public static CollisionInfo SphereToPlaneCollision(CollisionHull3D a, CollisionHull3D b)
{
// Find the relative centre by transforming the center of the circle to the local space of the AABB
Vector3 relativeCentre = b.GetComponent <Particle3D>().invTransformMatrix.MultiplyPoint(a.GetPosition());
Vector3 closestPointToCircle = new Vector3(Math.Max(b.GetMinimumCorner().x, Math.Min(relativeCentre.x, b.GetMaximumCorner().x)), Math.Max(b.GetMinimumCorner().y, Math.Min(relativeCentre.y, b.GetMaximumCorner().y)), Math.Max(b.GetMinimumCorner().z, Math.Min(relativeCentre.z, b.GetMaximumCorner().z)));
// Calculate the distance between both colliders
Vector3 distance = relativeCentre - closestPointToCircle;
// Are the Radii less than or equal to the distance between both circles?
if (Vector3.Dot(distance, distance) < a.GetDimensions().x *a.GetDimensions().x)
{
// If yes, then inform the parents of the complex shape object (if applicable)
ReportCollisionToParent(a, b);
}
else
{
// If no, return nothing
return(null);
}
float penetration = a.GetDimensions().x - Mathf.Sqrt(Vector3.Dot(distance, distance));
Vector3 closestPointWorld = b.GetComponent <Particle3D>().transformMatrix.MultiplyPoint(closestPointToCircle);
// Return result
return(new CollisionInfo(a, b, penetration, (closestPointWorld - a.GetPosition()).normalized, Vector3.zero, CollisionResolution3D.CalculateSeparatingVelocity(a, b, a.GetPosition(), closestPointWorld)));
}
// This function calculate Circle to ABB collisions
public static CollisionInfo CircleToOBBCollision(CollisionHull3D a, CollisionHull3D b)
{
// Find the relative centre by transforming the center of the circle to the local space of the AABB
Vector3 relativeCentre = b.GetComponent <Particle3D>().invTransformMatrix.MultiplyPoint(a.GetPosition());
Vector3 closestPointToCircle = new Vector3(Math.Max(b.GetMinimumCorner().x, Math.Min(relativeCentre.x, b.GetMaximumCorner().x)), Math.Max(b.GetMinimumCorner().y, Math.Min(relativeCentre.y, b.GetMaximumCorner().y)), Math.Max(b.GetMinimumCorner().z, Math.Min(relativeCentre.z, b.GetMaximumCorner().z)));
Vector3 distance = relativeCentre - closestPointToCircle;
float distanceSquared = Vector3.Dot(distance, distance);
float penetration = a.GetDimensions().x - Mathf.Sqrt(distanceSquared);
// Is the penetration a positive value
if (penetration >= 0)
{
// If yes, then inform the parents of the complex shape object (if applicable)
ReportCollisionToParent(a, b);
}
else
{
// If no, return nothing
return(null);
}
// Return full details of the Collision list if the two collide
return(new CollisionInfo(a, b, penetration, (closestPointToCircle - relativeCentre).normalized, closestPointToCircle, CollisionResolution3D.CalculateSeparatingVelocity(a, b, a.GetPosition(), b.GetPosition())));
}
// This function computes circle to circle collisions
public static CollisionInfo CircleToCircleCollision(CollisionHull3D a, CollisionHull3D b)
{
// Calculate the distance between both colliders
Vector3 distance = a.GetPosition() - b.GetPosition();
float penetration = a.GetDimensions().x + b.GetDimensions().x *(a.GetDimensions().x + b.GetDimensions().x) - Vector3.Dot(distance, distance);
// Are the Radii less than or equal to the distance between both circles?
