Finding reflection points in a scene - Trigonometry Help

Hey everyone,

I am attempting to do some first order reflection finding within my environment, for use in a later room acoustic model. The method I am using is the image source method, in which the reflections are found by first mirroring the scene and then drawing a line from the mirrored sources to the original listener. The point at which this line crosses the mirror line is the reflection point. This diagram from Aalto university shows the concept nicely.

I have a script which almost does this, except the locations of the reflections are slightly off: see this image of the scene

The centre of the cubes should be the reflection point, however they are slightly off the eviroment boundary.

the code used to create this is:

             foreach (Vector3 dir in simpleDirections) {

                 //find the point at which a ray travelling this dir will hit something in the room
                 // to use as our mirror line
                 Ray ray = new Ray (source.transform.position, dir);
                 RaycastHit hit;
                 if (Physics.Raycast (ray, out hit)) {
                     if (hit.collider.name != listener.name) {
 
                         // Create the image source and a ray traveling from this image source to the listener
                         Vector3 imageSource = hit.point + (dir * hit.distance);
                         Ray imageSourceRay = new Ray (imageSource, listener.transform.position - imageSource);
 
                         // Find the point of reflection, to do this we need to find how far along
                         // the imagesourceray to travel to reach the mirror line.
 
                         // some trig to find this distance - cotan(theta) * opposite
                         float dot = Vector3.Dot(imageSourceRay.direction,dir);
                         float theta = dot / (Mathf.Abs(imageSourceRay.direction.magnitude) * Mathf.Abs(dir.magnitude));
                         float len = Mathf.Abs(cotan (theta) * hit.distance);
 
                         Vector3 reflectionPoint = imageSource + (imageSourceRay.direction * len);
                         path currPath = new path (source.transform.position, listener.transform.position);
                         currPath.segments.Add (new Ray (source.transform.position, reflectionPoint - source.transform.position));
                         currPath.segments.Add (new Ray (reflectionPoint, listener.transform.position - reflectionPoint));
                         currPath.isValid = true;
                         reflections.Add (currPath);
                     }
                 }
             }

I can make the reflections appear in the correct place by raytracing the image source ray, as well as using convex colliders or double sided meshes. However the end application will use fairly large meshes so I would like a solution not using raytracing!

Currently I think that my problem is in calculating the distance from the image source to the boundary in order to find the reflection point. My method for this is in the above code as:

distance = cotan(theta) * opposite

where theta is the angle between: the vector from source - mirror image source and the vector from mirror image source to listener.

the opposite is the distance from the boundary (mirror line) to the image source.