public override bool ConvexCast(ConvexShape castShape, ref RigidTransform startingTransform, ref Vector3 sweep, Func<BroadPhaseEntry, bool> filter, out RayHit hit)
{
Vector3 swp = sweep;
double len = swp.Length();
swp /= len;
return ConvexCast(castShape, ref startingTransform, ref swp, len, MaterialSolidity.FULLSOLID, out hit);
}
/// <summary>
/// Computes the intersection, if any, between a ray and the objects in the character's bounding box.
/// </summary>
/// <param name="ray">Ray to test.</param>
/// <param name="length">Length of the ray to use in units of the ray's length.</param>
/// <param name="earliestHit">Earliest intersection location and information.</param>
/// <param name="hitObject">Collidable intersected by the ray, if any.</param>
/// <returns>Whether or not the ray hit anything.</returns>
public bool RayCast(Ray ray, float length, out RayHit earliestHit, out Collidable hitObject)
{
earliestHit = new RayHit();
earliestHit.T = float.MaxValue;
hitObject = null;
foreach (var collidable in characterBody.CollisionInformation.OverlappedCollidables)
{
//Check to see if the collidable is hit by the ray.
float t;
if (ray.Intersects(ref collidable.boundingBox, out t) && t < length)
{
//Is it an earlier hit than the current earliest?
RayHit hit;
if (collidable.RayCast(ray, length, SupportRayFilter, out hit) && hit.T < earliestHit.T)
{
earliestHit = hit;
hitObject = collidable;
}
}
}
if (earliestHit.T == float.MaxValue)
return false;
return true;
}
public bool ConvexCast(ConvexShape castShape, ref RigidTransform startingTransform, ref Vector3 sweepnorm, double slen, MaterialSolidity solidness, out RayHit hit)
{
RigidTransform rt;
RigidTransform.MultiplyByInverse(ref startingTransform, ref worldTransform, out rt);
Vector3 swp = Quaternion.Transform(sweepnorm, Quaternion.Inverse(worldTransform.Orientation));
RayHit rh;
bool h = ChunkShape.ConvexCast(castShape, ref rt, ref swp, slen, solidness, out rh);
RigidTransform.Transform(ref rh.Location, ref worldTransform, out hit.Location);
hit.Normal = rh.Normal;
hit.T = rh.T;
return h;
}
/// <summary> /// Tests a ray against the entry. /// </summary> /// <param name="ray">Ray to test.</param> /// <param name="maximumLength">Maximum length, in units of the ray's direction's length, to test.</param> /// <param name="rayHit">Hit location of the ray on the entry, if any.</param> /// <returns>Whether or not the ray hit the entry.</returns> public abstract bool RayCast(Ray ray, float maximumLength, out RayHit rayHit);
/// <summary>
/// Tests a ray against the entry.
/// </summary>
/// <param name="ray">Ray to test.</param>
/// <param name="maximumLength">Maximum length, in units of the ray's direction's length, to test.</param>
/// <param name="filter">Test to apply to the entry. If it returns true, the entry is processed, otherwise the entry is ignored. If a collidable hierarchy is present
/// in the entry, this filter will be passed into inner ray casts.</param>
/// <param name="rayHit">Hit location of the ray on the entry, if any.</param>
/// <returns>Whether or not the ray hit the entry.</returns>
public virtual bool RayCast(Ray ray, float maximumLength, Func<BroadPhaseEntry, bool> filter, out RayHit rayHit)
{
if (filter(this))
return RayCast(ray, maximumLength, out rayHit);
rayHit = new RayHit();
return false;
}
///<summary>
/// Casts a fat (sphere expanded) ray against the shape. If the raycast appears to be stuck in the shape, the cast will be attempted
/// with a smaller ray (scaled by the MotionSettings.CoreShapeScaling each time).
///</summary>
///<param name="ray">Ray to test against the shape.</param>
///<param name="radius">Radius of the ray.</param>
///<param name="target">Shape to test against.</param>
///<param name="shapeTransform">Transform to apply to the shape for the test.</param>
///<param name="maximumLength">Maximum length of the ray in units of the ray direction's length.</param>
///<param name="hit">Hit data of the sphere cast, if any.</param>
///<returns>Whether or not the sphere cast hit the shape.</returns>
public static bool CCDSphereCast( ref Ray ray, float radius, ConvexShape target, ref RigidTransform shapeTransform, float maximumLength,
out RayHit hit )
{
int iterations = 0;
while( true )
{
if( GJKToolbox.SphereCast( ray, radius, target, ref shapeTransform, maximumLength, out hit ) &&
hit.T > 0 )
{
//The ray cast isn't embedded in the shape, and it's less than maximum length away!
return true;
}
if( hit.T > maximumLength || hit.T < 0 )
return false; //Failure showed it was too far, or behind.
radius *= MotionSettings.CoreShapeScaling;
iterations++;
if( iterations > 3 ) //Limit could be configurable.
{
//It's iterated too much, let's just do a last ditch attempt using a raycast and hope that can help.
return GJKToolbox.RayCast( ray, target, ref shapeTransform, maximumLength, out hit ) && hit.T > 0;
}
}
}
///<summary>
/// Tests a ray against the triangle mesh.
///</summary>
///<param name="ray">Ray to test against the mesh.</param>
/// <param name="maximumLength">Maximum length of the ray in units of the ray direction's length.</param>
/// <param name="sidedness">Sidedness to apply to the mesh for the ray cast.</param>
///<param name="rayHit">Hit data for the ray, if any.</param>
///<returns>Whether or not the ray hit the mesh.</returns>
public bool RayCast(Ray ray, float maximumLength, TriangleSidedness sidedness, out RayHit rayHit)
{
var rayHits = CommonResources.GetRayHitList();
bool toReturn = RayCast(ray, maximumLength, sidedness, rayHits);
if (toReturn)
{
rayHit = rayHits[0];
for (int i = 1; i < rayHits.Count; i++)
{
RayHit hit = rayHits[i];
if (hit.T < rayHit.T)
rayHit = hit;
}
}
else
rayHit = new RayHit();
CommonResources.GiveBack(rayHits);
return toReturn;
}
private static void ScanObject(float rayIncrement, float maxLength, ref Vector3 increment1, ref Vector3 increment2, ref Ray ray, ref RayHit startHit, ref RayHit endHit, RawList<Vector3> pointContributions, out float volume)
{
Vector3 cell;
Vector3.Multiply(ref ray.Direction, rayIncrement, out cell);
Vector3.Add(ref increment1, ref cell, out cell);
Vector3.Add(ref increment2, ref cell, out cell);
float perCellVolume = cell.X * cell.Y * cell.Z;
volume = 0;
for (int i = (int)(startHit.T / rayIncrement); i <= (int)((maxLength - endHit.T) / rayIncrement); i++)
{
Vector3 position;
Vector3.Multiply(ref ray.Direction, (i + .5f) * rayIncrement, out position);
Vector3.Add(ref position, ref ray.Position, out position);
pointContributions.Add(position);
volume += perCellVolume;
}
}
///<summary>
/// Sweeps two shapes against another.
