/// <summary>
/// Determines whether the given BoundingOrientedBox contains/intersects/is disjoint from the triangle
/// (v0,v1,v2)
/// </summary>
public static ContainmentType Contains(ref BoundingOrientedBox obox, ref Vector3 v0, ref Vector3 v1, ref Vector3 v2)
{
// Transform the triangle into the local space of the box, so we can use a
// faster axis-aligned box test.
// Note than when transforming more than one point, using an intermediate matrix
// is faster than doing multiple quaternion transforms directly.
Quaternion qinv;
Quaternion.Conjugate(ref obox.Orientation, out qinv);
Matrix minv;
Matrix.CreateFromQuaternion(ref qinv, out minv);
Triangle localTri = new Triangle();
localTri.V0 = Vector3.TransformNormal(v0 - obox.Center, minv);
localTri.V1 = Vector3.TransformNormal(v1 - obox.Center, minv);
localTri.V2 = Vector3.TransformNormal(v2 - obox.Center, minv);
return OriginBoxContains(ref obox.HalfExtent, ref localTri);
}
public void DrawWireTriangle(Triangle t, Color color)
{
DrawWireTriangle(t.V0, t.V1, t.V2, color);
}
/// <summary>
/// Check if an origin-centered, axis-aligned box with the given half extents contains,
/// intersects, or is disjoint from the given triangle. This is used for the box and
/// frustum vs. triangle tests.
/// </summary>
public static ContainmentType OriginBoxContains(ref Vector3 halfExtent, ref Triangle tri)
{
BoundingBox triBounds = new BoundingBox(); // 'new' to work around NetCF bug
triBounds.Min.X = Math.Min(tri.V0.X, Math.Min(tri.V1.X, tri.V2.X));
triBounds.Min.Y = Math.Min(tri.V0.Y, Math.Min(tri.V1.Y, tri.V2.Y));
triBounds.Min.Z = Math.Min(tri.V0.Z, Math.Min(tri.V1.Z, tri.V2.Z));
triBounds.Max.X = Math.Max(tri.V0.X, Math.Max(tri.V1.X, tri.V2.X));
triBounds.Max.Y = Math.Max(tri.V0.Y, Math.Max(tri.V1.Y, tri.V2.Y));
triBounds.Max.Z = Math.Max(tri.V0.Z, Math.Max(tri.V1.Z, tri.V2.Z));
Vector3 triBoundhalfExtent;
triBoundhalfExtent.X = (triBounds.Max.X - triBounds.Min.X) * 0.5f;
triBoundhalfExtent.Y = (triBounds.Max.Y - triBounds.Min.Y) * 0.5f;
triBoundhalfExtent.Z = (triBounds.Max.Z - triBounds.Min.Z) * 0.5f;
Vector3 triBoundCenter;
triBoundCenter.X = (triBounds.Max.X + triBounds.Min.X) * 0.5f;
triBoundCenter.Y = (triBounds.Max.Y + triBounds.Min.Y) * 0.5f;
triBoundCenter.Z = (triBounds.Max.Z + triBounds.Min.Z) * 0.5f;
if (triBoundhalfExtent.X + halfExtent.X <= Math.Abs(triBoundCenter.X) ||
triBoundhalfExtent.Y + halfExtent.Y <= Math.Abs(triBoundCenter.Y) ||
triBoundhalfExtent.Z + halfExtent.Z <= Math.Abs(triBoundCenter.Z))
{
return ContainmentType.Disjoint;
}
if (triBoundhalfExtent.X + Math.Abs(triBoundCenter.X) <= halfExtent.X &&
triBoundhalfExtent.Y + Math.Abs(triBoundCenter.Y) <= halfExtent.Y &&
triBoundhalfExtent.Z + Math.Abs(triBoundCenter.Z) <= halfExtent.Z)
{
return ContainmentType.Contains;
}
Vector3 edge1, edge2, edge3;
Vector3.Subtract(ref tri.V1, ref tri.V0, out edge1);
Vector3.Subtract(ref tri.V2, ref tri.V0, out edge2);
Vector3 normal;
Vector3.Cross(ref edge1, ref edge2, out normal);
float triangleDist = Vector3.Dot(tri.V0, normal);
if(Math.Abs(normal.X*halfExtent.X) + Math.Abs(normal.Y*halfExtent.Y) + Math.Abs(normal.Z*halfExtent.Z) <= Math.Abs(triangleDist))
{
return ContainmentType.Disjoint;
}
// Worst case: we need to check all 9 possible separating planes
// defined by Cross(box edge,triangle edge)
// Check for separation in plane containing an axis of box A and and axis of box B
//
// We need to compute all 9 cross products to find them, but a lot of terms drop out
// since we're working in A's local space. Also, since each such plane is parallel
// to the defining axis in each box, we know those dot products will be 0 and can
// omit them.
