public void TestBoundingSphere()
{
Sphere3 sphere = new Sphere3(
new Vector3(15.0f, 15.0f, 15.0f), 5.0f
);
Sphere3 boundingSphere = sphere.BoundingSphere;
Assert.AreEqual(
sphere, boundingSphere,
"Bounding sphere for sphere is identical to the sphere itself"
);
}
public void TestBoundingBox()
{
Sphere3 sphere = new Sphere3(
new Vector3(15.0f, 15.0f, 15.0f), 5.0f
);
AxisAlignedBox3 boundingBox = sphere.BoundingBox;
Assert.AreEqual(
new Vector3(10.0f, 10.0f, 10.0f), boundingBox.Min,
"Minimum corner of bounding box correctly determined"
);
Assert.AreEqual(
new Vector3(20.0f, 20.0f, 20.0f), boundingBox.Max,
"Maximum corner of bounding box correctly determined"
);
}
public void TestBoundingSphere()
{
AxisAlignedBox3 box = new AxisAlignedBox3(
new Vector3(10.0f, 10.0f, 10.0f), new Vector3(20.0f, 20.0f, 20.0f)
);
Sphere3 boundingSphere = box.BoundingSphere;
Assert.AreEqual(
new Vector3(15.0f, 15.0f, 15.0f), boundingSphere.Center,
"Center of bounding sphere correctly determined"
);
Assert.AreEqual(
(float)Math.Sqrt(75.0f), boundingSphere.Radius,
"Radius of bounding sphere exactly encloses the box"
);
}
public void TestBoundingSphere()
{
Cylinder3 testCylinder = new Cylinder3(
Matrix.CreateTranslation(new Vector3(100.0f, 200.0f, 300.0f)), 10.0f, 20.0f
);
Sphere3 boundingSphere = testCylinder.BoundingSphere;
GeoAssertHelper.AreAlmostEqual(
new Vector3(100.0f, 200.0f, 300.0f), boundingSphere.Center,
Specifications.MaximumDeviation, "Center of bounding sphere correctly determined"
);
Assert.That(
boundingSphere.Radius,
Is.EqualTo(14.142135623730950488016887242097f).Within(
Specifications.MaximumDeviation
).Ulps,
"Radius of bounding sphere exactly encloses the box"
);
}
public void TestMassProperties()
{
Sphere3 testSphere =
new Sphere3(new Vector3(100.0f, 100.0f, 100.0f), 20.0f);
Assert.AreEqual(
new Vector3(100.0f, 100.0f, 100.0f), testSphere.CenterOfMass,
"Center of mass is correctly positioned"
);
Assert.AreEqual(
33510.32421875f, testSphere.Mass,
Specifications.MaximumDeviation,
"Mass of sphere is exactly determined"
);
Assert.AreEqual(
5026.5482457436692f, testSphere.SurfaceArea,
Specifications.MaximumDeviation,
"Surface area of sphere is exactly determined"
);
}
public void TestMassProperties() {
Sphere3 testSphere =
new Sphere3(new Vector3(100.0f, 100.0f, 100.0f), 20.0f);
Assert.AreEqual(
new Vector3(100.0f, 100.0f, 100.0f), testSphere.CenterOfMass,
"Center of mass is correctly positioned"
);
Assert.AreEqual(
33510.32421875f, testSphere.Mass,
Specifications.MaximumDeviation,
"Mass of sphere is exactly determined"
);
Assert.AreEqual(
5026.5482457436692f, testSphere.SurfaceArea,
Specifications.MaximumDeviation,
"Surface area of sphere is exactly determined"
);
}
public void TestRandomPointOnSurface()
{
Sphere3 unitSphere = new Sphere3(Vector3.Zero, 1.0f);
Sphere3 innerSphere = new Sphere3(Vector3.Zero, 1.0f - Specifications.HullAccuracy);
Sphere3 outerSphere = new Sphere3(Vector3.Zero, 1.0f + Specifications.HullAccuracy);
DefaultRandom random = new DefaultRandom();
Vector3 total = Vector3.Zero;
for (int i = 0; i < Specifications.ProbabilisticFunctionSamples; ++i)
{
Vector3 point = unitSphere.RandomPointOnSurface(random);
Assert.IsFalse(
innerSphere.Contains(point), "Random point lies on the sphere's hull"
);
Assert.IsTrue(
outerSphere.Contains(point), "Random point lies on the sphere's hull"
);
total += point;
}
total /= Specifications.ProbabilisticFunctionSamples;
Assert.AreEqual(
0.0f, total.X, Specifications.ProbabilisticFunctionDeviation,
"Random points average on the center of the sphere on the X axis"
);
Assert.AreEqual(
0.0f, total.Y, Specifications.ProbabilisticFunctionDeviation,
"Random points average on the center of the sphere on the Y axis"
);
Assert.AreEqual(
0.0f, total.Z, Specifications.ProbabilisticFunctionDeviation,
"Random points average on the center of the sphere on the Z axis"
);
}
/// <summary>Determines if the volume will impact on a sphere</summary>
/// <param name="thisVelocity">Velocity with which this volume is moving</param>
/// <param name="sphere">Sphere that will be checked for intersection</param>
/// <returns>The point of first contact, if any</returns>
/// <remarks>
/// <para>
/// Conventional tests that resort to stepping often fail to detect collisions
/// between fast-moving objects. This impact determination test will always
/// detect a collision if it occurs, giving the exact time of the impact.