///</summary>
///<param name="shapeA">First shape being swept.</param>
///<param name="shapeB">Second shape being swept.</param>
///<param name="sweepA">Sweep vector for the first shape.</param>
///<param name="sweepB">Sweep vector for the second shape.</param>
///<param name="transformA">Transform to apply to the first shape.</param>
///<param name="transformB">Transform to apply to the second shape.</param>
///<param name="hit">Hit data of the sweep test, if any.</param>
///<returns>Whether or not the swept shapes hit each other..</returns>
public static bool ConvexCast(ConvexShape shapeA, ConvexShape shapeB, ref Vector3 sweepA, ref Vector3 sweepB, ref RigidTransform transformA, ref RigidTransform transformB,
out RayHit hit)
{
//Put the velocity into shapeA's local space.
Vector3 velocityWorld;
Vector3.Subtract(ref sweepB, ref sweepA, out velocityWorld);
Quaternion conjugateOrientationA;
Quaternion.Conjugate(ref transformA.Orientation, out conjugateOrientationA);
Vector3 rayDirection;
Quaternion.Transform(ref velocityWorld, ref conjugateOrientationA, out rayDirection);
//Transform b into a's local space.
RigidTransform localTransformB;
Quaternion.Concatenate(ref transformB.Orientation, ref conjugateOrientationA, out localTransformB.Orientation);
Vector3.Subtract(ref transformB.Position, ref transformA.Position, out localTransformB.Position);
Quaternion.Transform(ref localTransformB.Position, ref conjugateOrientationA, out localTransformB.Position);
Vector3 w, p;
hit.T = 0;
hit.Location = Vector3.Zero; //The ray starts at the origin.
hit.Normal = Toolbox.ZeroVector;
Vector3 v = hit.Location;
RaySimplex simplex = new RaySimplex();
float vw, vdir;
int count = 0;
do
{
if (++count > MaximumGJKIterations)
{
//It's taken too long to find a hit. Numerical problems are probable; quit.
hit = new RayHit();
return false;
}
MinkowskiToolbox.GetLocalMinkowskiExtremePoint(shapeA, shapeB, ref v, ref localTransformB, out p);
Vector3.Subtract(ref hit.Location, ref p, out w);
Vector3.Dot(ref v, ref w, out vw);
if (vw > 0)
{
Vector3.Dot(ref v, ref rayDirection, out vdir);
if (vdir >= 0)
{
hit = new RayHit();
return false;
}
hit.T = hit.T - vw / vdir;
if (hit.T > 1)
{
//If we've gone beyond where the ray can reach, there's obviously no hit.
hit = new RayHit();
return false;
}
//Shift the ray up.
Vector3.Multiply(ref rayDirection, hit.T, out hit.Location);
//The ray origin is the origin! Don't need to add any ray position.
hit.Normal = v;
}
RaySimplex shiftedSimplex;
simplex.AddNewSimplexPoint(ref p, ref hit.Location, out shiftedSimplex);
shiftedSimplex.GetPointClosestToOrigin(ref simplex, out v);
//Could measure the progress of the ray. If it's too little, could early out.
//Not used by default since it's biased towards precision over performance.
} while (v.LengthSquared() >= Toolbox.Epsilon * simplex.GetErrorTolerance(ref Toolbox.ZeroVector));
//This epsilon has a significant impact on performance and accuracy. Changing it to use BigEpsilon instead increases speed by around 30-40% usually, but jigging is more evident.
//Transform the hit data into world space.
Quaternion.Transform(ref hit.Normal, ref transformA.Orientation, out hit.Normal);
Vector3.Multiply(ref velocityWorld, hit.T, out hit.Location);
Vector3.Add(ref hit.Location, ref transformA.Position, out hit.Location);
return true;
}
///<summary>
/// Tests a ray against the instance.
///</summary>
///<param name="ray">Ray to test.</param>
///<param name="maximumLength">Maximum length of the ray to test; in units of the ray's direction's length.</param>
///<param name="sidedness">Sidedness to use during the ray cast. This does not have to be the same as the mesh's sidedness.</param>
///<param name="rayHit">The hit location of the ray on the mesh, if any.</param>
///<returns>Whether or not the ray hit the mesh.</returns>
public bool RayCast(Ray ray, float maximumLength, TriangleSidedness sidedness, out RayHit rayHit)
{
//Put the ray into local space.
Ray localRay;
AffineTransform inverse;
AffineTransform.Invert(ref worldTransform, out inverse);
Matrix3x3.Transform(ref ray.Direction, ref inverse.LinearTransform, out localRay.Direction);
AffineTransform.Transform(ref ray.Position, ref inverse, out localRay.Position);
if (Shape.TriangleMesh.RayCast(localRay, maximumLength, sidedness, out rayHit))
{
//Transform the hit into world space.
Vector3.Multiply(ref ray.Direction, rayHit.T, out rayHit.Location);
Vector3.Add(ref rayHit.Location, ref ray.Position, out rayHit.Location);
Matrix3x3.TransformTranspose(ref rayHit.Normal, ref inverse.LinearTransform, out rayHit.Normal);
return true;
}
rayHit = new RayHit();
return false;
}
/// <summary>
/// Gets the intersection between the box and the ray.
