Arrow keys to rotate the model Mouse position to aim the ray See if you can get the ray to hit a sphere and reflect (multiple times). ;) The green line is the ray The blue line is the normal
This model demonstrates how a ray intersects with a sphere and then bounces off as a reflected ray. Given a set of objects (spheres), the program determines if and where an intersection occurs with the ray and any one sphere, then re-directs the ray back into the environment as a reflected ray. Assume the following: P is the point that starts the ray. R is the direction of the ray R' is the direction of the reflected ray S is the sphere's position r is the sphere's radius C is the intersection point N is the normal at the intersection point C The ray is defined as Position + (Direction * Time) Because position and direction are already given, time is what needs to be calculated: 1. V = S - P (find the distance squared between the ray and sphere) 2. d = R * V :: if dot product < 0, stop (if it occurs 'behind' the ray) 3. if d^2 - (V^2 - r^2) < 0, stop 4. C = ±sqrt(d^2 - (V^2 - r^2)) - d 5. C is the "time" it takes to intersect with the sphere, thus Intersections at P + R*(±sqrt(d^2 - (V^2 - r^2)) - d) 6. To calculate the normal, simply find the scalar value of C - S: N = (C - S) / ||C - S|| 7. Where the closest intersection occurs, that is where the reflected ray is calculated: 1) dot = R * N, 2) R' = R - 2dN Steps 1-7 are repeated until the closest intersection among the entire set of spheres is found. Depending on where the intersection occurs, a base color and shade are taken from the sphere that was hit. Then, diffuse lighting (how a sphere gets shaded by a light source) and phong lighting (the bright shiny spot where the light is most concentrated) are calculated using the normal. The full raytracer is here: http://scratch.mit.edu/projects/12558735 For more information, see: http://en.wikipedia.org/wiki/Ray_tracing
