[ 8 ] * b[ 8 ];
    return result;
  },
  m16m16: function ( a, b, result ) {
    result = result || new Float32Array( 16 );
    result[ 0 ] = a[ 0 ] * b[ 0 ] + a[ 4 ] * b[ 1 ] + a[ 8 ] * b[ 2 ] + a[ 12 ] * b[ 3 ];
    result[ 1 ] = a[ 1 ] * b[ 0 ] + a[ 5 ] * b[ 1 ] + a[ 9 ] * b[ 2 ] + a[ 13 ] * b[ 3 ];
    result[ 2 ] = a[ 2 ] * b[ 0 ] + a[ 6 ] * b[ 1 ] + a[ 10 ] * b[ 2 ] + a[ 14 ] * b[ 3 ];
    result[ 3 ] = a[ 3 ] * b[ 0 ] + a[ 7 ] * b[ 1 ] + a[ 11 ] * b[ 2 ] + a[ 15 ] * b[ 3 ];
    result[ 4 ] = a[ 0 ] * b[ 4 ] + a[ 4 ] * b[ 5 ] + a[ 8 ] * b[ 6 ] + a[ 12 ] * b[ 7 ];
    result[ 5 ] = a[ 1 ] * b[ 4 ] + a[ 5 ] * b[ 5 ] + a[ 9 ] * b[ 6 ] + a[ 13 ] * b[ 7 ];
    result[ 6 ] = a[ 2 ] * b[ 4 ] + a[ 6 ] * b[ 5 ] + a[ 10 ] * b[ 6 ] + a[ 14 ] * b[ 7 ];
    result[ 7 ] = a[ 3 ] * b[ 4 ] + a[ 7 ] * b[ 5 ] + a[ 11 ] * b[ 6 ] + a[ 15 ] * b[ 7 ];
    result[ 8 ] = a[ 0 ] * b[ 8 ] + a[ 4 ] * b[ 9 ] + a[ 8 ] * b[ 10 ] + a[ 12 ] * b[ 11 ];
    result[ 9 ] = a[ 1 ] * b[ 8 ] + a[ 5 ] * b[ 9 ] + a[ 9 ] * b[ 10 ] + a[ 13 ] * b[ 11 ];
    result[ 10 ] = a[ 2 ] * b[ 8 ] + a[ 6 ] * b[ 9 ] + a[ 10 ] * b[ 10 ] + a[ 14 ] * b[ 11 ];
    result[ 11 ] = a[ 3 ] * b[ 8 ] + a[ 7 ] * b[ 9 ] + a[ 11 ] * b[ 10 ] + a[ 15 ] * b[ 11 ];
    result[ 12 ] = a[ 0 ] * b[ 12 ] + a[ 4 ] * b[ 13 ] + a[ 8 ] * b[ 14 ] + a[ 12 ] * b[ 15 ];
    result[ 13 ] = a[ 1 ] * b[ 12 ] + a[ 5 ] * b[ 13 ] + a[ 9 ] * b[ 14 ] + a[ 13 ] * b[ 15 ];
    result[ 14 ] = a[ 2 ] * b[ 12 ] + a[ 6 ] * b[ 13 ] + a[ 10 ] * b[ 14 ] + a[ 14 ] * b[ 15 ];
    result[ 15 ] = a[ 3 ] * b[ 12 ] + a[ 7 ] * b[ 13 ] + a[ 11 ] * b[ 14 ] + a[ 15 ] * b[ 15 ];
    return result;
  },
  m16m4: function ( a, b, result ) {
    result = result || new Float32Array( 4 );
    result[ 0 ] = a[ 0 ] * b[ 0 ] + a[ 4 ] * b[ 1 ] + a[ 8 ] * b[ 2 ] + a[ 12 ] * b[ 3 ];
    result[ 1 ] = a[ 1 ] * b[ 0 ] + a[ 5 ] * b[ 1 ] + a[ 9 ] * b[ 2 ] + a[ 13 ] * b[ 3 ];
    result[ 2 ] = a[ 2 ] * b[ 0 ] + a[ 6 ] * b[ 1 ] + a[ 10 ] * b[ 2 ] + a[ 14 ] * b[ 3 ];
    result[ 3 ] = a[ 3 ] * b[ 0 ] + a[ 7 ] * b[ 1 ] + a[ 11 ] * b[ 2 ] + a[ 15 ] * b[ 3 ];
    return result;
  }
};

function mul( a, b, result ) {
  var f = MUL[ 'm' + a.length + 'm' + b.length ];
  if ( typeof f !== 'function' ) {
    throw Error( "[webgl.math.mul] I don't know how to multiply 'M" +
      a.length + "' with 'M" + b.length + "'!" );
  }
  return f( a, b, result );
}