define([], function () {
"use strict";
/**
* Mat3 - 3x3 Matrix
* @class Mat3
* @namespace kick.math
*/
return {
/**
* Creates a new identity Mat3 using the default array type<br>
* Any javascript array containing at least 9 numeric elements can serve as a mat3
* @method create
* @return {kick.math.Mat3} New mat3
* @static
*/
create: function () {
var out = new Float32Array(9);
out[0] = 1;
out[4] = 1;
out[8] = 1;
return out;
},
/**
* Copies the upper-left 3x3 values into the given mat3.
* @method fromMat4
* @param {kick.math.Mat3} out the receiving 3x3 matrix
* @param {kick.math.Mat4} a the source 4x4 matrix
* @return {kick.math.Mat3} out
*/
fromMat4: function(out, a) {
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
out[3] = a[4];
out[4] = a[5];
out[5] = a[6];
out[6] = a[8];
out[7] = a[9];
out[8] = a[10];
return out;
},
/**
* Creates a new mat3 initialized with values from an existing matrix
* @method clone
* @param {kick.math.Mat3} a matrix to clone
* @return {kick.math.Mat3} a new 3x3 matrix
* @static
*/
clone: function (a) {
var out = new Float32Array(9);
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];
return out;
},
/**
* Copies the values of one mat3 to another
* @method copy
* @param {kick.math.Mat3} out the receiving matrix
* @param {kick.math.Mat3} a the source matrix
* @return {kick.math.Mat3} out
* @static
*/
copy: function (out, a) {
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];
return out;
},
/**
* Sets a mat3 to an identity matrix
* @method identity
* @param {kick.math.Mat3} out mat3 to set
* @return {kick.math.Mat3} dest
* @static
*/
identity: function (out) {
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 1;
out[5] = 0;
out[6] = 0;
out[7] = 0;
out[8] = 1;
return out;
},
/**
* Transposes a mat3 (flips the values over the diagonal)
* @method transpose
* @param {kick.math.Mat3} out the receiving matrix
* @param {kick.math.Mat3} a the source matrix
* @return {kick.math.Mat3} out
* @static
*/
transpose: function (out, a) {
// If we are transposing ourselves we can skip a few steps but have to cache some values
if (out === a) {
var a01 = a[1], a02 = a[2], a12 = a[5];
out[1] = a[3];
out[2] = a[6];
out[3] = a01;
out[5] = a[7];
out[6] = a02;
out[7] = a12;
} else {
out[0] = a[0];
out[1] = a[3];
out[2] = a[6];
out[3] = a[1];
out[4] = a[4];
out[5] = a[7];
out[6] = a[2];
out[7] = a[5];
out[8] = a[8];
}
return out;
},
/**
* Inverts a Mat3
* @method invert
* @param {kick.math.Mat3} out the receiving matrix
* @param {kick.math.Mat3} a the source matrix
* @return {kick.math.Mat3} out
* @static
*/
invert: function (out, a) {
var a00 = a[0], a01 = a[1], a02 = a[2],
a10 = a[3], a11 = a[4], a12 = a[5],
a20 = a[6], a21 = a[7], a22 = a[8],
b01 = a22 * a11 - a12 * a21,
b11 = -a22 * a10 + a12 * a20,
b21 = a21 * a10 - a11 * a20,
// Calculate the determinant
det = a00 * b01 + a01 * b11 + a02 * b21;
if (!det) {
return null;
}
det = 1.0 / det;
out[0] = b01 * det;
out[1] = (-a22 * a01 + a02 * a21) * det;
out[2] = (a12 * a01 - a02 * a11) * det;
out[3] = b11 * det;
out[4] = (a22 * a00 - a02 * a20) * det;
out[5] = (-a12 * a00 + a02 * a10) * det;
out[6] = b21 * det;
out[7] = (-a21 * a00 + a01 * a20) * det;
out[8] = (a11 * a00 - a01 * a10) * det;
return out;
},
/**
* Calculates the adjugate of a mat3
* @method adjoint
* @param {kick.math.Mat3} out the receiving matrix
* @param {kick.math.Mat3} a the source matrix
* @return {kick.math.Mat3} out
* @static
*/
adjoint: function (out, a) {
var a00 = a[0], a01 = a[1], a02 = a[2],