/// </para>
/// <para>
/// This is a simplified test that assumes a linear trajectory and does
/// not take off-center object rotation into account. It is well suited to use
/// on two bounding spheres in order to determine if a collision between the
/// shape contained is possible at all.
/// </para>
/// <para>
/// Ideas taken from the "Simple Intersection Tests for Games" article
/// on gamasutra by Gomez.
/// </para>
/// </remarks>
public float[] LocateImpact(Vector3 thisVelocity, Sphere3 sphere)
{
Vector3 distance = Center - sphere.Center;
float radii = Radius + sphere.Radius;
float radii2 = radii * radii;
// Already inside the other circle
if (distance.LengthSquared() < radii2)
{
return new float[] { 0.0f }
}
;
float a = thisVelocity.LengthSquared();
float b = Vector3.Dot(thisVelocity, distance) * 2.0f;
float c = distance.LengthSquared() - radii2;
float q = b * b - 4.0f * a * c;
// If the other sphere is not crossing our location, then no impact will happen
if (q < 0.0)
{
return(null);
}
float sq = (float)Math.Sqrt(q);
float d = 1.0f / (2.0f * a);
float r1 = (-b + sq) * d;
float r2 = (-b - sq) * d;
if (r1 < r2)
{
return new float[] { r1 }
}
;
else
{
return new float[] { r2 }
};
}
public void TestMovingSphereIntersection() {
Sphere3 leftSphere = new Sphere3(new Vector3(0.0f, 0.0f, 0.0f), 10.0f);
Sphere3 rightSphere = new Sphere3(new Vector3(100.0f, 0.0f, 0.0f), 10.0f);
Assert.AreEqual(
new float[] { 0.0f },
leftSphere.LocateImpact(new Vector3(0.0f, 0.0f, 0.0f), leftSphere),
"Contact with clone occured immediately"
);
Assert.That(
leftSphere.LocateImpact(new Vector3(200.0f, 0.0f, 0.0f), rightSphere),
Is.EqualTo(new float[] { 0.4f }).Within(Specifications.MaximumDeviation).Ulps,
"Fast moving contact with right sphere is determined exactly"
);
Assert.That(
rightSphere.LocateImpact(new Vector3(-200.0f, 0.0f, 0.0f), leftSphere),
Is.EqualTo(new float[] { 0.4f }).Within(Specifications.MaximumDeviation).Ulps,
"Fast moving contact with left sphere is determined exactly"
);
}
public void TestMovingSphereIntersection()
{
Sphere3 leftSphere = new Sphere3(new Vector3(0.0f, 0.0f, 0.0f), 10.0f);
Sphere3 rightSphere = new Sphere3(new Vector3(100.0f, 0.0f, 0.0f), 10.0f);
Assert.AreEqual(
new float[] { 0.0f },
leftSphere.LocateImpact(new Vector3(0.0f, 0.0f, 0.0f), leftSphere),
"Contact with clone occured immediately"
);
Assert.That(
leftSphere.LocateImpact(new Vector3(200.0f, 0.0f, 0.0f), rightSphere),
Is.EqualTo(new float[] { 0.4f }).Within(Specifications.MaximumDeviation).Ulps,
"Fast moving contact with right sphere is determined exactly"
);
Assert.That(
rightSphere.LocateImpact(new Vector3(-200.0f, 0.0f, 0.0f), leftSphere),
Is.EqualTo(new float[] { 0.4f }).Within(Specifications.MaximumDeviation).Ulps,
"Fast moving contact with left sphere is determined exactly"
);
}
/// <summary>Visit a sphere</summary> /// <param name="sphere">Sphere to visit</param> public abstract void Visit(Sphere3 sphere);
/// <summary>Determines if the volume clips the circle</summary>
/// <param name="sphere">Circle that will be checked for intersection</param>
/// <returns>True if the objects overlap</returns>
public bool Intersects(Sphere3 sphere)
{
throw new NotImplementedException("Not implemented yet");
}
public Sphere3(Sphere3 other)
: this(other.Center, other.Radius) { }
/// <summary>Determines if the volume will impact on a sphere</summary>
/// <param name="thisVelocity">Velocity with which this volume is moving</param>