Vector3.Subtract(ref tri.V1, ref tri.V2, out edge3);
float dv0, dv1, dv2, dhalf;
// a.X ^ b.X = (1,0,0) ^ edge1
// axis = Vector3(0, -edge1.Z, edge1.Y);
dv0 = tri.V0.Z * edge1.Y - tri.V0.Y * edge1.Z;
dv1 = tri.V1.Z * edge1.Y - tri.V1.Y * edge1.Z;
dv2 = tri.V2.Z * edge1.Y - tri.V2.Y * edge1.Z;
dhalf = Math.Abs(halfExtent.Y * edge1.Z) + Math.Abs(halfExtent.Z * edge1.Y);
if (Math.Min(dv0, Math.Min(dv1, dv2)) >= dhalf || Math.Max(dv0, Math.Max(dv1, dv2)) <= -dhalf)
return ContainmentType.Disjoint;
// a.X ^ b.Y = (1,0,0) ^ edge2
// axis = Vector3(0, -edge2.Z, edge2.Y);
dv0 = tri.V0.Z * edge2.Y - tri.V0.Y * edge2.Z;
dv1 = tri.V1.Z * edge2.Y - tri.V1.Y * edge2.Z;
dv2 = tri.V2.Z * edge2.Y - tri.V2.Y * edge2.Z;
dhalf = Math.Abs(halfExtent.Y * edge2.Z) + Math.Abs(halfExtent.Z * edge2.Y);
if (Math.Min(dv0, Math.Min(dv1, dv2)) >= dhalf || Math.Max(dv0, Math.Max(dv1, dv2)) <= -dhalf)
return ContainmentType.Disjoint;
// a.X ^ b.Y = (1,0,0) ^ edge3
// axis = Vector3(0, -edge3.Z, edge3.Y);
dv0 = tri.V0.Z * edge3.Y - tri.V0.Y * edge3.Z;
dv1 = tri.V1.Z * edge3.Y - tri.V1.Y * edge3.Z;
dv2 = tri.V2.Z * edge3.Y - tri.V2.Y * edge3.Z;
dhalf = Math.Abs(halfExtent.Y * edge3.Z) + Math.Abs(halfExtent.Z * edge3.Y);
if (Math.Min(dv0, Math.Min(dv1, dv2)) >= dhalf || Math.Max(dv0, Math.Max(dv1, dv2)) <= -dhalf)
return ContainmentType.Disjoint;
// a.Y ^ b.X = (0,1,0) ^ edge1
// axis = Vector3(edge1.Z, 0, -edge1.X);
dv0 = tri.V0.X * edge1.Z - tri.V0.Z * edge1.X;
dv1 = tri.V1.X * edge1.Z - tri.V1.Z * edge1.X;
dv2 = tri.V2.X * edge1.Z - tri.V2.Z * edge1.X;
dhalf = Math.Abs(halfExtent.X * edge1.Z) + Math.Abs(halfExtent.Z * edge1.X);
if (Math.Min(dv0, Math.Min(dv1, dv2)) >= dhalf || Math.Max(dv0, Math.Max(dv1, dv2)) <= -dhalf)
return ContainmentType.Disjoint;
// a.Y ^ b.X = (0,1,0) ^ edge2
// axis = Vector3(edge2.Z, 0, -edge2.X);
dv0 = tri.V0.X * edge2.Z - tri.V0.Z * edge2.X;
dv1 = tri.V1.X * edge2.Z - tri.V1.Z * edge2.X;
dv2 = tri.V2.X * edge2.Z - tri.V2.Z * edge2.X;
dhalf = Math.Abs(halfExtent.X * edge2.Z) + Math.Abs(halfExtent.Z * edge2.X);
if (Math.Min(dv0, Math.Min(dv1, dv2)) >= dhalf || Math.Max(dv0, Math.Max(dv1, dv2)) <= -dhalf)
return ContainmentType.Disjoint;
// a.Y ^ b.X = (0,1,0) ^ bX
// axis = Vector3(edge3.Z, 0, -edge3.X);
dv0 = tri.V0.X * edge3.Z - tri.V0.Z * edge3.X;
dv1 = tri.V1.X * edge3.Z - tri.V1.Z * edge3.X;
dv2 = tri.V2.X * edge3.Z - tri.V2.Z * edge3.X;
dhalf = Math.Abs(halfExtent.X * edge3.Z) + Math.Abs(halfExtent.Z * edge3.X);
if (Math.Min(dv0, Math.Min(dv1, dv2)) >= dhalf || Math.Max(dv0, Math.Max(dv1, dv2)) <= -dhalf)
return ContainmentType.Disjoint;
// a.Y ^ b.X = (0,0,1) ^ edge1
// axis = Vector3(-edge1.Y, edge1.X, 0);
dv0 = tri.V0.Y * edge1.X - tri.V0.X * edge1.Y;
dv1 = tri.V1.Y * edge1.X - tri.V1.X * edge1.Y;
dv2 = tri.V2.Y * edge1.X - tri.V2.X * edge1.Y;
dhalf = Math.Abs(halfExtent.Y * edge1.X) + Math.Abs(halfExtent.X * edge1.Y);
if (Math.Min(dv0, Math.Min(dv1, dv2)) >= dhalf || Math.Max(dv0, Math.Max(dv1, dv2)) <= -dhalf)
return ContainmentType.Disjoint;
// a.Y ^ b.X = (0,0,1) ^ edge2
// axis = Vector3(-edge2.Y, edge2.X, 0);
