// Convert degrees to radians.
    var RAD2DEG = 180 / Math.PI
		var DEG2RAD = Math.PI / 180
    
    // Simple 2D Vector Math
    function subtract(a, b){
      return [a[0]-b[0], a[1]-b[1]];
    }
    function dotProduct(a, b){
      return a[0] * b[0] + a[1] * b[1];
    }
    function crossProduct(a, b){
      return a[0] * b[1] - b[0] * a[1]
    }
    
    
    // Check for the intersection of ray and a line in 2D.
    function rayLineIntersect(rayOrigin, rayDirection, point1, point2){
      v1 = subtract(rayOrigin, point1);
      v2 = subtract(point2, point1);
      v3 = [-rayDirection[1], rayDirection[0]];

      dot = dotProduct(v2, v3);
      if (Math.abs(dot) < 0.000001) {
        return false;
      }
			
      t1 = (crossProduct(v2, v1)) / dot;
      t2 = dotProduct(v1,v3) / dot;

      if (t1 >= 0.0 && (t2 >= 0.0 && t2 <= 1.0)){
        return true;
      }

      return false;
    }
    
    
    // Perform intersection calculation for a grid of points and set of extrusions in three dimensions.    
    function threeDIntersect(sunVectors, pointGrid, windowExtrusions, shadeExtrusions, timeinterval = 1){
      // Create an empty list of results for the point grid.
      var results = []
      for(var i = 0; i < pointGrid.length; i++) {
        results.push(0)
    	}
      
      // Loop through all of the vectors and extrusions to find which points see the sun
      for (j = 0; j < sunVectors.length; j++) {
        // Convert the sun vector into a series of 2D rays
        sunVec = sunVectors[j]
        xySunVec = [sunVec.x, sunVec.y]
        yzSunVec = [sunVec.y, sunVec.z]
        xzSunVec = [sunVec.x, sunVec.z]
        
        for (var i = 0; i < pointGrid.length; i++) {
          rayOriginxy = [pointGrid[i].x,pointGrid[i].y]
          rayOriginyz = [pointGrid[i].y,pointGrid[i].z]
          rayOriginxz = [pointGrid[i].x,pointGrid[i].z]
          
          for (var k = 0; k < windowExtrusions.length; k++) {
            xyIntersect = rayLineIntersect(rayOriginxy, xySunVec, windowExtrusions[k].xy[0], windowExtrusions[k].xy[1])
            yzIntersect = rayLineIntersect(rayOriginyz, yzSunVec, windowExtrusions[k].yz[0], windowExtrusions[k].yz[1])
            if (xyIntersect == true && yzIntersect == true){
              results[i] = results[i] + timeinterval
            }
        	}
        }
      }
      return results
    }