matrix from points

gistfile1.txt

var sylvester = require('sylvester'), glMatrix = require('gl-matrix');

var points = {
	topLeft : sylvester.Vector.create([-3.5530766369047617, 1.3324590773809524, 2.1444642857142853]),
	topRight : sylvester.Vector.create([0.15434523809523798, -0.19136904761904774, 0.048714285714285266]),
	bottomLeft : sylvester.Vector.create([-2.5932031249999996, 1.403546875, 4.597250000000001])
};

var mat = mapping(82,46,points.topLeft,points.topRight,points.bottomLeft);

for(var i = 0; i < 16; i++){
	var r = Math.floor(i/4)+1;
	var c = i%4+1
	console.log('transformMat.M'+r+c+" = "+matl[i]+';');
}

console.log(applyMatrixByHand([1.265,-.157,2.451]));

function fromColumns(a,b,c,d){
	var matrixArray = [[1,0,0,0],
					   [0,1,0,0],
					   [0,0,1,0],
					   [0,0,0,1]];
	for(var i=0;i<3;i++){
		matrixArray[0][i] = a.elements[i];
		matrixArray[1][i] = b.elements[i];
		matrixArray[2][i] = c.elements[i];
		matrixArray[3][i] = d.elements[i];
	}
	var out = sylvester.Matrix.create(matrixArray);
	return out;
}
function scaleMatrix(m,x,y,z) {
	for(i = 0; i <= 3; i++) {
		m[i][0] *= x;
		m[i][1] *= y;
		m[i][2] *= z;
		}
}
function mapping(wd, ht, a, b, c) {
	var dx = b.subtract(a);
	var dy = c.subtract(a);
	var dz = dy.cross(dx);
	var ma = a.dup();
	
	var byExample= fromColumns(dx,dy,dz,ma);
	
	byExample = byExample.inverse();
	console.log(byExample);
	scaleMatrix(byExample.elements,wd,ht,wd*ht);
	var temp = new Array();
	for (var i = 0; byExample.elements[i]; i++){
		temp.push(byExample.elements[i][0]);
		temp.push(byExample.elements[i][1]);
		temp.push(byExample.elements[i][2]);
		temp.push(byExample.elements[i][3]);
	}
	byExample = glMatrix.mat4.create(temp);
	return byExample;
}

function applyMatrix(vec){
	var inV;
	if(vec.length){
		inV = glMatrix.vec3.create([vec[0],vec[1],vec[2],1]);
	} else {
		inV = glMatrix.vec3.create([vec.x,vec.y,vec.z,1]);
	}
	var outV = glMatrix.vec3.create();
	return glMatrix.mat4.multiplyVec3(mat,inV,outV);
}

function applyMatrixByHand(vec){
	var x = mat[0] * vec[0] + mat[4] * vec[1] + mat[8] * vec[2] + mat[12];
	var y = mat[1] * vec[0] + mat[5] * vec[1] + mat[9] * vec[2] + mat[13];
	var z = mat[2] * vec[0] + mat[6] * vec[1] + mat[10] * vec[2] + mat[14];
	//var w = mat[3] * vec[0] + mat[7] * vec[1] + mat[11] * vec[2] + mat[15];
	return [x,y,z];
}

function Vector(a){
	this.x = a[0];
	this.y = a[1];
	this.z = a[2];
	this.add = function(v){
		var ox = this.x + v.x;
		var oy = this.y + v.y;
		var oz = this.z + v.z;
		return new Vector([ox,oy,oz]);
	}
	this.subtract = function(v){
		var ox = this.x - v.x;
		var oy = this.y - v.y;
		var oz = this.z - v.z;
		return new Vector([ox,oy,oz]);
	}
	this.scale = function(s){
		var ox = this.x * s;
		var oy = this.y * s;
		var oz = this.z * s;
		return new Vector([ox,oy,oz]);
	}
	this.normalize = function(){
		var length = Math.sqrt(Math.pow(this.x,2) + Math.pow(this.y,2) + Math.pow(this.z,2))
		var ox = this.x/length;
    	var oy = this.y/length;
    	var oz = this.z/length;
    	return new Vector([ox,oy,oz]);
	}
	return this;
}