/// </summary>
/// <param name="ray">Ray to test against the box.</param>
/// <param name="transform">Transform of the shape.</param>
/// <param name="maximumLength">Maximum distance to travel in units of the direction vector's length.</param>
/// <param name="hit">Hit data for the raycast, if any.</param>
/// <returns>Whether or not the ray hit the target.</returns>
public override bool RayTest(ref Ray ray, ref RigidTransform transform, float maximumLength, out RayHit hit)
{
hit = new RayHit();
System.Numerics.Quaternion conjugate;
QuaternionEx.Conjugate(ref transform.Orientation, out conjugate);
System.Numerics.Vector3 localOrigin;
Vector3Ex.Subtract(ref ray.Position, ref transform.Position, out localOrigin);
QuaternionEx.Transform(ref localOrigin, ref conjugate, out localOrigin);
System.Numerics.Vector3 localDirection;
QuaternionEx.Transform(ref ray.Direction, ref conjugate, out localDirection);
System.Numerics.Vector3 normal = Toolbox.ZeroVector;
float temp, tmin = 0, tmax = maximumLength;
if (Math.Abs(localDirection.X) < Toolbox.Epsilon && (localOrigin.X < -halfWidth || localOrigin.X > halfWidth))
return false;
float inverseDirection = 1 / localDirection.X;
float t1 = (-halfWidth - localOrigin.X) * inverseDirection;
float t2 = (halfWidth - localOrigin.X) * inverseDirection;
var tempNormal = new System.Numerics.Vector3(-1, 0, 0);
if (t1 > t2)
{
temp = t1;
t1 = t2;
t2 = temp;
tempNormal *= -1;
}
temp = tmin;
tmin = Math.Max(tmin, t1);
if (temp != tmin)
normal = tempNormal;
tmax = Math.Min(tmax, t2);
if (tmin > tmax)
return false;
if (Math.Abs(localDirection.Y) < Toolbox.Epsilon && (localOrigin.Y < -halfHeight || localOrigin.Y > halfHeight))
return false;
inverseDirection = 1 / localDirection.Y;
t1 = (-halfHeight - localOrigin.Y) * inverseDirection;
t2 = (halfHeight - localOrigin.Y) * inverseDirection;
tempNormal = new System.Numerics.Vector3(0, -1, 0);
if (t1 > t2)
{
temp = t1;
t1 = t2;
t2 = temp;
tempNormal *= -1;
}
temp = tmin;
tmin = Math.Max(tmin, t1);
if (temp != tmin)
normal = tempNormal;
tmax = Math.Min(tmax, t2);
if (tmin > tmax)
return false;
if (Math.Abs(localDirection.Z) < Toolbox.Epsilon && (localOrigin.Z < -halfLength || localOrigin.Z > halfLength))
return false;
inverseDirection = 1 / localDirection.Z;
t1 = (-halfLength - localOrigin.Z) * inverseDirection;
t2 = (halfLength - localOrigin.Z) * inverseDirection;
tempNormal = new System.Numerics.Vector3(0, 0, -1);
if (t1 > t2)
{
temp = t1;
t1 = t2;
t2 = temp;
tempNormal *= -1;
}
temp = tmin;
tmin = Math.Max(tmin, t1);
if (temp != tmin)
normal = tempNormal;
tmax = Math.Min(tmax, t2);
if (tmin > tmax)
return false;
hit.T = tmin;
Vector3Ex.Multiply(ref ray.Direction, tmin, out hit.Location);
Vector3Ex.Add(ref hit.Location, ref ray.Position, out hit.Location);
QuaternionEx.Transform(ref normal, ref transform.Orientation, out normal);
hit.Normal = normal;
return true;
}
/// <summary>
/// Tests a ray against the entry.
/// </summary>
/// <param name="ray">Ray to test.</param>
/// <param name="maximumLength">Maximum length, in units of the ray's direction's length, to test.</param>
/// <param name="rayHit">Hit location of the ray on the entry, if any.</param>
/// <returns>Whether or not the ray hit the entry.</returns>
public override bool RayCast(Ray ray, float maximumLength, out RayHit rayHit)
{
//Put the ray into local space.
Ray localRay;
Matrix3x3 orientation;
Matrix3x3.CreateFromQuaternion(ref worldTransform.Orientation, out orientation);
Matrix3x3.TransformTranspose(ref ray.Direction, ref orientation, out localRay.Direction);
Vector3.Subtract(ref ray.Position, ref worldTransform.Position, out localRay.Position);
Matrix3x3.TransformTranspose(ref localRay.Position, ref orientation, out localRay.Position);
if (Shape.solidity == MobileMeshSolidity.Solid)
{
//Find all hits. Use the count to determine the ray started inside or outside.
//If it starts inside and we're in 'solid' mode, then return the ray start.
//The raycast must be of infinite length at first. This allows it to determine
//if it is inside or outside.
if (Shape.IsLocalRayOriginInMesh(ref localRay, out rayHit))
{
//It was inside!
rayHit = new RayHit() { Location = ray.Position, Normal = Vector3.Zero, T = 0 };
return true;
}
else
{
if (rayHit.T < maximumLength)
{
//Transform the hit into world space.
Vector3.Multiply(ref ray.Direction, rayHit.T, out rayHit.Location);
Vector3.Add(ref rayHit.Location, ref ray.Position, out rayHit.Location);
Matrix3x3.Transform(ref rayHit.Normal, ref orientation, out rayHit.Normal);
}
else
{
//The hit was too far away, or there was no hit (in which case T would be float.MaxValue).
return false;
}
return true;
}
}
else
{
//Just do a normal raycast since the object isn't solid.
TriangleSidedness sidedness;
switch (Shape.solidity)
{
case MobileMeshSolidity.Clockwise:
sidedness = TriangleSidedness.Clockwise;
break;
case MobileMeshSolidity.Counterclockwise:
sidedness = TriangleSidedness.Counterclockwise;
break;
default:
sidedness = TriangleSidedness.DoubleSided;
break;
}
if (Shape.TriangleMesh.RayCast(localRay, maximumLength, sidedness, out rayHit))
{
//Transform the hit into world space.
Vector3.Multiply(ref ray.Direction, rayHit.T, out rayHit.Location);
Vector3.Add(ref rayHit.Location, ref ray.Position, out rayHit.Location);
Matrix3x3.Transform(ref rayHit.Normal, ref orientation, out rayHit.Normal);
return true;
}
}
rayHit = new RayHit();
return false;
}
/// <summary>
/// Tests a ray against the entry.
/// </summary>
/// <param name="ray">Ray to test.</param>
/// <param name="maximumLength">Maximum length, in units of the ray's direction's length, to test.</param>
/// <param name="rayHit">Hit location of the ray on the entry, if any.</param>
/// <returns>Whether or not the ray hit the entry.</returns>
public override bool RayCast(Ray ray, float maximumLength, out RayHit rayHit)
{
return RayCast(ray, maximumLength, sidedness, out rayHit);
}
/// <summary>
/// Casts a convex shape against the collidable.
/// </summary>
/// <param name="castShape">Shape to cast.</param>
/// <param name="startingTransform">Initial transform of the shape.</param>
/// <param name="sweep">Sweep to apply to the shape.</param>
/// <param name="hit">Hit data, if any.</param>
/// <returns>Whether or not the cast hit anything.</returns>
public override bool ConvexCast(ConvexShape castShape, ref RigidTransform startingTransform, ref Vector3 sweep, out RayHit hit)
{
if (Shape.solidity == MobileMeshSolidity.Solid)
{
//If the convex cast is inside the mesh and the mesh is solid, it should return t = 0.
