public void GetSupportPoint()
{
ConvexHullOfPoints emptyConvexHullOfPoints = new ConvexHullOfPoints(Enumerable.Empty<Vector3F>());
Assert.AreEqual(new Vector3F(0, 0, 0), emptyConvexHullOfPoints.GetSupportPoint(new Vector3F(1, 0, 0)));
Assert.AreEqual(new Vector3F(0, 0, 0), emptyConvexHullOfPoints.GetSupportPoint(new Vector3F(0, 1, 0)));
Assert.AreEqual(new Vector3F(0, 0, 0), emptyConvexHullOfPoints.GetSupportPoint(new Vector3F(0, 0, 1)));
Assert.AreEqual(new Vector3F(0, 0, 0), emptyConvexHullOfPoints.GetSupportPoint(new Vector3F(1, 1, 1)));
Vector3F p0 = new Vector3F(2, 0, 0);
Vector3F p1 = new Vector3F(-1, -1, -2);
Vector3F p2 = new Vector3F(0, 2, -3);
Assert.AreEqual(p0, new ConvexHullOfPoints(new[] { p0, p1, p2 }).GetSupportPoint(new Vector3F(1, 0, 0)));
Assert.AreEqual(p2, new ConvexHullOfPoints(new[] { p0, p1, p2 }).GetSupportPoint(new Vector3F(0, 1, 0)));
Assert.AreEqual(p2, new ConvexHullOfPoints(new[] { p0, p1, p2 }).GetSupportPoint(new Vector3F(0, 0, -1)));
Assert.AreEqual(p1, new ConvexHullOfPoints(new[] { p0, p1, p2 }).GetSupportPoint(new Vector3F(-1, 0, 1)));
}
public void GetSupportPoint()
{
ConvexHullOfPoints emptyConvexHullOfPoints = new ConvexHullOfPoints(Enumerable.Empty <Vector3>());
Assert.AreEqual(new Vector3(0, 0, 0), emptyConvexHullOfPoints.GetSupportPoint(new Vector3(1, 0, 0)));
Assert.AreEqual(new Vector3(0, 0, 0), emptyConvexHullOfPoints.GetSupportPoint(new Vector3(0, 1, 0)));
Assert.AreEqual(new Vector3(0, 0, 0), emptyConvexHullOfPoints.GetSupportPoint(new Vector3(0, 0, 1)));
Assert.AreEqual(new Vector3(0, 0, 0), emptyConvexHullOfPoints.GetSupportPoint(new Vector3(1, 1, 1)));
Vector3 p0 = new Vector3(2, 0, 0);
Vector3 p1 = new Vector3(-1, -1, -2);
Vector3 p2 = new Vector3(0, 2, -3);
Assert.AreEqual(p0, new ConvexHullOfPoints(new[] { p0, p1, p2 }).GetSupportPoint(new Vector3(1, 0, 0)));
Assert.AreEqual(p2, new ConvexHullOfPoints(new[] { p0, p1, p2 }).GetSupportPoint(new Vector3(0, 1, 0)));
Assert.AreEqual(p2, new ConvexHullOfPoints(new[] { p0, p1, p2 }).GetSupportPoint(new Vector3(0, 0, -1)));
Assert.AreEqual(p1, new ConvexHullOfPoints(new[] { p0, p1, p2 }).GetSupportPoint(new Vector3(-1, 0, 1)));
}
public void RandomConvexHullOfPoints()
{
// Use a fixed seed.
RandomHelper.Random = new Random(12345);
// Try polyhedra with 0, 1, 2, ... points.
for (int numberOfPoints = 0; numberOfPoints < 100; numberOfPoints++)
{
List <Vector3> points = new List <Vector3>(numberOfPoints);
// Create random polyhedra.
for (int i = 0; i < numberOfPoints; i++)
{
points.Add(
new Vector3(
RandomHelper.Random.NextFloat(-10, 10),
RandomHelper.Random.NextFloat(-20, 20),
RandomHelper.Random.NextFloat(-100, 100)));
}
ConvexHullOfPoints convex = new ConvexHullOfPoints(points);
// Sample primary directions
Vector3 right = new Vector3(2, 0, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(right, points), convex.GetSupportPoint(right), right);
Vector3 left = new Vector3(-2, 0, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(left, points), convex.GetSupportPoint(left), left);
Vector3 up = new Vector3(0, 2, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(up, points), convex.GetSupportPoint(up), up);
Vector3 down = new Vector3(0, -2, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(down, points), convex.GetSupportPoint(down), down);
Vector3 back = new Vector3(0, 0, 2);
AssertSupportPointsAreEquivalent(GetSupportPoint(back, points), convex.GetSupportPoint(back), back);
Vector3 front = new Vector3(0, 0, -2);
AssertSupportPointsAreEquivalent(GetSupportPoint(front, points), convex.GetSupportPoint(front), front);
// Sample random directions
for (int i = 0; i < 10; i++)
{
Vector3 direction = RandomHelper.Random.NextVector3(-1, 1);
if (direction.IsNumericallyZero)
{
continue;
}
Vector3 supportPoint = convex.GetSupportPoint(direction);
Vector3 reference = GetSupportPoint(direction, points);
// The support points can be different, e.g. if a an edge of face is normal to the
// direction. When projected onto the direction both support points must be at equal
// distance.