if (penetration > 0)
{
// If yes, then inform the parents of the complex shape object (if applicable)
ReportCollisionToParent(a, b);
}
else
{
// If no, return nothing
return(null);
}
// Return result
return(new CollisionInfo(a, b, penetration));
}
// This function calculates OBB to OBB colisions
public static CollisionInfo OBBToOBBCollision(CollisionHull3D a, CollisionHull3D b)
{
List <float> overlaps = new List <float>();
List <Vector3> axes = new List <Vector3>();
// Get the transform values for each axis for each shape
Vector3 x1 = a.GetComponent <Particle3D>().transformMatrix.GetColumn(0);
Vector3 y1 = a.GetComponent <Particle3D>().transformMatrix.GetColumn(1);
Vector3 z1 = a.GetComponent <Particle3D>().transformMatrix.GetColumn(2);
Vector3 x2 = b.GetComponent <Particle3D>().transformMatrix.GetColumn(0);
Vector3 y2 = b.GetComponent <Particle3D>().transformMatrix.GetColumn(1);
Vector3 z2 = b.GetComponent <Particle3D>().transformMatrix.GetColumn(2);
// Go through and check through all overlapping axes
// Face/Face Object 1
overlaps.Add(CheckOBBAxis(a, b, x1));
axes.Add(x1);
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, y1));
axes.Add(y1);
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, z1));
axes.Add(z1);
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
// Face/Face Object 2
overlaps.Add(CheckOBBAxis(a, b, x2));
axes.Add(x2);
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, y2));
axes.Add(y2);
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, z2));
axes.Add(z2);
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
// Edge/Edge
overlaps.Add(CheckOBBAxis(a, b, Vector3.Cross(x1, x2)));
axes.Add(Vector3.Cross(x1, x2));
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, Vector3.Cross(x1, y2)));
axes.Add(Vector3.Cross(x1, y2));
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, Vector3.Cross(x1, z2)));
axes.Add(Vector3.Cross(x1, z2));
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, Vector3.Cross(y1, x2)));
axes.Add(Vector3.Cross(y1, x2));
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, Vector3.Cross(y1, y2)));
axes.Add(Vector3.Cross(y1, y2));
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, Vector3.Cross(y1, z2)));
axes.Add(Vector3.Cross(y1, z2));
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, Vector3.Cross(z1, x2)));
axes.Add(Vector3.Cross(z1, x2));
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, Vector3.Cross(z1, y2)));
axes.Add(Vector3.Cross(z1, y2));
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
overlaps.Add(CheckOBBAxis(a, b, Vector3.Cross(z1, z2)));
axes.Add(Vector3.Cross(z1, z2));
if (overlaps[overlaps.Count - 1] < 0)
{
return(null);
}
float bestOverlap = Mathf.Infinity;
int bestIndex = 0;
for (int i = 0; i < overlaps.Count; i++)
{
if (overlaps[i] < bestOverlap)
{
bestOverlap = overlaps[i];
bestIndex = i;
}
}
if (bestIndex > 2)
{
Vector3 normal = axes[bestIndex];
Vector3 axis = axes[bestIndex];
if (Vector3.Dot(axis, (b.GetPosition() - a.GetPosition())) > 0)
{
axis *= -1;
}
Vector3 vertex = a.GetDimensions();
if (Vector3.Dot(a.GetComponent <Particle3D>().transformMatrix.GetColumn(0), normal) > 0)
{
vertex.x = -vertex.x;
}
if (Vector3.Dot(a.GetComponent <Particle3D>().transformMatrix.GetColumn(1), normal) > 0)
{
vertex.y = -vertex.y;
}
if (Vector3.Dot(a.GetComponent <Particle3D>().transformMatrix.GetColumn(2), normal) > 0)
{
vertex.z = -vertex.z;
}
vertex = a.GetComponent <Particle3D>().invTransformMatrix.MultiplyPoint(vertex);
// If all axis are overlaping, then we have a collision
ReportCollisionToParent(a, b);
return(new CollisionInfo(a, b, CollisionResolution.GetFinalPenetration(overlaps), normal, vertex, CollisionResolution3D.CalculateSeparatingVelocity(a, b, a.GetPosition(), b.GetPosition())));
}
else if (bestIndex > 5)
{
Vector3 normal = axes[bestIndex];
Vector3 axis = axes[bestIndex];
if (Vector3.Dot(axis, (a.GetPosition() - b.GetPosition())) > 0)
{
axis *= -1;
}
Vector3 vertex = b.GetDimensions();
if (Vector3.Dot(b.GetComponent <Particle3D>().transformMatrix.GetColumn(0), normal) > 0)
{
vertex.x = -vertex.x;
}
if (Vector3.Dot(b.GetComponent <Particle3D>().transformMatrix.GetColumn(1), normal) > 0)
{
vertex.y = -vertex.y;
}
if (Vector3.Dot(b.GetComponent <Particle3D>().transformMatrix.GetColumn(2), normal) > 0)
