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// matrix and vector functions.
//
//
function vector_add(a, b, result){
if(!result) result = [];
if(!a) throw "first argument to vector_add missing";
if(!b) throw "second argument to vector_add missing";
if(a.length > b.lemgth){
var tmp = a;
a = b; b = tmp; }
for(var i = 0; i < a.length; ++i){
result[i] = a[i] + b[i]; }
for(var i = a.length; i < b.length; ++i){
result[i] = b[i]; }
return result; }
function vector_cpy(result, a){
if(!a) throw "first argument to vector_cpy missing";
for(var i = 0; i < a.length; ++i){
result[i] = a[i]; }
}
function vector_minus(a, b, result){
if(!result) result = [];
if(!a) throw "first argument to vector_minus missing";
if(!b) throw "second argument to vector_minus missing";
var lim = Math.max(a.length, b.length);
for(var i = 0; i < lim; ++i){
var aValue, bValue;
if(i < a.length)
aValue = a[i];
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return result; }
function vector_dot(a, b){
var lim = Math.min(a.length, b.length);
if(!a) throw "first argument to vector_dot missing";
if(!b) throw "second argument to vector_dot missing";
var result = 0;
for(var i = 0; i < lim; ++i){
result += a[i] * b[i]; }
return result; }
function vector_norm(a){
if(!a) throw "argument to vector_norm missing";
return Math.sqrt(vector_dot(a,a)); }
function vector_scale(a, s, result){
if(!a) throw "first argument to vector_scale missing";
if(s === undefined || s === null) throw "scalar argument to vector_scale missing";
if(!result) result = [];
for(var i = 0; i < a.length; ++i){
result[i] = s * a[i]; }
return result; }
// returns true iff the zero tail padded vectors match
function vector_cmp(a, b){
if(!a) throw "first argument to vector_cmp missing";
if(!b) throw "second argument to vector_cmp missing";
if(a.length > b.length){
var tmp = a;
a = b; b = tmp; }
for(var i = 0; i < a.length; ++i){
if(a[i] != b[i])
return false; }
for(var i = a.length; i < b.length; ++i){
if(b[i] != 0)
return false; }
return true; }
function midpoint(a, b, result){
function vector_midpoint(a, b, result){
if(!a) throw "first argument to vector_midpoint missing";
if(!b) throw "second argument to vector_midpoint missing";
if(b.length > a.length){
var tmp = a;
a = b; b = tmp; }
if(!result) result = new Array(b.length);
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}
//this function may not care, but the expected matrix format in this project is a list of column vectors.
function matrix_transpose(matrix){
if(!matrix) throw "argument to matrix_transpose missing";
var result = [];
var dim0 = matrix.length;
if(!dim0)
return result;
var dim1 = matrix[0].length;
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function matrix_mult(a, b){
if(!a) throw "first argument to matrix_mult missing";
if(!b) throw "second argument to matrix_mult missing";
var result = [];
var a = matrix_transpose(a);
var dim0 = a.length;
var dim1 = b.length;
for(var i = 0; i < dim1; ++i){
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// finds the inverse of a 3 by 3 matrix, returns false if matrix has determinant zero.
//
function matrix33inv(m){
if(!m) throw "argument to matrix33inv missing";
// the matrix format is a list of column vectors.
var a = m[0][0];
var b = m[1][0];
var c = m[2][0];
var d = m[0][1];
var e = m[1][1];
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// the matrix format is a list of column vectors.
var result = [[di*A, di*B, di*C],
[di*D, di*E, di*F],
[di*G, di*H, di*K]];
return result; }
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//
// equation at:
// http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/ArbitraryAxisRotation.html
// creates a rotation matrix about the given vector.
//
function vector_rotation(vector, s){
if(!vector) throw "vector argument to vector_rotation missing";
if(!s) throw "angle argument to vector_rotation missing";
var len = Math.sqrt(vector[0]*vector[0]
+ vector[1]*vector[1]
+ vector[2]*vector[2]);
var u = vector[0]/len;
var v = vector[1]/len;
var w = vector[2]/len;
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