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Adding some Quaternion love.
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@philogb
philogb committed May 9, 2011
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309 changes: 309 additions & 0 deletions src/math.js
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Expand Up @@ -669,9 +669,318 @@
})(method);
}

//Quaternion class
var Quat = function(x, y, z, w) {
this.x = x || 0;
this.y = y || 0;
this.z = z || 0;
this.w = w || 0;
};

generics = {

clone: function(dest) {
return new Quat(dest.x, dest.y, dest.z, dest.w);
},

neg: function(dest) {
return new Quat(-dest.x, -dest.y, -dest.z, -dest.w);
},

$neg: function(dest) {
dest.x = -dest.x;
dest.y = -dest.y;
dest.z = -dest.z;
dest.w = -dest.w;

return dest;
},

add: function(dest, q) {
return new Quat(dest.x + q.x,
dest.y + q.y,
dest.z + q.z,
dest.w + q.w);
},

$add: function(dest, q) {
dest.x += q.x;
dest.y += q.y;
dest.z += q.z;
dest.w += q.w;

return dest;
},

sub: function(dest, q) {
return new Quat(dest.x - q.x,
dest.y - q.y,
dest.z - q.z,
dest.w - q.w);
},

$sub: function(dest, q) {
dest.x -= q.x;
dest.y -= q.y;
dest.z -= q.z;
dest.w -= q.w;

return dest;
},

scale: function(dest, s) {
return new Quat(dest.x * s,
dest.y * s,
dest.z * s,
dest.w * s);
},

$scale: function(dest, s) {
dest.x *= s;
dest.y *= s;
dest.z *= s;
dest.w *= s;

return dest;
},

mulQuat: function(dest, q) {
var aX = dest.x,
aY = dest.y,
aZ = dest.z,
aW = dest.w,
bX = q.x,
bY = q.y,
bZ = q.z,
bW = q.w;

return new Quat(aW * bX + aX * bW + aY * bZ - aZ * bY,
aW * bY + aY * bW + aZ * bX - aX * bZ,
aW * bZ + aZ * bW + aX * bY - aY * bX,
aW * bW - aX * bX - aY * bY - aZ * bZ);
},

$mulQuat: function(dest, q) {
var aX = dest.x,
aY = dest.y,
aZ = dest.z,
aW = dest.w,
bX = q.x,
bY = q.y,
bZ = q.z,
bW = q.w;

dest.a = aW * bX + aX * bW + aY * bZ - aZ * bY;
dest.b = aW * bY + aY * bW + aZ * bX - aX * bZ;
dest.c = aW * bZ + aZ * bW + aX * bY - aY * bX;
dest.d = aW * bW - aX * bX - aY * bY - aZ * bZ;

return dest;
},

div: function(dest, q) {
var aX = dest.x,
aY = dest.y,
aZ = dest.z,
aW = dest.w,
bX = q.x,
bY = q.y,
bZ = q.z,
bW = q.w;

var d = 1 / (bW * bW + bX * bX + bY * bY + bZ * bZ);

return new Quat((aX * bW - aW * bX - aY * bZ + aZ * bY) * d,
(aX * bZ - aW * bY + aY * bW - aZ * bX) * d,
(aY * bX + aZ * bW - aW * bZ - aX * bY) * d,
(aW * bW + aX * bX + aY * bY + aZ * bZ) * d);
},

$div: function(dest, q) {
var aX = dest.x,
aY = dest.y,
aZ = dest.z,
aW = dest.w,
bX = q.x,
bY = q.y,
bZ = q.z,
bW = q.w;

var d = 1 / (bW * bW + bX * bX + bY * bY + bZ * bZ);

dest.a = (aX * bW - aW * bX - aY * bZ + aZ * bY) * d;
dest.b = (aX * bZ - aW * bY + aY * bW - aZ * bX) * d;
dest.c = (aY * bX + aZ * bW - aW * bZ - aX * bY) * d;
dest.d = (aW * bW + aX * bX + aY * bY + aZ * bZ) * d;

return dest;
},

invert: function(dest) {
var q0 = dest.x,
q1 = dest.y,
q2 = dest.z,
q3 = dest.w;

var d = 1 / (q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);