var ray = new Ray() { Position = startingTransform.Position, Direction = Toolbox.UpVector };
if (Shape.IsLocalRayOriginInMesh(ref ray, out hit))
{
hit = new RayHit() { Location = startingTransform.Position, Normal = new Vector3(), T = 0 };
return true;
}
}
hit = new RayHit();
BoundingBox boundingBox;
var transform = new AffineTransform {Translation = worldTransform.Position};
Matrix3x3.CreateFromQuaternion(ref worldTransform.Orientation, out transform.LinearTransform);
castShape.GetSweptLocalBoundingBox(ref startingTransform, ref transform, ref sweep, out boundingBox);
var tri = PhysicsResources.GetTriangle();
var hitElements = CommonResources.GetIntList();
if (this.Shape.TriangleMesh.Tree.GetOverlaps(boundingBox, hitElements))
{
hit.T = float.MaxValue;
for (int i = 0; i < hitElements.Count; i++)
{
Shape.TriangleMesh.Data.GetTriangle(hitElements[i], out tri.vA, out tri.vB, out tri.vC);
AffineTransform.Transform(ref tri.vA, ref transform, out tri.vA);
AffineTransform.Transform(ref tri.vB, ref transform, out tri.vB);
AffineTransform.Transform(ref tri.vC, ref transform, out tri.vC);
Vector3 center;
Vector3.Add(ref tri.vA, ref tri.vB, out center);
Vector3.Add(ref center, ref tri.vC, out center);
Vector3.Multiply(ref center, 1f / 3f, out center);
Vector3.Subtract(ref tri.vA, ref center, out tri.vA);
Vector3.Subtract(ref tri.vB, ref center, out tri.vB);
Vector3.Subtract(ref tri.vC, ref center, out tri.vC);
tri.maximumRadius = tri.vA.LengthSquared();
float radius = tri.vB.LengthSquared();
if (tri.maximumRadius < radius)
tri.maximumRadius = radius;
radius = tri.vC.LengthSquared();
if (tri.maximumRadius < radius)
tri.maximumRadius = radius;
tri.maximumRadius = (float)Math.Sqrt(tri.maximumRadius);
tri.collisionMargin = 0;
var triangleTransform = new RigidTransform {Orientation = Quaternion.Identity, Position = center};
RayHit tempHit;
if (MPRToolbox.Sweep(castShape, tri, ref sweep, ref Toolbox.ZeroVector, ref startingTransform, ref triangleTransform, out tempHit) && tempHit.T < hit.T)
{
hit = tempHit;
}
}
tri.maximumRadius = 0;
PhysicsResources.GiveBack(tri);
CommonResources.GiveBack(hitElements);
return hit.T != float.MaxValue;
}
PhysicsResources.GiveBack(tri);
CommonResources.GiveBack(hitElements);
return false;
}
///<summary>
/// Tests a ray against the surface of the mesh. This does not take into account solidity.
///</summary>
///<param name="ray">Ray to test.</param>
///<param name="maximumLength">Maximum length of the ray to test; in units of the ray's direction's length.</param>
///<param name="sidedness">Sidedness to use during the ray cast. This does not have to be the same as the mesh's sidedness.</param>
///<param name="rayHit">The hit location of the ray on the mesh, if any.</param>
///<returns>Whether or not the ray hit the mesh.</returns>
public bool RayCast(Ray ray, float maximumLength, TriangleSidedness sidedness, out RayHit rayHit)
{
//Put the ray into local space.
Ray localRay;
Matrix3x3 orientation;
Matrix3x3.CreateFromQuaternion(ref worldTransform.Orientation, out orientation);
Matrix3x3.TransformTranspose(ref ray.Direction, ref orientation, out localRay.Direction);
Vector3.Subtract(ref ray.Position, ref worldTransform.Position, out localRay.Position);
Matrix3x3.TransformTranspose(ref localRay.Position, ref orientation, out localRay.Position);
if (Shape.TriangleMesh.RayCast(localRay, maximumLength, sidedness, out rayHit))
{
//Transform the hit into world space.
Vector3.Multiply(ref ray.Direction, rayHit.T, out rayHit.Location);
Vector3.Add(ref rayHit.Location, ref ray.Position, out rayHit.Location);
Matrix3x3.Transform(ref rayHit.Normal, ref orientation, out rayHit.Normal);
return true;
}
rayHit = new RayHit();
return false;
}
/// <summary>
/// Gets the intersection between the convex shape and the ray.
/// </summary>
/// <param name="ray">Ray to test.</param>
/// <param name="transform">Transform of the convex shape.</param>
/// <param name="maximumLength">Maximum distance to travel in units of the ray direction's length.</param>
/// <param name="hit">Ray hit data, if any.</param>
/// <returns>Whether or not the ray hit the target.</returns>
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);
Quaternion.Transform(ref localRay.Position, ref conjugate, out localRay.Position);
Quaternion.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.
Quaternion.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.
Quaternion.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.
Quaternion.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.
Quaternion.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;
}
///<summary>
/// Tests a ray against the terrain shape.
///</summary>
///<param name="ray">Ray to test against the shape.</param>
///<param name="maximumLength">Maximum length of the ray in units of the ray direction's length.</param>
///<param name="transform">Transform to apply to the terrain shape during the test.</param>
///<param name="hit">Hit data of the ray cast, if any.</param>
///<returns>Whether or not the ray hit the transformed terrain shape.</returns>
public bool RayCast(ref Ray ray, float maximumLength, ref AffineTransform transform, out RayHit hit)
{
return RayCast(ref ray, maximumLength, ref transform, TriangleSidedness.Counterclockwise, out hit);
}
public override bool RayCast(Ray ray, float maximumLength, out RayHit rayHit)
{
return triangleMesh.RayCast(ray, maximumLength, TriangleSidedness.DoubleSided, out rayHit);
}
///<summary>
/// Tests a ray against the terrain shape.
///</summary>
///<param name="ray">Ray to test against the shape.</param>
///<param name="maximumLength">Maximum length of the ray in units of the ray direction's length.</param>
///<param name="transform">Transform to apply to the terrain shape during the test.</param>
///<param name="sidedness">Sidedness of the triangles to use when raycasting.</param>
///<param name="hit">Hit data of the ray cast, if any.</param>
///<returns>Whether or not the ray hit the transformed terrain shape.</returns>
public bool RayCast(ref Ray ray, float maximumLength, ref AffineTransform transform, TriangleSidedness sidedness, out RayHit hit)
{
hit = new RayHit();
//Put the ray into local space.
Ray localRay;
AffineTransform inverse;
AffineTransform.Invert(ref transform, out inverse);
Matrix3x3.Transform(ref ray.Direction, ref inverse.LinearTransform, out localRay.Direction);
AffineTransform.Transform(ref ray.Position, ref inverse, out localRay.Position);
//Use rasterizey traversal.
//The origin is at 0,0,0 and the map goes +X, +Y, +Z.
//if it's before the origin and facing away, or outside the max and facing out, early out.
float maxX = heights.GetLength(0) - 1;
float maxZ = heights.GetLength(1) - 1;
Vector3 progressingOrigin = localRay.Position;
float distance = 0;
//Check the outside cases first.
if (progressingOrigin.X < 0)
{
if (localRay.Direction.X > 0)
{
//Off the left side.
float timeToMinX = -progressingOrigin.X / localRay.Direction.X;
distance += timeToMinX;
Vector3 increment;
Vector3.Multiply(ref localRay.Direction, timeToMinX, out increment);
Vector3.Add(ref increment, ref progressingOrigin, out progressingOrigin);
}
else
return false; //Outside and pointing away from the terrain.