/// <param name="sphere">Sphere that will be checked for intersection</param>
/// <returns>The point of first contact, if any</returns>
/// <remarks>
/// <para>
/// Conventional tests that resort to stepping often fail to detect collisions
/// between fast-moving objects. This impact determination test will always
/// detect a collision if it occurs, giving the exact time of the impact.
/// </para>
/// <para>
/// This is a simplified test that assumes a linear trajectory and does
/// not take off-center object rotation into account. It is well suited to use
/// on two bounding spheres in order to determine if a collision between the
/// shape contained is possible at all.
/// </para>
/// <para>
/// Ideas taken from the "Simple Intersection Tests for Games" article
/// on gamasutra by Gomez.
/// </para>
/// </remarks>
public float[] LocateImpact(Vector3 thisVelocity, Sphere3 sphere) {
Vector3 distance = Center - sphere.Center;
float radii = Radius + sphere.Radius;
float radii2 = radii * radii;
// Already inside the other circle
if(distance.LengthSquared() < radii2)
return new float[] { 0.0f };
float a = thisVelocity.LengthSquared();
float b = Vector3.Dot(thisVelocity, distance) * 2.0f;
float c = distance.LengthSquared() - radii2;
float q = b * b - 4.0f * a * c;
// If the other sphere is not crossing our location, then no impact will happen
if(q < 0.0)
return null;
float sq = (float)Math.Sqrt(q);
float d = 1.0f / (2.0f * a);
float r1 = (-b + sq) * d;
float r2 = (-b - sq) * d;
if(r1 < r2)
return new float[] { r1 };
else
return new float[] { r2 };
}
/// <summary>Determines if the volume clips the circle</summary>
/// <param name="sphere">Circle that will be checked for intersection</param>
/// <returns>True if the objects overlap</returns>
public bool Intersects(Sphere3 sphere) {
return Collisions.SphereSphereCollider.CheckContact(
this.Center, this.Radius, sphere.Center, sphere.Radius
);
}
/// <summary>Determines if the volume clips the circle</summary>
/// <param name="sphere">Circle that will be checked for intersection</param>
/// <returns>True if the objects overlap</returns>
public bool Intersects(Sphere3 sphere)
{
return(Collisions.ObbSphereCollider.CheckContact(
this.Transform, this.Extents, sphere.Center, sphere.Radius
));
}
/// <summary>Determines if the volume clips the circle</summary>
/// <param name="sphere">Circle that will be checked for intersection</param>
/// <returns>True if the objects overlap</returns>
public bool Intersects(Sphere3 sphere)
{
return(Collisions.MeshSphereCollider.CheckContact(
this, sphere.Center, sphere.Radius
));
}
public Sphere3(Sphere3 other)
: this(other.Center, other.Radius)
{
}
public void TestBoundingBox() {
Sphere3 sphere = new Sphere3(
new Vector3(15.0f, 15.0f, 15.0f), 5.0f
);
AxisAlignedBox3 boundingBox = sphere.BoundingBox;
Assert.AreEqual(
new Vector3(10.0f, 10.0f, 10.0f), boundingBox.Min,
"Minimum corner of bounding box correctly determined"
);
Assert.AreEqual(
new Vector3(20.0f, 20.0f, 20.0f), boundingBox.Max,
"Maximum corner of bounding box correctly determined"
);
}
/// <summary>Determines if the volume clips the circle</summary>
/// <param name="sphere">Circle that will be checked for intersection</param>
/// <returns>True if the objects overlap</returns>
public bool Intersects(Sphere3 sphere)
{
return(Collisions.AabbSphereCollider.CheckContact(