return new Quat(-q0 * d, -q1 * d, -q2 * d, q3 * d);
},

$invert: function(dest) {
var q0 = dest.x,
q1 = dest.y,
q2 = dest.z,
q3 = dest.w;

var d = 1 / (q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);

dest.a = -q0 * d;
dest.b = -q1 * d;
dest.c = -q2 * d;
dest.d = q3 * d;

return dest;
},

norm: function(dest) {
var a = dest.x,
b = dest.y,
c = dest.z,
d = dest.w;

return sqrt(a * a + b * b + c * c + d * d);
},

normSq: function(dest) {
var a = dest.x,
b = dest.y,
c = dest.z,
d = dest.w;

return a * a + b * b + c * c + d * d;
},

unit: function(dest) {
return Quat.scale(dest, 1 / Quat.norm(dest));
},

$unit: function(dest) {
return Quat.$scale(dest, 1 / Quat.norm(dest));
},

conjugate: function(dest) {
return new Quat(-dest.x,
-dest.y,
-dest.z,
dest.w);
},

$conjugate: function(dest) {
dest.x = -dest.x;
dest.y = -dest.y;
dest.z = -dest.z;

return dest;
}
};
//add generics and instance methods
proto = Quat.prototype = {};
for (method in generics) {
Quat[method] = generics[method];
proto[method] = (function (m) {
return function() {
var args = slice.call(arguments);

args.unshift(this);
return Quat[m].apply(Quat, args);
};
})(method);
}

//Add static methods
Vec3.fromQuat = function(q) {
return new Vec3(q.x, q.y, q.z);
};

Quat.fromVec3 = function(v, r) {
return new Quat(v.x, v.y, v.z, r || 0);
};

Quat.fromMat4 = function(m) {
var u;
var v;
var w;

// Choose u, v, and w such that u is the index of the biggest diagonal entry
// of m, and u v w is an even permutation of 0 1 and 2.
if (m.n11 > m.n22 && m.n11 > m.n33) {
u = 0;
v = 1;
w = 2;
} else if (m.n22 > m.n11 && m.n22 > m.n33]) {
u = 1;
v = 2;
w = 0;
} else {
u = 2;
v = 0;
w = 1;
}

var r = sqrt(1 + m['n' + u + '' + u] - m['n' + v + '' + v] - m['n' + w + '' + w]);
var q = new Quat,
props = ['x', 'y', 'z'];

q[props[u]] = 0.5 * r;
q[props[v]] = 0.5 * (m['n' + v + '' + u] + m['n' + u + '' + v]) / r;
q[props[w]] = 0.5 * (m['n' + u + '' + w] + m['n' + w + '' + u]) / r;
q.w = 0.5 * (m['n' + v + '' + w] - m['n' + w + '' + v]) / r;

return q;
};

Quat.fromXRotation = function(angle) {
return new Quat(sin(angle / 2), 0, 0, cos(angle / 2));
};

Quat.fromYRotation = function(angle) {
return new Quat(0, sin(angle / 2), 0, cos(angle / 2));
};

Quat.fromZRotation = function(angle) {
return new Quat(0, 0, sin(angle / 2), cos(angle / 2));
};

Quat.fromAxisRotation = function(vec, angle) {
var x = vec.x,
y = vec.y,
z = vec.z,
d = 1 / sqrt(x * x + y * y + z * z),
s = sin(angle / 2),
c = cos(angle / 2);

return new Quat(s * x * d,
s * y * d,
s * z * d,
c);
};

Mat4.fromQuat = function(q) {
var a = q.w,
b = q.x,
c = q.y,
d = q.z;

return new Mat4(a * a + b * b - c * c - d * d, 2 * b * c - 2 * a * d, 2 * b * d + 2 * a * c, 0,
2 * b * c + 2 * a * d, a * a - b * b + c * c - d * d, 2 * c * d - 2 * a * b, 0,
2 * b * d - 2 * a * c, 2 * c * d + 2 * a * b, a * a - b * b - c * c + d * d, 0,
0, 0, 0, 1);
};

PhiloGL.Vec3 = Vec3;
PhiloGL.Mat4 = Mat4;
PhiloGL.Quat = Quat;

})();

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