}
else if (progressingOrigin.X > maxX)
{
if (localRay.Direction.X < 0)
{
//Off the left side.
float timeToMinX = -(progressingOrigin.X - maxX) / localRay.Direction.X;
distance += timeToMinX;
Vector3 increment;
Vector3.Multiply(ref localRay.Direction, timeToMinX, out increment);
Vector3.Add(ref increment, ref progressingOrigin, out progressingOrigin);
}
else
return false; //Outside and pointing away from the terrain.
}
if (progressingOrigin.Z < 0)
{
if (localRay.Direction.Z > 0)
{
float timeToMinZ = -progressingOrigin.Z / localRay.Direction.Z;
distance += timeToMinZ;
Vector3 increment;
Vector3.Multiply(ref localRay.Direction, timeToMinZ, out increment);
Vector3.Add(ref increment, ref progressingOrigin, out progressingOrigin);
}
else
return false;
}
else if (progressingOrigin.Z > maxZ)
{
if (localRay.Direction.Z < 0)
{
float timeToMinZ = -(progressingOrigin.Z - maxZ) / localRay.Direction.Z;
distance += timeToMinZ;
Vector3 increment;
Vector3.Multiply(ref localRay.Direction, timeToMinZ, out increment);
Vector3.Add(ref increment, ref progressingOrigin, out progressingOrigin);
}
else
return false;
}
if (distance > maximumLength)
return false;
//By now, we should be entering the main body of the terrain.
int xCell = (int)progressingOrigin.X;
int zCell = (int)progressingOrigin.Z;
//If it's hitting the border and going in, then correct the index
//so that it will initially target a valid quad.
//Without this, a quad beyond the border would be tried and failed.
if (xCell == heights.GetLength(0) - 1 && localRay.Direction.X < 0)
xCell = heights.GetLength(0) - 2;
if (zCell == heights.GetLength(1) - 1 && localRay.Direction.Z < 0)
zCell = heights.GetLength(1) - 2;
while (true)
{
//Check for a miss.
if (xCell < 0 ||
zCell < 0 ||
xCell >= heights.GetLength(0) - 1 ||
zCell >= heights.GetLength(1) - 1)
return false;
//Test the triangles of this cell.
Vector3 v1, v2, v3, v4;
// v3 v4
// v1 v2
GetLocalPosition(xCell, zCell, out v1);
GetLocalPosition(xCell + 1, zCell, out v2);
GetLocalPosition(xCell, zCell + 1, out v3);
GetLocalPosition(xCell + 1, zCell + 1, out v4);
RayHit hit1, hit2;
bool didHit1;
bool didHit2;
//Don't bother doing ray intersection tests if the ray can't intersect it.
float highest = v1.Y;
float lowest = v1.Y;
if (v2.Y > highest)
highest = v2.Y;
else if (v2.Y < lowest)
lowest = v2.Y;
if (v3.Y > highest)
highest = v3.Y;
else if (v3.Y < lowest)
lowest = v3.Y;
if (v4.Y > highest)
highest = v4.Y;
else if (v4.Y < lowest)
lowest = v4.Y;
if (!(progressingOrigin.Y > highest && localRay.Direction.Y > 0 ||
progressingOrigin.Y < lowest && localRay.Direction.Y < 0))
{
if (quadTriangleOrganization == QuadTriangleOrganization.BottomLeftUpperRight)
{
//Always perform the raycast as if Y+ in local space is the way the triangles are facing.
didHit1 = Toolbox.FindRayTriangleIntersection(ref localRay, maximumLength, sidedness, ref v1, ref v2, ref v3, out hit1);
didHit2 = Toolbox.FindRayTriangleIntersection(ref localRay, maximumLength, sidedness, ref v2, ref v4, ref v3, out hit2);
}
else //if (quadTriangleOrganization == CollisionShapes.QuadTriangleOrganization.BottomRightUpperLeft)
{
didHit1 = Toolbox.FindRayTriangleIntersection(ref localRay, maximumLength, sidedness, ref v1, ref v2, ref v4, out hit1);
didHit2 = Toolbox.FindRayTriangleIntersection(ref localRay, maximumLength, sidedness, ref v1, ref v4, ref v3, out hit2);
}
if (didHit1 && didHit2)
{
if (hit1.T < hit2.T)
{
Vector3.Multiply(ref ray.Direction, hit1.T, out hit.Location);
Vector3.Add(ref hit.Location, ref ray.Position, out hit.Location);
Matrix3x3.TransformTranspose(ref hit1.Normal, ref inverse.LinearTransform, out hit.Normal);
hit.T = hit1.T;
return true;
}
Vector3.Multiply(ref ray.Direction, hit2.T, out hit.Location);
Vector3.Add(ref hit.Location, ref ray.Position, out hit.Location);
Matrix3x3.TransformTranspose(ref hit2.Normal, ref inverse.LinearTransform, out hit.Normal);
hit.T = hit2.T;
return true;
}
else if (didHit1)
{
Vector3.Multiply(ref ray.Direction, hit1.T, out hit.Location);
Vector3.Add(ref hit.Location, ref ray.Position, out hit.Location);
Matrix3x3.TransformTranspose(ref hit1.Normal, ref inverse.LinearTransform, out hit.Normal);
hit.T = hit1.T;
return true;
}
else if (didHit2)
{
Vector3.Multiply(ref ray.Direction, hit2.T, out hit.Location);
Vector3.Add(ref hit.Location, ref ray.Position, out hit.Location);
Matrix3x3.TransformTranspose(ref hit2.Normal, ref inverse.LinearTransform, out hit.Normal);
hit.T = hit2.T;
return true;
}
}
//Move to the next cell.
float timeToX;
if (localRay.Direction.X < 0)
timeToX = -(progressingOrigin.X - xCell) / localRay.Direction.X;
else if (ray.Direction.X > 0)
timeToX = (xCell + 1 - progressingOrigin.X) / localRay.Direction.X;
else
timeToX = float.MaxValue;
float timeToZ;
if (localRay.Direction.Z < 0)
timeToZ = -(progressingOrigin.Z - zCell) / localRay.Direction.Z;
else if (localRay.Direction.Z > 0)
timeToZ = (zCell + 1 - progressingOrigin.Z) / localRay.Direction.Z;
else
timeToZ = float.MaxValue;
//Move to the next cell.
if (timeToX < timeToZ)
{
if (localRay.Direction.X < 0)
xCell--;
else
xCell++;
distance += timeToX;
if (distance > maximumLength)
return false;
Vector3 increment;
Vector3.Multiply(ref localRay.Direction, timeToX, out increment);
Vector3.Add(ref increment, ref progressingOrigin, out progressingOrigin);
}
else
{
if (localRay.Direction.Z < 0)
zCell--;
else
zCell++;
distance += timeToZ;
if (distance > maximumLength)
return false;
Vector3 increment;
Vector3.Multiply(ref localRay.Direction, timeToZ, out increment);
Vector3.Add(ref increment, ref progressingOrigin, out progressingOrigin);
}
}
}
//TODO: Consider changing the termination epsilons on these casts. Epsilon * Modifier is okay, but there might be better options.