a10 = a[3], a11 = a[4], a12 = a[5],
a20 = a[6], a21 = a[7], a22 = a[8];
out[0] = (a11 * a22 - a12 * a21);
out[1] = (a02 * a21 - a01 * a22);
out[2] = (a01 * a12 - a02 * a11);
out[3] = (a12 * a20 - a10 * a22);
out[4] = (a00 * a22 - a02 * a20);
out[5] = (a02 * a10 - a00 * a12);
out[6] = (a10 * a21 - a11 * a20);
out[7] = (a01 * a20 - a00 * a21);
out[8] = (a00 * a11 - a01 * a10);
return out;
},
/**
* Calculates the determinant of a Mat3
* @method determinant
* @param {kick.math.Mat3} a the source matrix
* @return {Number} determinant of a matrix
* @static
*/
determinant: function (a) {
var a00 = a[0], a01 = a[1], a02 = a[2],
a10 = a[3], a11 = a[4], a12 = a[5],
a20 = a[6], a21 = a[7], a22 = a[8];
return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20);
},
/**
* Copies the elements of a mat3 into the upper 3x3 elements of a mat4
* @method toMat4
* @param {kick.math.Mat4} out mat4 receiving copied values
* @param {kick.math.Mat3} mat mat3 containing values to copy
* @return {kick.math.Mat4} out
* @static
*/
toMat4: function (out, mat) {
out[15] = 1;
out[14] = 0;
out[13] = 0;
out[12] = 0;
out[11] = 0;
out[10] = mat[8];
out[9] = mat[7];
out[8] = mat[6];
out[7] = 0;
out[6] = mat[5];
out[5] = mat[4];
out[4] = mat[3];
out[3] = 0;
out[2] = mat[2];
out[1] = mat[1];
out[0] = mat[0];
return out;
},
/**
* Multiplies two mat3's
* @method multiply
* @param {kick.math.Mat3} out the receiving matrix
* @param {kick.math.Mat3} a the first operand
* @param {kick.math.Mat3} b the second operand
* @return {kick.math.Mat3} out
* @static
*/
multiply: function (out, a, b) {
var a00 = a[0], a01 = a[1], a02 = a[2],
a10 = a[3], a11 = a[4], a12 = a[5],
a20 = a[6], a21 = a[7], a22 = a[8],
b00 = b[0], b01 = b[1], b02 = b[2],
b10 = b[3], b11 = b[4], b12 = b[5],
b20 = b[6], b21 = b[7], b22 = b[8];
out[0] = b00 * a00 + b01 * a10 + b02 * a20;
out[1] = b00 * a01 + b01 * a11 + b02 * a21;
out[2] = b00 * a02 + b01 * a12 + b02 * a22;
out[3] = b10 * a00 + b11 * a10 + b12 * a20;
out[4] = b10 * a01 + b11 * a11 + b12 * a21;
out[5] = b10 * a02 + b11 * a12 + b12 * a22;
out[6] = b20 * a00 + b21 * a10 + b22 * a20;
out[7] = b20 * a01 + b21 * a11 + b22 * a21;
out[8] = b20 * a02 + b21 * a12 + b22 * a22;
return out;
},
/**
* Translate a mat3 by the given vector
* @method translate
* @param {kick.math.Mat3} out the receiving matrix
* @param {kick.math.Mat3} a the matrix to translate
* @param {kick.math.Vec2} v vector to translate by
* @return {kick.math.Mat3} out
* @static
*/
translate: function(out, a, v) {
var a00 = a[0], a01 = a[1], a02 = a[2],
a10 = a[3], a11 = a[4], a12 = a[5],
a20 = a[6], a21 = a[7], a22 = a[8],
x = v[0], y = v[1];
out[0] = a00;
out[1] = a01;
out[2] = a02;
out[3] = a10;
out[4] = a11;
out[5] = a12;
out[6] = x * a00 + y * a10 + a20;
out[7] = x * a01 + y * a11 + a21;
out[8] = x * a02 + y * a12 + a22;
return out;
},
/**
* Rotates a mat3 by the given angle
* @method rotate
* @param {kick.math.Mat3} out the receiving matrix
* @param {kick.math.Mat3} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @return {kick.math.Mat3} out
* @static
*/
rotate: function (out, a, rad) {
var a00 = a[0], a01 = a[1], a02 = a[2],
a10 = a[3], a11 = a[4], a12 = a[5],
a20 = a[6], a21 = a[7], a22 = a[8],
s = Math.sin(rad),
c = Math.cos(rad);
out[0] = c * a00 + s * a10;
out[1] = c * a01 + s * a11;
out[2] = c * a02 + s * a12;
out[3] = c * a10 - s * a00;
out[4] = c * a11 - s * a01;
out[5] = c * a12 - s * a02;
out[6] = a20;
out[7] = a21;
out[8] = a22;
return out;
},
/**
