How can the resultant velocity of an object after a potential collision be predicted?

Questions & Answers
1

I’m creating a game with a mechanic similar to Peggle. I’m launching a small spherical projectile at a capsule. The rigidbodies of the objects are constrained such that the collision is effectively 2D (just two circles colliding). I want to calculate the direction the projectile will be heading after the collision.

Currently this is my process:

  1. Call Physics.SphereCast along the path of the projectile.
  2. Reflect the projectile velocity about the RaycastHit.normal vector.
  3. Place an arrow object at RaycastHit.point facing the direction of the reflection vector.

Here’s the relevant code (the projectile is launched from the origin):

var raycastHit:RaycastHit; 
if(Physics.SphereCast(Vector3.zero, radius, projectileDirection, raycastHit, range)) {
	arrow.position = raycastHit.point;
	arrow.LookAt(raycastHit.point + Vector3.Reflect(projectileDirection, raycastHit.normal), Vector3.up);
}

With this method, I’m having two problems:

  1. The arrow direction is not accurate (as much as 15 degrees off).
  2. Physics.SphereCast detects collisions that the actual projectile never hits (the radius of the sphere collider and the radius parameter passed to SphereCast are the same).

I have a hunch that this means the actual physics calculation is done differently than I am doing it here (which is the typical “reflect the velocity vector around the contact normal” model). What I need to know is: how can I more accurately predict what the result of the collision is going to be, preferably without writing physics code myself?

2

I’m not sure, but I suspect the raycasthit.normal is the normal of the triangle hit, not the normal at the collider’s surface - it could explain the inaccuracy. Since things are limited to a plane, I think it’s better to calculate yourself the direction: create a line equation for the vector projectileDirection and a circle equation for the cylinder, then replace x and y in the circle equation and find the intersection points - it’s a quadratic equation, so you usually ends with two points; the nearest one is the contact point. With the contact point, calculate a line from this point to the center of the cylinder - that’s the normal line - and reflects the vector projectileDirection along this normal… A piece of cake, no? Don’t panic! You can find the equations in:

http://mathforum.org/library/drmath/view/55134.html

If you need some additional help on this, let me know and I’ll try to help you.