@@ -4,10 +4,12 @@
 //
 //
 
 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; }
 
@@ -19,18 +21,21 @@
 
     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;
@@ -51,25 +56,31 @@
    
 
 
 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]; }
@@ -78,10 +89,12 @@
 
 
 
 // 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; }
 
@@ -95,11 +108,13 @@
             
     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; }
         
@@ -117,10 +132,11 @@
 
 
 
 //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;
@@ -141,10 +157,12 @@
 
     
     
 
 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;
@@ -162,10 +180,11 @@
     
 // 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];
@@ -205,12 +224,16 @@
 		          [di*D, di*E, di*F],
 		          [di*G, di*H, di*K]];
 
 	return result;  }
 
-    
+	
+// does not check if function is differentiable.
+
 function compute_gradient(func, point, error){
+	if(!func) throw "function argument to compute_gradient missing";
+	if(!point) throw "point argument to compute_gradient missing";
 
     if(!error) error = 0.00001;
 
     // find gradient
     var otherpoint = point.slice(0);
@@ -234,11 +257,13 @@
 // 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;