///<summary>
/// Tests a ray against a convex shape.
///</summary>
///<param name="ray">Ray to test against the shape.</param>
///<param name="shape">Shape to test.</param>
///<param name="shapeTransform">Transform to apply to the shape for the test.</param>
///<param name="maximumLength">Maximum length of the ray in units of the ray direction's length.</param>
///<param name="hit">Hit data of the ray cast, if any.</param>
///<returns>Whether or not the ray hit the shape.</returns>
public static bool RayCast(Ray ray, ConvexShape shape, ref RigidTransform shapeTransform, float maximumLength,
out RayHit hit)
{
//Transform the ray into the object's local space.
Vector3.Subtract(ref ray.Position, ref shapeTransform.Position, out ray.Position);
Quaternion conjugate;
Quaternion.Conjugate(ref shapeTransform.Orientation, out conjugate);
Quaternion.Transform(ref ray.Position, ref conjugate, out ray.Position);
Quaternion.Transform(ref ray.Direction, ref conjugate, out ray.Direction);
Vector3 extremePointToRayOrigin, extremePoint;
hit.T = 0;
hit.Location = ray.Position;
hit.Normal = Toolbox.ZeroVector;
Vector3 closestOffset = hit.Location;
RaySimplex simplex = new RaySimplex();
float vw, closestPointDotDirection;
int count = 0;
//This epsilon has a significant impact on performance and accuracy. Changing it to use BigEpsilon instead increases speed by around 30-40% usually, but jigging is more evident.
while (closestOffset.LengthSquared() >= Toolbox.Epsilon * simplex.GetErrorTolerance(ref ray.Position))
{
if (++count > MaximumGJKIterations)
{
//It's taken too long to find a hit. Numerical problems are probable; quit.
hit = new RayHit();
return false;
}
shape.GetLocalExtremePoint(closestOffset, out extremePoint);
Vector3.Subtract(ref hit.Location, ref extremePoint, out extremePointToRayOrigin);
Vector3.Dot(ref closestOffset, ref extremePointToRayOrigin, out vw);
//If the closest offset and the extreme point->ray origin direction point the same way,
//then we might be able to conservatively advance the point towards the surface.
if (vw > 0)
{
Vector3.Dot(ref closestOffset, ref ray.Direction, out closestPointDotDirection);
if (closestPointDotDirection >= 0)
{
hit = new RayHit();
return false;
}
hit.T = hit.T - vw / closestPointDotDirection;
if (hit.T > maximumLength)
{
//If we've gone beyond where the ray can reach, there's obviously no hit.
hit = new RayHit();
return false;
}
//Shift the ray up.
Vector3.Multiply(ref ray.Direction, hit.T, out hit.Location);
Vector3.Add(ref hit.Location, ref ray.Position, out hit.Location);
hit.Normal = closestOffset;
}
RaySimplex shiftedSimplex;
simplex.AddNewSimplexPoint(ref extremePoint, ref hit.Location, out shiftedSimplex);
//Compute the offset from the simplex surface to the origin.
shiftedSimplex.GetPointClosestToOrigin(ref simplex, out closestOffset);
}
//Transform the hit data into world space.
Quaternion.Transform(ref hit.Normal, ref shapeTransform.Orientation, out hit.Normal);
Quaternion.Transform(ref hit.Location, ref shapeTransform.Orientation, out hit.Location);
Vector3.Add(ref hit.Location, ref shapeTransform.Position, out hit.Location);
return true;
}
///<summary>
/// Tests a ray against a sphere.
///</summary>
///<param name="ray">Ray to test.</param>
///<param name="spherePosition">Position of the sphere.</param>
///<param name="radius">Radius of the sphere.</param>
///<param name="maximumLength">Maximum length of the ray in units of the ray direction's length.</param>
///<param name="hit">Hit data of the ray, if any.</param>
///<returns>Whether or not the ray hits the sphere.</returns>
public static bool RayCastSphere(ref Ray ray, ref Vector3 spherePosition, float radius, float maximumLength, out RayHit hit)
{
Vector3 normalizedDirection;
float length = ray.Direction.Length();
Vector3.Divide(ref ray.Direction, length, out normalizedDirection);
maximumLength *= length;
hit = new RayHit();
Vector3 m;
Vector3.Subtract(ref ray.Position, ref spherePosition, out m);
float b = Vector3.Dot(m, normalizedDirection);
float c = m.LengthSquared() - radius * radius;
if (c > 0 && b > 0)
return false;
float discriminant = b * b - c;
if (discriminant < 0)
return false;
hit.T = -b - (float)Math.Sqrt(discriminant);
if (hit.T < 0)
hit.T = 0;
if (hit.T > maximumLength)
return false;
hit.T /= length;
Vector3.Multiply(ref normalizedDirection, hit.T, out hit.Location);
Vector3.Add(ref hit.Location, ref ray.Position, out hit.Location);
Vector3.Subtract(ref hit.Location, ref spherePosition, out hit.Normal);
hit.Normal.Normalize();
return true;
}
///<summary>
/// Tests a ray against the triangle mesh.