* Scales the mat3 by the dimensions in the given vec2
* @method scale
* @param {kick.math.Mat3} out the receiving matrix
* @param {kick.math.Mat3} a the matrix to rotate
* @param {kick.math.Vec2} v the vec2 to scale the matrix by
* @return {kick.math.Mat3} out
* @static
**/
scale: function(out, a, v) {
var x = v[0], y = v[2];
out[0] = x * a[0];
out[1] = x * a[1];
out[2] = x * a[2];
out[3] = y * a[3];
out[4] = y * a[4];
out[5] = y * a[5];
out[6] = a[6];
out[7] = a[7];
out[8] = a[8];
return out;
},
/**
* Copies the values from a mat2d into a mat3
* @method fromMat2d
* @param {kick.math.Mat3} out the receiving matrix
* @param {kick.math.Mat3} a the matrix to rotate
* @return {kick.math.Mat3} out
* @static
**/
fromMat2d: function(out, a) {
out[0] = a[0];
out[1] = a[1];
out[2] = 0;
out[3] = a[2];
out[4] = a[3];
out[5] = 0;
out[6] = a[4];
out[7] = a[5];
out[8] = 1;
return out;
},
/**
* Calculates a 3x3 matrix from the given quaternion
* @method fromQuat
* @param {kick.math.Mat3} out mat3 receiving operation result
* @param {kick.math.Quat} q Quaternion to create matrix from
*
* @return {kick.math.Mat3} out
* @static
*/
fromQuat: function (out, q) {
var x = q[0], y = q[1], z = q[2], w = q[3],
x2 = x + x,
y2 = y + y,
z2 = z + z,
xx = x * x2,
xy = x * y2,
xz = x * z2,
yy = y * y2,
yz = y * z2,
zz = z * z2,
wx = w * x2,
wy = w * y2,
wz = w * z2;
out[0] = 1 - (yy + zz);
out[1] = xy + wz;
out[2] = xz - wy;
out[3] = xy - wz;
out[4] = 1 - (xx + zz);
out[5] = yz + wx;
out[6] = xz + wy;
out[7] = yz - wx;
out[8] = 1 - (xx + yy);
return out;
},
/**
* Transform a mat3 into a rotation (quaternion).
* @method toQuat
* @param {kick.math.Quat} out
* @param {kick.math.Mat3} mat
* @return {kick.math.Quat}
* @static
*/
toQuat: function (out, mat) {
// Code based on http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
var m00 = mat[0], m10 = mat[1], m20 = mat[2],
m01 = mat[3], m11 = mat[4], m21 = mat[5],
m02 = mat[6], m12 = mat[7], m22 = mat[8],
trace = m00 + m11 + m22, // trace of matrix
s;
if (!out) {
out = new Float32Array(4);
}
if (trace > 0) {
s = 0.5 / Math.sqrt(trace + 1.0);
out[0] = (m21 - m12) * s;
out[1] = (m02 - m20) * s;
out[2] = (m10 - m01) * s;
out[3] = 0.25 / s;
} else {
if (m00 > m11 && m00 > m22) {
s = 2.0 * Math.sqrt(1.0 + m00 - m11 - m22);
out[0] = 0.25 * s;
out[1] = (m01 + m10) / s;
out[2] = (m02 + m20) / s;
out[3] = (m21 - m12) / s;
} else if (m11 > m22) {
s = 2.0 * Math.sqrt(1.0 + m11 - m00 - m22);
out[0] = (m01 + m10) / s;
out[1] = 0.25 * s;
out[2] = (m12 + m21) / s;
out[3] = (m02 - m20) / s;
} else {
s = 2.0 * Math.sqrt(1.0 + m22 - m00 - m11);
out[0] = (m02 + m20) / s;
out[1] = (m12 + m21) / s;
out[2] = 0.25 * s;
out[3] = (m10 - m01) / s;
}
}
return out;
},
/**
* Returns a string representation of a mat3
* @method str
* @param {kick.math.Mat3} mat mat3 to represent as a string
* @return {String} string representation of mat
* @static
*/
str: function (mat) {
return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] +
', ' + mat[3] + ', ' + mat[4] + ', ' + mat[5] +
', ' + mat[6] + ', ' + mat[7] + ', ' + mat[8] + ']';
},
/**
* Returns a string representation of a mat3 printed as a 4x4 matrix (on 3 lines)
* @method strPretty
* @param {kick.math.Mat3} mat mat3 to represent as a string
* @return {String} string representation of mat
* @static
*/
strPretty: function (mat) {
return '[' + mat[0] + ', ' + mat[3] + ', ' + mat[6] + '\n' +
', ' + mat[1] + ', ' + mat[4] + ', ' + mat[7] + '\n' +
', ' + mat[2] + ', ' + mat[5] + ', ' + mat[8] + ']';
}
};
});
