@@ -30,9 +30,9 @@ In `Particle::update`, use this integrator to step the current particle forward
The more substantial part of this task is colliding each particle with the rest of our scene geometry. Thankfully, you've already done most of the work required here during A3: we can use Scotty3D's ray-tracing capabilities to find collisions along our particles' paths.
During each timestep, we know that in the absence of a collision, our particle will travel in the direction of velocity for distance `||velocity|| * dt`. We can create a ray representing this position and velocity and use its distance bound to restrict how far we travel this time-step. If the ray intersects with our scene, we know if and when the particle experiences a collision. Note that since we are representing particles as small spheres, you must take `radius` into account when looking for collisions. If the center of our particle can see collisions up to distance `||velocity|| * dt`, what distance can the closest point on the sphere collide up to?
During each timestep, we know that in the absence of a collision, our particle will travel in the direction of velocity for distance `||velocity|| * dt`. We can create a ray representing this position and velocity to look for collisions during the time-step. If the ray intersects with the scene, we can compute when the particle would experience a collision. Note that since we are representing particles as small spheres, you must take `radius` into account when finding the collision point. If the path intersects a surface, at what distance does the closest point on the sphere start colliding? (Hint - it depends on the angle of intersection.) Also note that if a collision would occur after the end of the current timestep, it may be ignored.
If our ray hit the scene, we can use its hit distance to figure out at what time our particle hit the surface. Again, be careful about the radius here. (Where was the center of the particle when the closest point started intersecting?) We could just place the particle at the collision point and be done, but we don't want our particles to simply stick the surface! Instead, we will assume all particles collide elastically (and massless-ly) - that is, the magnitude of their velocity should be the same before and after the collision, and its direction should be reflected about the normal of the collision surface.
When we find a collision, we could just place the particle at the collision point and be done, but we don't want our particles to simply stick the surface! Instead, we will assume all particles collide elastically (and massless-ly) - that is, the magnitude of their velocity should be the same before and after the collision, and its direction should be reflected about the normal of the collision surface.
Finally, once we have a reflected velocity, we can compute how much of the time step remains after the collision, and step the particle forward that amount. However, what if the particle collided with the scene _again_ before the end of the time-step? If we are using very small time-steps, it might be OK to ignore this possibility, but we want to be able to resolve all collisions. So, we can repeat the ray-casting procedure in a loop until we have used up the entire time-step (up to some epsilon). Remember to only use the remaining portion of the time-step each iteration, and to step forward both the velocity and position at each sub-step.
