Wrote unit tests

- Added intersect.js file in lib/expression/docs
- added an entry in the index.js file in expression/docs
- modified intersect.js to give appropriate error messages
- added an entry in lib/math.js so that the test case file could find
the function
- wrote the test cases for intersect

lib/expression/docs/function/geometry/intersect.js

@@ -0,0 +1,14 @@
+module.exports = {
+  'name': 'intersect',
+  'category': 'Geometry',
+  'syntax': [
+    'intersect(expr1, expr2, expr3, expr4)',
+    'intersect(expr1, expr2, expr3)'
+  ],
+  'description': 'Computes the intersection point of lines and/or planes.',
+  'examples': [
+    'intersect([0, 0], [10, 10], [10, 0], [0, 10])',
+    'intersect([1, 0, 1],  [4, -2, 2], [1, 1, 1, 6])'
+  ],
+  'seealso': []
+};

lib/expression/docs/index.js

@@ -78,6 +78,9 @@ exports.unit = require('./function/construction/unit');
 exports['eval'] =  require('./function/expression/eval');
 exports.help =  require('./function/expression/help');
 
+// functions - geometry
+exports.intersect = require('./function/geometry/intersect');
+
 // functions - logical
 exports['and'] = require('./function/logical/and');
 exports['not'] = require('./function/logical/not');

lib/function/geometry/intersect.js

@@ -33,11 +33,6 @@ module.exports = function(math) {
   * @return {Array}              Returns the point of intersection of lines/lines-planes
   */
   math.intersect = function intersect(w, x, y, z) {
-    //check for number of arguments
-    if (arguments.length !== 3 || arguments.length !== 4){
-      throw new math.error.ArgumentsError('intersect', arguments.length, 3, 4);
-    }
-    
     //check for correct type and modify it accordingly
     if (w instanceof Matrix) {
       w = w.toArray();
@@ -51,7 +46,7 @@ module.exports = function(math) {
     else if (z instanceof Matrix) {
       z = z.toArray();
     }
-    
+
     if (!(Array.isArray(w) || Array.isArray(x) || Array.isArray(y) || Array.isArray(z))){
       throw new math.error.UnsupportedTypeError('intersect', math['typeof'](w), math['typeof'](x), math['typeof'](y), math['typeof'](z));
     }
@@ -59,7 +54,12 @@ module.exports = function(math) {
     //decide which function to call based on type of arguments
     switch (arguments.length) {
       case 3:
-        return _intersectLinePlane(arguments[0][0], arguments[0][1], arguments[0][2], arguments[1][0], arguments[1][1], arguments[1][2], arguments[2][0], arguments[2][1], arguments[2][2], arguments[2][3]);
+        if(arguments[0].length === 3 && arguments[1].length === 3 && arguments[2].length === 4){
+          return _intersectLinePlane(arguments[0][0], arguments[0][1], arguments[0][2], arguments[1][0], arguments[1][1], arguments[1][2], arguments[2][0], arguments[2][1], arguments[2][2], arguments[2][3]);
+        }
+        else{
+          throw new TypeError('Arguments are not correct');
+        }
         break;
       case 4:
         var is2D = (arguments[0].length === 2 && arguments[1].length === 2 && arguments[2].length === 2 && arguments[3].length === 2);
@@ -73,7 +73,7 @@ module.exports = function(math) {
           break
         }
       default:
-        throw new TypeError('Arguments are not correct');
+        throw new math.error.ArgumentsError('intersect', arguments.length, 3, 4);
       }
     };
 
@@ -84,7 +84,7 @@ module.exports = function(math) {
     var d4343 = (x4 - x3)*(x4 - x3) + (y4 - y3)*(y4 - y3);
     var d2121 = (x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1);
     var ta = ( d1343*d4321 - d1321*d4343 ) / ( d2121*d4343 - d4321*d4321 );
-    var tb = ( d1343 + mua * d4321 ) / (d4343);
+    var tb = ( d1343 + ta * d4321 ) / (d4343);
    
     var pax = x1 + ta * (x2 - x1);
     var pay = y1 + ta * (y2 - y1);
@@ -105,7 +105,7 @@ module.exports = function(math) {
     var d4343 = (x4 - x3)*(x4 - x3) + (y4 - y3)*(y4 - y3) + (z4 - z3)*(z4 - z3);
     var d2121 = (x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1) + (z2 - z1)*(z2 - z1);
     var ta = ( d1343*d4321 - d1321*d4343 ) / ( d2121*d4343 - d4321*d4321 );
-    var tb = ( d1343 + mua * d4321 ) / (d4343);
+    var tb = ( d1343 + ta * d4321 ) / (d4343);
     
     var pax = x1 + ta * (x2 - x1);
     var pay = y1 + ta * (y2 - y1);
@@ -127,5 +127,8 @@ module.exports = function(math) {
     var py = y1 + t * (y2 - y1);
     var pz = z1 + t * (z2 - z1);
     return [px, py, pz];
+    // TODO: Add cases when line is parallel to the plane:
+    //       (a) no intersection,
+    //       (b) line contained in plane
   }
 }

lib/math.js

@@ -277,7 +277,10 @@ function create (config) {
   require('./function/complex/conj')(math, _config);
   require('./function/complex/re')(math, _config);
   require('./function/complex/im')(math, _config);
-
+  
+  // functions - geometry
+  require('./function/geometry/intersect')(math, _config);
+  
   // functions - logical
   require('./function/logical/and')(math, _config);
   require('./function/logical/not')(math, _config);

test/function/geometry/intersect.test.js

@@ -0,0 +1,35 @@
+var assert = require('assert');
+var error = require('../../../lib/error/index');
+var math = require('../../../index');
+
+describe('intersect', function() {
+  it('should calculate the intersection point of two 2D lines', function() {
+    assert.deepEqual(math.intersect([0, 0], [10, 10], [10, 0], [0, 10]), [5, 5]);
+  });
+
+  it('should calculate the intersection point of two 3D lines', function() {
+    assert.deepEqual(math.intersect([0, 0, 0], [10, 10, 0], [10, 0, 0], [0, 10, 0]), [5, 5, 0]);
+  });
+
+  it('should calculate the intersection point of a line and a plane', function() {
+    assert.deepEqual(math.intersect([1, 0, 1], [4, -2, 2], [1, 1, 1, 6]), [7, -4, 3]);
+  });
+  
+  it('should return null if the points do not intersect', function() {
+    assert.deepEqual(math.intersect([0, 1, 0], [0, 0, 0], [1, 1, 0], [1, 0, 0]), null);
+    assert.deepEqual(math.intersect([0, 1], [0, 0], [1, 1], [1, 0]), null);
+  });
+
+  it('should throw an error when number of arguments are other than 3 or 4', function() {
+    assert.throws(function () {math.intersect([2, 0, 1], [1, 1, 1, 6])});
+    assert.throws(function () {math.intersect([2, 0, 1], [1, 1, 6], [2, 0, 1], [1, 1, 6], [0, 8, 1])});
+  });
+  
+  it('should throw an error for incompatible parameter types', function() {
+    assert.throws(function () {math.intersect(2, 3, 6)}, TypeError);
+    assert.throws(function () {math.intersect([2, 0, 1], [1, 1, 1], [5, 1, 10])}, /Arguments are not correct/);
+    assert.throws(function () {math.intersect([], [], [], [])});
+    assert.throws(function () {math.intersect([2, 8, 9], 3, 6)}, TypeError);
+    assert.throws(function () {math.intersect(a, b, c, d)});
+  });
+});