this.Min, this.Max, sphere.Center, sphere.Radius
));
}
/// <summary>Determines if the volume clips the circle</summary>
/// <param name="sphere">Circle that will be checked for intersection</param>
/// <returns>True if the objects overlap</returns>
public bool Intersects(Sphere3 sphere) {
return Collisions.AabbSphereCollider.CheckContact(
this.Min, this.Max, sphere.Center, sphere.Radius
);
}
public void TestRandomPointOnSurface() {
Sphere3 unitSphere = new Sphere3(Vector3.Zero, 1.0f);
Sphere3 innerSphere = new Sphere3(Vector3.Zero, 1.0f - Specifications.HullAccuracy);
Sphere3 outerSphere = new Sphere3(Vector3.Zero, 1.0f + Specifications.HullAccuracy);
DefaultRandom random = new DefaultRandom();
Vector3 total = Vector3.Zero;
for(int i = 0; i < Specifications.ProbabilisticFunctionSamples; ++i) {
Vector3 point = unitSphere.RandomPointOnSurface(random);
Assert.IsFalse(
innerSphere.Contains(point), "Random point lies on the sphere's hull"
);
Assert.IsTrue(
outerSphere.Contains(point), "Random point lies on the sphere's hull"
);
total += point;
}
total /= Specifications.ProbabilisticFunctionSamples;
Assert.AreEqual(
0.0f, total.X, Specifications.ProbabilisticFunctionDeviation,
"Random points average on the center of the sphere on the X axis"
);
Assert.AreEqual(
0.0f, total.Y, Specifications.ProbabilisticFunctionDeviation,
"Random points average on the center of the sphere on the Y axis"
);
Assert.AreEqual(
0.0f, total.Z, Specifications.ProbabilisticFunctionDeviation,
"Random points average on the center of the sphere on the Z axis"
);
}
public void TestBoundingSphere() {
Sphere3 sphere = new Sphere3(
new Vector3(15.0f, 15.0f, 15.0f), 5.0f
);
Sphere3 boundingSphere = sphere.BoundingSphere;
Assert.AreEqual(
sphere, boundingSphere,
"Bounding sphere for sphere is identical to the sphere itself"
);
}
/// <summary>Determines where the range clips a sphere</summary>
/// <param name="sphere">Sphere that will be checked for intersection</param>
/// <returns>The times at which the range enters or leaves the volume</returns>
public LineContacts FindContacts(Sphere3 sphere) {
return Collisions.Ray3Sphere3Collider.FindContacts(
Origin, Direction, sphere.Center, sphere.Radius
);
}
/// <summary>Determines if the volume clips the circle</summary>
/// <param name="sphere">Circle that will be checked for intersection</param>
/// <returns>True if the objects overlap</returns>
public bool Intersects(Sphere3 sphere) {
return Collisions.ObbSphereCollider.CheckContact(
this.Transform, this.Extents, sphere.Center, sphere.Radius
);
}
/// <summary>Determines where the range clips a sphere</summary>
/// <param name="sphere">Sphere that will be checked for intersection</param>
/// <returns>The times at which the range enters or leaves the volume</returns>
public LineContacts FindContacts(Sphere3 sphere) {
throw new NotImplementedException();
/*
return filterContacts(
Collisions.Line3Sphere3Collider.FindContacts(
this.Start, this.End - this.Start, sphere.Center, sphere.Radius
)
);
*/
}
/// <summary>Visit a sphere</summary> /// <param name="sphere">Sphere to visit</param> public abstract void Visit(Sphere3 sphere);
/// <summary>Determines if the volume clips the circle</summary>
/// <param name="sphere">Circle that will be checked for intersection</param>
/// <returns>True if the objects overlap</returns>
public bool Intersects(Sphere3 sphere) {
throw new NotImplementedException("Not implemented yet");
}