{
vertex.z = -vertex.z;
}
vertex = b.GetComponent <Particle3D>().invTransformMatrix.MultiplyPoint(vertex);
// If all axis are overlaping, then we have a collision
ReportCollisionToParent(a, b);
return(new CollisionInfo(a, b, CollisionResolution.GetFinalPenetration(overlaps), normal, vertex, CollisionResolution3D.CalculateSeparatingVelocity(a, b, a.GetPosition(), b.GetPosition())));
}
else
{
int index = bestIndex - 6;
int oneIndex = index / 3;
int twoIndex = index % 3;
Vector3 oneAxis = axes[oneIndex];
Vector3 twoAxis = axes[twoIndex];
Vector3 axis = axes[bestIndex].normalized;
if (Vector3.Dot(axis, b.GetPosition() - a.GetPosition()) > 0)
{
axis *= -1;
}
Vector3 pointOnOneEdge = a.GetDimensions();
Vector3 pointOnTwoEdge = b.GetDimensions();
if (oneIndex == 0)
{
pointOnOneEdge.x = 0;
}
else if (Vector2.Dot(x1, axis) > 0)
{
pointOnOneEdge.x = -pointOnOneEdge.x;
}
if (twoIndex == 3)
{
pointOnTwoEdge.x = 0;
}
else if (Vector2.Dot(x2, axis) > 0)
{
pointOnTwoEdge.x = -pointOnTwoEdge.x;
}
if (oneIndex == 1)
{
pointOnOneEdge.y = 0;
}
else if (Vector2.Dot(y1, axis) > 0)
{
pointOnOneEdge.y = -pointOnOneEdge.y;
}
if (twoIndex == 4)
{
pointOnTwoEdge.y = 0;
}
else if (Vector2.Dot(y2, axis) > 0)
{
pointOnTwoEdge.y = -pointOnTwoEdge.y;
}
if (oneIndex == 2)
{
pointOnOneEdge.z = 0;
}
else if (Vector2.Dot(z1, axis) > 0)
{
pointOnOneEdge.z = -pointOnOneEdge.z;
}
if (twoIndex == 5)
{
pointOnTwoEdge.z = 0;
}
else if (Vector2.Dot(z2, axis) > 0)
{
pointOnTwoEdge.z = -pointOnTwoEdge.z;
}
pointOnOneEdge = a.GetComponent <Particle3D>().invTransformMatrix.MultiplyPoint(pointOnOneEdge);
pointOnTwoEdge = b.GetComponent <Particle3D>().invTransformMatrix.MultiplyPoint(pointOnTwoEdge);
Vector3 contactPoint = GetCollisionPoint(pointOnOneEdge, oneAxis, a.GetDimensions().x, pointOnTwoEdge, twoAxis, b.GetDimensions().x, bestIndex > 2);
ReportCollisionToParent(a, b);
return(new CollisionInfo(a, b, CollisionResolution.GetFinalPenetration(overlaps), axis, contactPoint, CollisionResolution3D.CalculateSeparatingVelocity(a, b, a.GetPosition(), b.GetPosition())));
}
}
// This function computes AABB to AABB collisions
public static CollisionInfo AABBToAABBCollision(CollisionHull3D a, CollisionHull3D b)
{
// Get the penetration values for both axes
float penetration = 0.0f;
// Calculate half extents along x axis for each object
float a_extent = a.GetDimensions().x;
float b_extent = b.GetDimensions().x;
// Get the distance between a and b
Vector3 n = (b.GetPosition() - a.GetPosition());
n = new Vector3(Mathf.Abs(n.x), Mathf.Abs(n.y), Mathf.Abs(n.z));
// Calculate overlap on x axis
float x_overlap = a_extent + b_extent - Mathf.Abs(n.x);
// SAT test on x axis
if (x_overlap > 0)
{
// Calculate half extents along x axis for each object
a_extent = a.GetDimensions().y;
b_extent = b.GetDimensions().y;
// Calculate overlap on y axis
float y_overlap = a_extent + b_extent - Mathf.Abs(n.y);
// SAT test on y axis
if (y_overlap > 0)
{
a_extent = a.GetDimensions().z;
b_extent = b.GetDimensions().z;
float z_overlap = a_extent + b_extent - Mathf.Abs(n.z);
if (z_overlap > 0)
{
// Find out which axis is axis of least penetration
if (x_overlap > y_overlap && y_overlap < z_overlap)
{
// If it is Y, then return Y's overlap
penetration = y_overlap;
}
else if (x_overlap < y_overlap && x_overlap < z_overlap)
{
penetration = x_overlap;
}
else
{
// If it is Y, then return X's overlap
penetration = z_overlap;
}
}
}
}
// Do the two checks pass?
if (penetration > 0)
{
// If yes, then inform the parents of the complex shape object (if applicable)
ReportCollisionToParent(a, b);
}
else
{
// If no, return nothing
return(null);
}
// Return full details of the Collision list if the two collide
return(new CollisionInfo(a, b, penetration));
}
public static float transformToOBBAxis(CollisionHull3D shape, Vector3 rotationAxis)
{
return(shape.GetDimensions().x *Mathf.Abs(Vector3.Dot(shape.GetComponent <Particle3D>().transformMatrix.GetColumn(0), rotationAxis)) +
shape.GetDimensions().y *Mathf.Abs(Vector3.Dot(shape.GetComponent <Particle3D>().transformMatrix.GetColumn(1), rotationAxis)) +
shape.GetDimensions().z *Mathf.Abs(Vector3.Dot(shape.GetComponent <Particle3D>().transformMatrix.GetColumn(2), rotationAxis)));
}