JS Matrix Constructors

JS-Matrix-Constructors.js

// [Not sure how to implement multiple constructors for the same object using a psuedo-static method
// (hence return this)... FIXME if incorrect.

/**
 * Construct a 2 dimensional rotation matrix about the point (0,0)
 * @param {Number} theta the angle to rotate
 */
function Matrix.create2DRotation(theta) {
   this.columnns = this.rows = 2;
   var sinTheta = Math.sin(theta);
   var cosTheta = Math.cos(theta);
   // [DF] may need to switch elements at index 1 and 2, depending on your v * M implemntation. (vector column/row)
   // Assumed: [x,y,z] * M
   // Same applies for all following matrices. Just take the transpose if you've done it the other way.
   this.elements = [cosTheta, -sinTheta, sinTheta, cosTheta];
   return this;
}

/**
 * Construct a 3 dimensional rotation matrix about the X axis
 * @param {Number} theta the angle to rotate about the X axis
 */
function Matrix.createRotationX(theta) {
   this.columns = this.rows = 3;
   var sinTheta = Math.sin(theta);
   var cosTheta = Math.cos(theta);
   this.elements = [
         1, 0, 0,
         0, cosTheta, sinTheta,
         0, -sinTheta, cosTheta      
   ];
   return this;
}

/**
 * Construct a 3 dimensional rotation matrix about the Y axis
 * @param {Number} theta the angle to rotate about the Y axis
 */
function Matrix.createRotationY(theta) {
   this.columns = this.rows = 3;
   var sinTheta = Math.sin(theta);
   var cosTheta = Math.cos(theta);
   this.elements = [
         cosTheta, 0, -sinTheta,
         0, 0, 1,
         sinTheta, 0, cosTheta      
   ];
   return this;
}

/**
 * Construct a 3 dimensional rotation matrix about the Z axis
 * @param {Number} theta the angle to rotate about the Z axis
 */
function Matrix.createRotationZ(theta) {
   this.columns = this.rows = 3;
   var sinTheta = Math.sin(theta);
   var cosTheta = Math.cos(theta);
   this.elements = [
         cosTheta, sinTheta, 0, 
         -sinTheta, cosTheta, 1,
         0, 0, 1      
   ];
   return this;
}

/**
 * Construct a 3 dimensional rotation matrix about an arbitrary axis
 * @param {Number} theta the angle to rotate about the axis
 * @param {Vector} axis the Vector representing the axis
 */
function Matrix.createRotationFromAxis(theta, axis) {
   this.columns = this.rows = 3;
   var sinT = Math.sin(theta);
   var cosT = Math.cos(theta);
   var cTI = 1 - cosT;
   var n = axis.normalize():
   var nx = n.components[0] || throw "Illegal Vector";
   var ny = n.components[1] || throw "Illegal Vector";
   var nz = n.components[2] || throw "Illegal Vector";
   this.elements = [ // ermagherd, arbitrary arity!
         nx * nx * cTI + cosT,        nx * ny * cTI + nz * sinT,   nx * nz * cTI - ny * sinT,
         nx * ny * cTI + nz * sinT,   ny * ny * cTI + cosT,        ny * nz * cTI + nx * sinT,
         nx * nz * cTI + ny * sinT,   ny * nz * cTI - nx * sinT,   nz * nz * cTI + cosT
   ];
   return this;
}

/**
 * Construct a 3D scaling matrix
 * @param {Vector} the vector to scale by
 * @param {Number} the scalar quantity
 */
function Matrix.createScale(vector, k) {
   this.rows = this.columns = 3;
      if (vector.components.length != 3)
         throw "Illegal Vector";
   var n = vector.normalize();
   var nx = n.components[0] || throw "Illegal Vector";
   var ny = n.components[1] || throw "Illegal Vector";
   var nz = n.components[2] || throw "Illegal Vector";
   var km1 = k - 1;
   this.elements = [
         1 + km1  * nx * nx,   km1 * nx * nz,       km1 * nx * nz,
         km1 * nx * ny,        1 + km1 * ny * ny,   km1 * ny * nz,
         km1 * nx * nz,        km1 * ny * nz,       1 + km1 * nz * nz
   ];
   return this;
}


/**
 * Construct a 2D scaling matrix
 * @param {Vector} the vector to scale by
 * @param {Number} the scalar quantity
 */
function Matrix.createScale(vector, k) {
   if (vector.components.length != 2)
         throw "Illegal Vector";
   this.rows = this.columns = 3;
   var n = vector.normalize();
   var nx = n.components[0] || throw "Illegal Vector";
   var ny = n.components[1] || throw "Illegal Vector";
   var km1 = k - 1;
   this.elements = [
         1 + km1  * nx * nx, km1 * nx * ny,      
         km1 * nx * ny, 1 + km1 * ny * ny 
   ];
   return this;
}

/**
 * Construct a rotation to peform a 3D affine translation
 *
 *        // Example Usage:
 *        var rotation = new Matrix.createRotationY(Math.PI/4);
 *        var translation = new Matrix.createTranlation(5, 0, 0);
 *        // rotate foo 45deg then tranlate 5 units in it's object x-direction
 *        foo.position = rotation.multiply(translation); 
 *
 * @param {Number} dx x displacement
 * @param {Number} dy y displacement
 * @param {Number} dz z displacement
 */
function Matrix.createTranlation(dx, dy, dz) {
   this.columns = this.rows = 4;
   this.elements = [
         1, 0, 0, 0, 
         0, 1, 0, 0,
         0, 0, 1, 0,
         dx, dy, dz, 1
   ];
   return this;
}

/**
 * Construct a rotation to peform a 2D affine translation
 * @param {Number} dx x displacement
 * @param {Number} dy y displacement
 */
function Matrix.createTranslation(dx, dy) {
   this.columns = this.rows = 3;
   this.elements = [
         1, 0, 0, 
         0, 1, 0,
         dx, dy, 1
   ];
   return this;   
}