///</summary>
///<param name="ray">Ray to test against the mesh.</param>
/// <param name="sidedness">Sidedness to apply to the mesh for the ray cast.</param>
///<param name="rayHit">Hit data for the ray, if any.</param>
///<returns>Whether or not the ray hit the mesh.</returns>
public bool RayCast(Ray ray, TriangleSidedness sidedness, out RayHit rayHit)
{
return RayCast(ray, float.MaxValue, sidedness, out rayHit);
}
public override bool ConvexCast(ConvexShape castShape, ref RigidTransform startingTransform, ref Vector3 sweep, out RayHit hit)
{
hit = new RayHit();
BoundingBox boundingBox;
castShape.GetSweptBoundingBox(ref startingTransform, ref sweep, out boundingBox);
var tri = PhysicsResources.GetTriangle();
var hitElements = CommonResources.GetIntList();
if (triangleMesh.Tree.GetOverlaps(boundingBox, hitElements))
{
hit.T = float.MaxValue;
for (int i = 0; i < hitElements.Count; i++)
{
triangleMesh.Data.GetTriangle(hitElements[i], out tri.vA, out tri.vB, out tri.vC);
Vector3 center;
Vector3.Add(ref tri.vA, ref tri.vB, out center);
Vector3.Add(ref center, ref tri.vC, out center);
Vector3.Multiply(ref center, 1f / 3f, out center);
Vector3.Subtract(ref tri.vA, ref center, out tri.vA);
Vector3.Subtract(ref tri.vB, ref center, out tri.vB);
Vector3.Subtract(ref tri.vC, ref center, out tri.vC);
tri.maximumRadius = tri.vA.LengthSquared();
float radius = tri.vB.LengthSquared();
if (tri.maximumRadius < radius)
tri.maximumRadius = radius;
radius = tri.vC.LengthSquared();
if (tri.maximumRadius < radius)
tri.maximumRadius = radius;
tri.maximumRadius = (float)Math.Sqrt(tri.maximumRadius);
tri.collisionMargin = 0;
var triangleTransform = new RigidTransform { Orientation = Quaternion.Identity, Position = center };
RayHit tempHit;
if (MPRToolbox.Sweep(castShape, tri, ref sweep, ref Toolbox.ZeroVector, ref startingTransform, ref triangleTransform, out tempHit) && tempHit.T < hit.T)
{
hit = tempHit;
}
}
tri.maximumRadius = 0;
PhysicsResources.GiveBack(tri);
CommonResources.GiveBack(hitElements);
return hit.T != float.MaxValue;
}
PhysicsResources.GiveBack(tri);
CommonResources.GiveBack(hitElements);
return false;
}
/// <summary>
/// Determines the intersection between a ray and a triangle.
/// </summary>
/// <param name="ray">Ray to test.</param>
/// <param name="maximumLength">Maximum length to travel in units of the direction's length.</param>
/// <param name="sidedness">Sidedness of the triangle to test.</param>
/// <param name="a">First vertex of the triangle.</param>
/// <param name="b">Second vertex of the triangle.</param>
/// <param name="c">Third vertex of the triangle.</param>
/// <param name="hit">Hit data of the ray, if any</param>
/// <returns>Whether or not the ray and triangle intersect.</returns>
public static bool FindRayTriangleIntersection(ref Ray ray, float maximumLength, TriangleSidedness sidedness, ref Vector3 a, ref Vector3 b, ref Vector3 c, out RayHit hit)
{
hit = new RayHit();
Vector3 ab, ac;
Vector3.Subtract(ref b, ref a, out ab);
Vector3.Subtract(ref c, ref a, out ac);
Vector3.Cross(ref ab, ref ac, out hit.Normal);
if (hit.Normal.LengthSquared() < Epsilon)
return false; //Degenerate triangle!
float d;
Vector3.Dot(ref ray.Direction, ref hit.Normal, out d);
d = -d;
switch (sidedness)
{
case TriangleSidedness.DoubleSided:
if (d <= 0) //Pointing the wrong way. Flip the normal.
{
Vector3.Negate(ref hit.Normal, out hit.Normal);
d = -d;
}
break;
case TriangleSidedness.Clockwise:
if (d <= 0) //Pointing the wrong way. Can't hit.
return false;
break;
case TriangleSidedness.Counterclockwise:
if (d >= 0) //Pointing the wrong way. Can't hit.
return false;
Vector3.Negate(ref hit.Normal, out hit.Normal);
d = -d;
break;
}
Vector3 ap;
Vector3.Subtract(ref ray.Position, ref a, out ap);
Vector3.Dot(ref ap, ref hit.Normal, out hit.T);
hit.T /= d;
if (hit.T < 0 || hit.T > maximumLength)
return false;//Hit is behind origin, or too far away.
Vector3.Multiply(ref ray.Direction, hit.T, out hit.Location);
Vector3.Add(ref ray.Position, ref hit.Location, out hit.Location);
// Compute barycentric coordinates
Vector3.Subtract(ref hit.Location, ref a, out ap);
float ABdotAB, ABdotAC, ABdotAP;
float ACdotAC, ACdotAP;
Vector3.Dot(ref ab, ref ab, out ABdotAB);
Vector3.Dot(ref ab, ref ac, out ABdotAC);
Vector3.Dot(ref ab, ref ap, out ABdotAP);
Vector3.Dot(ref ac, ref ac, out ACdotAC);
Vector3.Dot(ref ac, ref ap, out ACdotAP);
float denom = 1 / (ABdotAB * ACdotAC - ABdotAC * ABdotAC);
float u = (ACdotAC * ABdotAP - ABdotAC * ACdotAP) * denom;
float v = (ABdotAB * ACdotAP - ABdotAC * ABdotAP) * denom;
return (u >= -Toolbox.BigEpsilon) && (v >= -Toolbox.BigEpsilon) && (u + v <= 1 + Toolbox.BigEpsilon);
}
///<summary>
/// Sweeps a shape against another shape using a given sweep vector.
///</summary>
///<param name="sweptShape">Shape to sweep.</param>
///<param name="target">Shape being swept against.</param>
///<param name="sweep">Sweep vector for the sweptShape.</param>
///<param name="startingSweptTransform">Starting transform of the sweptShape.</param>
///<param name="targetTransform">Transform to apply to the target shape.</param>
///<param name="hit">Hit data of the sweep test, if any.</param>
///<returns>Whether or not the swept shape hit the other shape.</returns>
public static bool ConvexCast(ConvexShape sweptShape, ConvexShape target, ref Vector3 sweep, ref RigidTransform startingSweptTransform, ref RigidTransform targetTransform,
out RayHit hit)
{
return ConvexCast(sweptShape, target, ref sweep, ref Toolbox.ZeroVector, ref startingSweptTransform, ref targetTransform, out hit);
}
/// <summary>
/// Determines the intersection between a ray and a triangle.
/// </summary>
/// <param name="ray">Ray to test.</param>
/// <param name="maximumLength">Maximum length to travel in units of the direction's length.</param>
/// <param name="a">First vertex of the triangle.</param>
/// <param name="b">Second vertex of the triangle.</param>
/// <param name="c">Third vertex of the triangle.</param>
/// <param name="hitClockwise">True if the the triangle was hit on the clockwise face, false otherwise.</param>
/// <param name="hit">Hit data of the ray, if any</param>
/// <returns>Whether or not the ray and triangle intersect.</returns>
public static bool FindRayTriangleIntersection(ref Ray ray, float maximumLength, ref Vector3 a, ref Vector3 b, ref Vector3 c, out bool hitClockwise, out RayHit hit)
{
hitClockwise = false;
hit = new RayHit();
Vector3 ab, ac;
Vector3.Subtract(ref b, ref a, out ab);
Vector3.Subtract(ref c, ref a, out ac);
Vector3.Cross(ref ab, ref ac, out hit.Normal);
if (hit.Normal.LengthSquared() < Epsilon)
return false; //Degenerate triangle!
float d;
Vector3.Dot(ref ray.Direction, ref hit.Normal, out d);
d = -d;
hitClockwise = d >= 0;
Vector3 ap;
Vector3.Subtract(ref ray.Position, ref a, out ap);
Vector3.Dot(ref ap, ref hit.Normal, out hit.T);
hit.T /= d;
if (hit.T < 0 || hit.T > maximumLength)
return false;//Hit is behind origin, or too far away.
