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allandippy

Collision Detection and Response

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Can anyone tell me how to detect collision using a sphere-plane routine and respond to it? Take it easy on me because this is my first thread. Hehehe.

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basically if you have your point A and you want to test whether it intersects B with radius r.
Well if (Ax-Bx)^2 + (Ay-By)^2 <= r^2
A is inside the circle with center B and radius r because of pythagoras theoreum.

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Guest Anonymous Poster
Here's the sphere/plane code from my intersection library:


// --------------------------------------------------------------------------------------
bool Intersection::SpherePlane(const Sphere& sphere, const Plane& plane)
{
return fabsf(Distance::PointPlane(sphere.GetCenter(), plane) <= sphere.GetRadius());
}
// --------------------------------------------------------------------------------------
bool Intersection::SpherePlane(const Sphere& sphere, const Vector3& spherevel,
const Plane& plane, float& time, Vector3& intersection,
bool statictest)
{
// Static test if requested
if (statictest && SpherePlane(sphere, plane))
{
time = 0.0f;
return true;
}

// No collision if no velocity
if (spherevel == Vector3::ZERO)
return false;

// Local variables for convenience
Vector3 normal = plane.GetNormal();
Vector3 center = sphere.GetCenter();
float radius = sphere.GetRadius();

// Distance from sphere center to plane
float distcenterplane = Distance::PointPlane(center, plane);

// Only collide with plane if approaching from front and not already intersecting
if (distcenterplane <= radius)
return false;

// Velocity vector projected onto plane normal
float projectedvel = spherevel.Dot(normal);

// Distance from sphere to plane
float distsphereplane = distcenterplane - radius;

// If the velocity vector does not reach the plane, no collision
if (-projectedvel < distsphereplane)
return false;

// The first time of intersection with the plane
time = distsphereplane / -projectedvel;

// The point on the sphere that will intersect the plane
Vector3 spherepoint = center - radius * normal;

// The intersection point
intersection = spherepoint + time * spherevel;

// Collision found
return true;
}
// --------------------------------------------------------------------------------------



There's some support stuff there, but it should be fairly self-explanatory. Sphere is just a class with a center and radius, and plane is a class with a normal and distance.

This function takes a sphere, a plane, and a sphere velocity and returns the first time of intersection and the intersection point.

Response depends on what you want to do - bounce, slide, etc. Sliding is more complicated, but bouncing can be done by reflecting the velocity vector. To reflect the velocity around the plane normal:

Vector3 newvel = vel - 2.0f * vel.Dot(normal) * normal;

Hope that helps.

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