dv0 = tri.V0.Y * edge2.X - tri.V0.X * edge2.Y;
dv1 = tri.V1.Y * edge2.X - tri.V1.X * edge2.Y;
dv2 = tri.V2.Y * edge2.X - tri.V2.X * edge2.Y;
dhalf = Math.Abs(halfExtent.Y * edge2.X) + Math.Abs(halfExtent.X * edge2.Y);
if (Math.Min(dv0, Math.Min(dv1, dv2)) >= dhalf || Math.Max(dv0, Math.Max(dv1, dv2)) <= -dhalf)
return ContainmentType.Disjoint;
// a.Y ^ b.X = (0,0,1) ^ edge3
// axis = Vector3(-edge3.Y, edge3.X, 0);
dv0 = tri.V0.Y * edge3.X - tri.V0.X * edge3.Y;
dv1 = tri.V1.Y * edge3.X - tri.V1.X * edge3.Y;
dv2 = tri.V2.Y * edge3.X - tri.V2.X * edge3.Y;
dhalf = Math.Abs(halfExtent.Y * edge3.X) + Math.Abs(halfExtent.X * edge3.Y);
if (Math.Min(dv0, Math.Min(dv1, dv2)) >= dhalf || Math.Max(dv0, Math.Max(dv1, dv2)) <= -dhalf)
return ContainmentType.Disjoint;
return ContainmentType.Intersects;
}
/// <summary>
/// Tests whether the given box contains, intersects, or is disjoint from the given triangle.
/// </summary>
public static ContainmentType Contains(ref BoundingBox box, ref Triangle triangle)
{
return Contains(ref box, ref triangle.V0, ref triangle.V1, ref triangle.V2);
}
/// <summary>
/// Determine whether the given triangle intersects the given ray. If there is intersection,
/// returns the parametric value of the intersection point on the ray. Otherwise returns null.
/// </summary>
public static float? Intersects(ref Ray ray, ref Triangle tri)
{
return Intersects(ref ray, ref tri.V0, ref tri.V1, ref tri.V2);
}
/// <summary>
/// Returns true if the given sphere intersects the given triangle.
/// </summary>
public static bool Intersects(ref BoundingSphere sphere, ref Triangle t)
{
Vector3 p = NearestPointOnTriangle(ref sphere.Center, ref t.V0, ref t.V1, ref t.V2);
return Vector3.DistanceSquared(sphere.Center, p) < sphere.Radius * sphere.Radius;
}
/// <summary>
/// Returns true if the given box intersects the triangle (v0,v1,v2).
/// </summary>
public static bool Intersects(ref BoundingBox box, ref Vector3 v0, ref Vector3 v1, ref Vector3 v2)
{
Vector3 boxCenter = (box.Max + box.Min) * 0.5f;
Vector3 boxHalfExtent = (box.Max - box.Min) * 0.5f;
// Transform the triangle into the local space with the box center at the origin
Triangle localTri = new Triangle();
Vector3.Subtract(ref v0, ref boxCenter, out localTri.V0);
Vector3.Subtract(ref v1, ref boxCenter, out localTri.V1);
Vector3.Subtract(ref v2, ref boxCenter, out localTri.V2);
return OriginBoxContains(ref boxHalfExtent, ref localTri) != ContainmentType.Disjoint;
}
/// <summary>
/// Determines whether the given frustum contains/intersects/is disjoint from the
/// given triangle.
/// </summary>
public static ContainmentType Contains(BoundingFrustum frustum, ref Triangle triangle)
{
return Contains(frustum, ref triangle.V0, ref triangle.V1, ref triangle.V2);
}
/// <summary>
/// Determines whether the given sphere contains/intersects/is disjoint from the
/// given triangle.
/// </summary>
public static ContainmentType Contains(ref BoundingSphere sphere, ref Triangle triangle)
{
return Contains(ref sphere, ref triangle.V0, ref triangle.V1, ref triangle.V2);
}
