public override bool RayTest(ref Ray ray, ref RigidTransform transform, float maximumLength, out RayHit hit)
{
//Put the ray into local space.
Quaternion conjugate;
Quaternion.Conjugate(ref transform.Orientation, out conjugate);
Ray localRay;
Vector3.Subtract(ref ray.Position, ref transform.Position, out localRay.Position);
Vector3.Transform(ref localRay.Position, ref conjugate, out localRay.Position);
Vector3.Transform(ref ray.Direction, ref conjugate, out localRay.Direction);
//Check for containment.
if (localRay.Position.Y >= -halfHeight && localRay.Position.Y <= halfHeight && localRay.Position.X * localRay.Position.X + localRay.Position.Z * localRay.Position.Z <= radius * radius)
{
//It's inside!
hit.T = 0;
hit.Location = localRay.Position;
hit.Normal = new Vector3(hit.Location.X, 0, hit.Location.Z);
float normalLengthSquared = hit.Normal.LengthSquared();
if (normalLengthSquared > 1e-9f)
Vector3.Divide(ref hit.Normal, (float)Math.Sqrt(normalLengthSquared), out hit.Normal);
else
hit.Normal = new Vector3();
//Pull the hit into world space.
Vector3.Transform(ref hit.Normal, ref transform.Orientation, out hit.Normal);
RigidTransform.Transform(ref hit.Location, ref transform, out hit.Location);
return true;
}
//Project the ray direction onto the plane where the cylinder is a circle.
//The projected ray is then tested against the circle to compute the time of impact.
//That time of impact is used to compute the 3d hit location.
Vector2 planeDirection = new Vector2(localRay.Direction.X, localRay.Direction.Z);
float planeDirectionLengthSquared = planeDirection.LengthSquared();
if (planeDirectionLengthSquared < Toolbox.Epsilon)
{
//The ray is nearly parallel with the axis.
//Skip the cylinder-sides test. We're either inside the cylinder and won't hit the sides, or we're outside
//and won't hit the sides.
if (localRay.Position.Y > halfHeight)
goto upperTest;
if (localRay.Position.Y < -halfHeight)
goto lowerTest;
hit = new RayHit();
return false;
}
Vector2 planeOrigin = new Vector2(localRay.Position.X, localRay.Position.Z);
float dot;
Vector2.Dot(ref planeDirection, ref planeOrigin, out dot);
float closestToCenterT = -dot / planeDirectionLengthSquared;
Vector2 closestPoint;
Vector2.Multiply(ref planeDirection, closestToCenterT, out closestPoint);
Vector2.Add(ref planeOrigin, ref closestPoint, out closestPoint);
//How close does the ray come to the circle?
float squaredDistance = closestPoint.LengthSquared();
if (squaredDistance > radius * radius)
{
//It's too far! The ray cannot possibly hit the capsule.
hit = new RayHit();
return false;
}
//With the squared distance, compute the distance backward along the ray from the closest point on the ray to the axis.
float backwardsDistance = radius * (float)Math.Sqrt(1 - squaredDistance / (radius * radius));
float tOffset = backwardsDistance / (float)Math.Sqrt(planeDirectionLengthSquared);
hit.T = closestToCenterT - tOffset;
//Compute the impact point on the infinite cylinder in 3d local space.
Vector3.Multiply(ref localRay.Direction, hit.T, out hit.Location);
Vector3.Add(ref hit.Location, ref localRay.Position, out hit.Location);
//Is it intersecting the cylindrical portion of the capsule?
if (hit.Location.Y <= halfHeight && hit.Location.Y >= -halfHeight && hit.T < maximumLength)
{
//Yup!
hit.Normal = new Vector3(hit.Location.X, 0, hit.Location.Z);
float normalLengthSquared = hit.Normal.LengthSquared();
if (normalLengthSquared > 1e-9f)
Vector3.Divide(ref hit.Normal, (float)Math.Sqrt(normalLengthSquared), out hit.Normal);
else
hit.Normal = new Vector3();
//Pull the hit into world space.
Vector3.Transform(ref hit.Normal, ref transform.Orientation, out hit.Normal);
RigidTransform.Transform(ref hit.Location, ref transform, out hit.Location);
return true;
}
if (hit.Location.Y < halfHeight)
goto lowerTest;
upperTest:
//Nope! It may be intersecting the ends of the cylinder though.
//We're above the cylinder, so cast a ray against the upper cap.
if (localRay.Direction.Y > -1e-9)
{
//Can't hit the upper cap if the ray isn't pointing down.
hit = new RayHit();
return false;
}
float t = (halfHeight - localRay.Position.Y) / localRay.Direction.Y;
Vector3 planeIntersection;
Vector3.Multiply(ref localRay.Direction, t, out planeIntersection);
Vector3.Add(ref localRay.Position, ref planeIntersection, out planeIntersection);
if(planeIntersection.X * planeIntersection.X + planeIntersection.Z * planeIntersection.Z < radius * radius + 1e-9 && t < maximumLength)
{
//Pull the hit into world space.
Vector3.Transform(ref Toolbox.UpVector, ref transform.Orientation, out hit.Normal);
RigidTransform.Transform(ref planeIntersection, ref transform, out hit.Location);
hit.T = t;
return true;
}
//No intersection! We can't be hitting the other sphere, so it's over!
hit = new RayHit();
return false;
lowerTest:
//Is it intersecting the bottom cap?
if (localRay.Direction.Y < 1e-9)
{
//Can't hit the bottom cap if the ray isn't pointing up.
hit = new RayHit();
return false;
}
t = (-halfHeight - localRay.Position.Y) / localRay.Direction.Y;
Vector3.Multiply(ref localRay.Direction, t, out planeIntersection);
Vector3.Add(ref localRay.Position, ref planeIntersection, out planeIntersection);
if (planeIntersection.X * planeIntersection.X + planeIntersection.Z * planeIntersection.Z < radius * radius + 1e-9 && t < maximumLength)
{
//Pull the hit into world space.
Vector3.Transform(ref Toolbox.DownVector, ref transform.Orientation, out hit.Normal);
RigidTransform.Transform(ref planeIntersection, ref transform, out hit.Location);
hit.T = t;
return true;
}
//No intersection! We can't be hitting the other sphere, so it's over!
hit = new RayHit();
return false;
}