Vector3.Multiply(ref ray.Direction, hit.T, out hit.Location);
Vector3.Add(ref ray.Position, ref hit.Location, out hit.Location);
// Compute barycentric coordinates
Vector3.Subtract(ref hit.Location, ref a, out ap);
float ABdotAB, ABdotAC, ABdotAP;
float ACdotAC, ACdotAP;
Vector3.Dot(ref ab, ref ab, out ABdotAB);
Vector3.Dot(ref ab, ref ac, out ABdotAC);
Vector3.Dot(ref ab, ref ap, out ABdotAP);
Vector3.Dot(ref ac, ref ac, out ACdotAC);
Vector3.Dot(ref ac, ref ap, out ACdotAP);
float denom = 1 / (ABdotAB * ACdotAC - ABdotAC * ABdotAC);
float u = (ACdotAC * ABdotAP - ABdotAC * ACdotAP) * denom;
float v = (ABdotAB * ACdotAP - ABdotAC * ABdotAP) * denom;
return (u >= -Toolbox.BigEpsilon) && (v >= -Toolbox.BigEpsilon) && (u + v <= 1 + Toolbox.BigEpsilon);
}
///<summary>
/// Casts a fat (sphere expanded) ray against the shape.
///</summary>
///<param name="ray">Ray to test against the shape.</param>
///<param name="radius">Radius of the ray.</param>
///<param name="shape">Shape to test against.</param>
///<param name="shapeTransform">Transform to apply to the shape for the test.</param>
///<param name="maximumLength">Maximum length of the ray in units of the ray direction's length.</param>
///<param name="hit">Hit data of the sphere cast, if any.</param>
///<returns>Whether or not the sphere cast hit the shape.</returns>
public static bool SphereCast(Ray ray, float radius, ConvexShape shape, ref RigidTransform shapeTransform, float maximumLength,
out RayHit hit)
{
//Transform the ray into the object's local space.
Vector3.Subtract(ref ray.Position, ref shapeTransform.Position, out ray.Position);
Quaternion conjugate;
Quaternion.Conjugate(ref shapeTransform.Orientation, out conjugate);
Quaternion.Transform(ref ray.Position, ref conjugate, out ray.Position);
Quaternion.Transform(ref ray.Direction, ref conjugate, out ray.Direction);
Vector3 w, p;
hit.T = 0;
hit.Location = ray.Position;
hit.Normal = Toolbox.ZeroVector;
Vector3 v = hit.Location;
RaySimplex simplex = new RaySimplex();
float vw, vdir;
int count = 0;
//This epsilon has a significant impact on performance and accuracy. Changing it to use BigEpsilon instead increases speed by around 30-40% usually, but jigging is more evident.
while (v.LengthSquared() >= Toolbox.Epsilon * simplex.GetErrorTolerance(ref ray.Position))
{
if (++count > MaximumGJKIterations)
{
//It's taken too long to find a hit. Numerical problems are probable; quit.
hit = new RayHit();
return false;
}
shape.GetLocalExtremePointWithoutMargin(ref v, out p);
Vector3 contribution;
MinkowskiToolbox.ExpandMinkowskiSum(shape.collisionMargin, radius, ref v, out contribution);
Vector3.Add(ref p, ref contribution, out p);
Vector3.Subtract(ref hit.Location, ref p, out w);
Vector3.Dot(ref v, ref w, out vw);
if (vw > 0)
{
Vector3.Dot(ref v, ref ray.Direction, out vdir);
hit.T = hit.T - vw / vdir;
if (vdir >= 0)
{
//We would have to back up!
return false;
}
if (hit.T > maximumLength)
{
//If we've gone beyond where the ray can reach, there's obviously no hit.
return false;
}
//Shift the ray up.
Vector3.Multiply(ref ray.Direction, hit.T, out hit.Location);
Vector3.Add(ref hit.Location, ref ray.Position, out hit.Location);
hit.Normal = v;
}
RaySimplex shiftedSimplex;
simplex.AddNewSimplexPoint(ref p, ref hit.Location, out shiftedSimplex);
shiftedSimplex.GetPointClosestToOrigin(ref simplex, out v);
}
//Transform the hit data into world space.
Quaternion.Transform(ref hit.Normal, ref shapeTransform.Orientation, out hit.Normal);
Quaternion.Transform(ref hit.Location, ref shapeTransform.Orientation, out hit.Location);
Vector3.Add(ref hit.Location, ref shapeTransform.Position, out hit.Location);
return true;
}
/// <summary> /// Sweeps a convex shape against the entry. /// </summary> /// <param name="castShape">Swept shape.</param> /// <param name="startingTransform">Beginning location and orientation of the cast shape.</param> /// <param name="sweep">Sweep motion to apply to the cast shape.</param> /// <param name="hit">Hit data of the cast on the entry, if any.</param> /// <returns>Whether or not the cast hit the entry.</returns> public abstract bool ConvexCast(ConvexShape castShape, ref RigidTransform startingTransform, ref Vector3 sweep, out RayHit hit);
/// <summary>
/// Gets the intersection between the sphere and the ray.
/// </summary>
/// <param name="ray">Ray to test against the sphere.</param>
/// <param name="transform">Transform applied to the convex for the test.</param>
/// <param name="maximumLength">Maximum distance to travel in units of the ray direction's length.</param>
/// <param name="hit">Ray hit data, if any.</param>
/// <returns>Whether or not the ray hit the target.</returns>
public override bool RayTest(ref Ray ray, ref RigidTransform transform, float maximumLength, out RayHit hit)
{
return Toolbox.RayCastSphere(ref ray, ref transform.Position, collisionMargin, maximumLength, out hit);
}
/// <summary>
/// Sweeps a convex shape against the entry.
/// </summary>
/// <param name="castShape">Swept shape.</param>
/// <param name="startingTransform">Beginning location and orientation of the cast shape.</param>
/// <param name="sweep">Sweep motion to apply to the cast shape.</param>
/// <param name="filter">Test to apply to the entry. If it returns true, the entry is processed, otherwise the entry is ignored. If a collidable hierarchy is present
/// in the entry, this filter will be passed into inner ray casts.</param>
/// <param name="hit">Hit data of the cast on the entry, if any.</param>
/// <returns>Whether or not the cast hit the entry.</returns>
public virtual bool ConvexCast(ConvexShape castShape, ref RigidTransform startingTransform, ref Vector3 sweep, Func<BroadPhaseEntry, bool> filter, out RayHit hit)
{
if (filter(this))
return ConvexCast(castShape, ref startingTransform, ref sweep, out hit);
hit = new RayHit();
return false;
}