/// <summary>
/// Determine whether two spheres intersect.
/// </summary>
/// <param name="firstSphere">The first sphere</param>
/// <param name="secondSphere">The second sphere</param>
public static bool SphereSphereCollision(SphereBody firstSphere, SphereBody secondSphere)
{
var maxDistanceSquared = Math.Pow(firstSphere.Radius + secondSphere.Radius, 2);
var distanceSquared = Vector3.DistanceSquared(firstSphere.Position, secondSphere.Position);
return(distanceSquared < maxDistanceSquared);
}
/// <summary>
/// Determine whether a box and a sphere intersect.
/// </summary>
/// <param name="box">Box physics object</param>
/// <param name="sphere">Sphere physics object</param>
public static bool BoxSphereCollision(BoxBody box, SphereBody sphere)
{
// reference frame: box at (0, 0, 0), sides aligned with axes
var sphereCoordsRelative = sphere.Position - box.Position;
// to transform coordinate system to have box be axis-aligned, we apply
// the reverse of the rotation to the sphere coordinates
var inverse = new Quaternion(box.Rotation.X, box.Rotation.Y, box.Rotation.Z, -box.Rotation.W);
var sphereCoordsTransformed = Vector3.Transform(sphereCoordsRelative, inverse);
// to check collision, we need to know if the shortest distance between the box
// and the center of the sphere is smaller than the radius of the sphere
// X coordinate of closest point = sphere.X if sphere.x is between the minimum
// and maximum x coordinate of the box - same for y and z
var boxMinX = -box.Size.X / 2;
var boxMaxX = +box.Size.X / 2;
var boxMinY = -box.Size.Y / 2;
var boxMaxY = +box.Size.Y / 2;
var boxMinZ = -box.Size.Z / 2;
var boxMaxZ = +box.Size.Z / 2;
var closestPointToSphereX = Math.Clamp(sphereCoordsTransformed.X, boxMinX, boxMaxX);
var closestPointToSphereY = Math.Clamp(sphereCoordsTransformed.Y, boxMinY, boxMaxY);
var closestPointToSphereZ = Math.Clamp(sphereCoordsTransformed.Z, boxMinZ, boxMaxZ);
return(Vector3.DistanceSquared(sphereCoordsTransformed, new Vector3(closestPointToSphereX, closestPointToSphereY, closestPointToSphereZ))
< Math.Pow(sphere.Radius, 2));
}
/// <summary>
/// Creates a sphere body.
/// </summary>
/// <param name="simulation">The simulation to use.</param>
/// <param name="position">The position of the body.</param>
/// <param name="radius">The radius of the sphere.</param>
/// <returns>The sphere body that was created.</returns>
public static SphereBody Create(PhysicsSimulation simulation, Vector3 position, float radius)
{
var obj = new SphereBody(simulation);
obj.Position = position;
obj.Radius = radius;
simulation.Register(obj);
return(obj);
}
/// <summary>
/// Determine whether a capsule and a sphere intersect.
/// </summary>
/// <param name="capsule">Capsule physics object</param>
/// <param name="sphere">Sphere physics object</param>
public static bool CapsuleSphereCollision(CapsuleBody capsule, SphereBody sphere)
{
// reference frame: capsule at (0, 0, 0), pointing in positive y direction
var sphereCoordsRelative = sphere.Position - capsule.Position;
// to transform coordinate system to have capsule be axis-aligned, we apply
// the reverse of the rotation to the sphere coordinates
var inverse = new Quaternion(capsule.Rotation.X, capsule.Rotation.Y, capsule.Rotation.Z, -capsule.Rotation.W);
var sphereCoordsTransformed = Vector3.Transform(sphereCoordsRelative, inverse);
// coordinates of the line in the centre of the cylinder part
const int capsuleMinY = 0;
var capsuleMaxY = capsule.Height;
const int closestPointToSphereX = 0;
var closestPointToSphereY = Math.Clamp(sphereCoordsTransformed.Y, capsuleMinY, capsuleMaxY);
const int closestPointToSphereZ = 0;
return(Vector3.DistanceSquared(sphereCoordsTransformed,
new Vector3(closestPointToSphereX, closestPointToSphereY, closestPointToSphereZ))
< Math.Pow(capsule.Radius + sphere.Radius, 2));
}