AssertSupportPointsAreEquivalent(reference, supportPoint, direction);
}
}
}
public void SimpleTetrahedron()
{
List <Vector3> points = new List <Vector3>
{
new Vector3(0, 0, 0),
new Vector3(0, 1, 0),
new Vector3(1, 0, 0),
new Vector3(0, 0, 1),
};
ConvexHullOfPoints convex = new ConvexHullOfPoints(points);
// Sample primary directions
Vector3 right = new Vector3(2, 0, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(right, points), convex.GetSupportPoint(right), right);
Vector3 left = new Vector3(-2, 0, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(left, points), convex.GetSupportPoint(left), left);
Vector3 up = new Vector3(0, 2, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(up, points), convex.GetSupportPoint(up), up);
Vector3 down = new Vector3(0, -2, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(down, points), convex.GetSupportPoint(down), down);
Vector3 back = new Vector3(0, 0, 2);
AssertSupportPointsAreEquivalent(GetSupportPoint(back, points), convex.GetSupportPoint(back), back);
Vector3 front = new Vector3(0, 0, -2);
AssertSupportPointsAreEquivalent(GetSupportPoint(front, points), convex.GetSupportPoint(front), front);
// Sample random directions
for (int i = 0; i < 10; i++)
{
Vector3 direction = RandomHelper.Random.NextVector3(-1, 1);
Vector3 supportPoint = convex.GetSupportPoint(direction);
Vector3 reference = GetSupportPoint(direction, points);
// The support points can be different, e.g. if a an edge of face is normal to the
// direction. When projected onto the direction both support points must be at equal
// distance.
AssertSupportPointsAreEquivalent(reference, supportPoint, direction);
}
}
public void RandomConvexHullOfPoints()
{
// Use a fixed seed.
RandomHelper.Random = new Random(12345);
// Try polyhedra with 0, 1, 2, ... points.
for (int numberOfPoints = 0; numberOfPoints < 100; numberOfPoints++)
{
List<Vector3F> points = new List<Vector3F>(numberOfPoints);
// Create random polyhedra.
for (int i = 0; i < numberOfPoints; i++)
points.Add(
new Vector3F(
RandomHelper.Random.NextFloat(-10, 10),
RandomHelper.Random.NextFloat(-20, 20),
RandomHelper.Random.NextFloat(-100, 100)));
ConvexHullOfPoints convex = new ConvexHullOfPoints(points);
// Sample primary directions
Vector3F right = new Vector3F(2, 0, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(right, points), convex.GetSupportPoint(right), right);
Vector3F left = new Vector3F(-2, 0, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(left, points), convex.GetSupportPoint(left), left);
Vector3F up = new Vector3F(0, 2, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(up, points), convex.GetSupportPoint(up), up);
Vector3F down = new Vector3F(0, -2, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(down, points), convex.GetSupportPoint(down), down);
Vector3F back = new Vector3F(0, 0, 2);
AssertSupportPointsAreEquivalent(GetSupportPoint(back, points), convex.GetSupportPoint(back), back);
Vector3F front = new Vector3F(0, 0, -2);
AssertSupportPointsAreEquivalent(GetSupportPoint(front, points), convex.GetSupportPoint(front), front);
// Sample random directions
for (int i = 0; i < 10; i++)
{
Vector3F direction = RandomHelper.Random.NextVector3F(-1, 1);
if (direction.IsNumericallyZero)
continue;
Vector3F supportPoint = convex.GetSupportPoint(direction);
Vector3F reference = GetSupportPoint(direction, points);
// The support points can be different, e.g. if a an edge of face is normal to the
// direction. When projected onto the direction both support points must be at equal
// distance.
AssertSupportPointsAreEquivalent(reference, supportPoint, direction);
}
}
}
public void SimpleTetrahedron()
{
List<Vector3F> points = new List<Vector3F>
{
new Vector3F(0, 0, 0),
new Vector3F(0, 1, 0),
new Vector3F(1, 0, 0),
new Vector3F(0, 0, 1),
};
ConvexHullOfPoints convex = new ConvexHullOfPoints(points);
// Sample primary directions
Vector3F right = new Vector3F(2, 0, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(right, points), convex.GetSupportPoint(right), right);
Vector3F left = new Vector3F(-2, 0, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(left, points), convex.GetSupportPoint(left), left);
Vector3F up = new Vector3F(0, 2, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(up, points), convex.GetSupportPoint(up), up);
Vector3F down = new Vector3F(0, -2, 0);
AssertSupportPointsAreEquivalent(GetSupportPoint(down, points), convex.GetSupportPoint(down), down);
Vector3F back = new Vector3F(0, 0, 2);
AssertSupportPointsAreEquivalent(GetSupportPoint(back, points), convex.GetSupportPoint(back), back);
Vector3F front = new Vector3F(0, 0, -2);
AssertSupportPointsAreEquivalent(GetSupportPoint(front, points), convex.GetSupportPoint(front), front);
// Sample random directions
for (int i = 0; i < 10; i++)
{
Vector3F direction = RandomHelper.Random.NextVector3F(-1, 1);
Vector3F supportPoint = convex.GetSupportPoint(direction);
Vector3F reference = GetSupportPoint(direction, points);
// The support points can be different, e.g. if a an edge of face is normal to the
// direction. When projected onto the direction both support points must be at equal
// distance.
AssertSupportPointsAreEquivalent(reference, supportPoint, direction);
}
}