public static double GetRotationAngle(Vector3D axis, Vector3D startNormal, Vector3D endNormal)
{
if (startNormal.IsSame(endNormal))
return 0;
if (startNormal.IsSame(-endNormal))
return 180;
var cross = startNormal.Cross(axis);
return cross.IsSame(endNormal) ? 90 : -90;
}
public static double GetRotationAngle(Vector3D axis, Vector3D startNormal, Vector3D endNormal)
{
if (startNormal.IsSame(endNormal))
return Direction.Zero;
if (startNormal.IsSame(-endNormal))
return Direction.Twice;
var cross = startNormal.Cross(axis);
return cross.IsSame(endNormal) ? Direction.Clockwise : Direction.CounterClockwise;
}
public Direction(Vector3D front, Vector3D up)
{
Origin = new Point3D(0, 0, 0);
Front = front;
Back = -Front;
Up = up;
Down = -Up;
Right = up.Cross(front);
Left = -Right;
All = new[] { Front, Back, Right, Left, Up, Down };
}
/// <summary>
/// The three points p0, p0 + u and p0 + v make up a triangle. If 'divisions' is 1 and 'doQuad' is false,<para/>
/// exactly this triangle will be added to the mesh. If 'divisions' is larger than 1, the triangle will be subdivided.<para/>
/// If 'doQuad' is true, the triangle is expanded to a parallelogram using the fourth point p0 + u + v.
/// </summary>
public static void AddTriangles(MeshGeometry3D mesh, int divisions, Point3D p0, Vector3D u, Vector3D v, double tu0, double tu1, bool doQuad = true)
{
TextureTransform tt = new TextureTransform(0, divisions, tu0, tu1, 1, 0);
Vector3D du = u / (double)divisions;
Vector3D dv = v / (double)divisions;
Vector3D n = u.Cross(v);
n.Normalize();
for (int iv = 0; iv < divisions; iv++)
{
int iuMax = doQuad ? divisions : divisions - iv;
for (int iu = 0; iu < iuMax; iu++)
{
Point3D p1 = p0 + iu * du + iv * dv;
Point3D p2 = p1 + du;
Point3D p3 = p1 + dv;
Point3D p4 = p2 + dv;
mesh.Positions.Add(p1);
mesh.Normals.Add(n);
mesh.TextureCoordinates.Add(tt.Transform(iu, iv));
mesh.Positions.Add(p2);
mesh.Normals.Add(n);
mesh.TextureCoordinates.Add(tt.Transform(iu + 1, iv));
mesh.Positions.Add(p3);
mesh.Normals.Add(n);
mesh.TextureCoordinates.Add(tt.Transform(iu, iv + 1));
int i = mesh.Positions.Count - 3;
AddTriangleIndices(mesh, i, i + 1, i + 2);
bool doUpperTriangle = doQuad ? true : iu < iuMax - 1;
if (doUpperTriangle)
{
mesh.Positions.Add(p4);
mesh.Normals.Add(n);
mesh.TextureCoordinates.Add(tt.Transform(iu + 1, iv + 1));
AddTriangleIndices(mesh, i + 1, i + 3, i + 2);
continue;
}
}
}
}
public static Transform3D Rotate(Vector3D axis, Point3D point, Vector3D startNormal, Vector3D endNormal)
{
var angle = GetRotationAngle(axis, startNormal, endNormal);
var cross = startNormal.Cross(axis);
return Rotate(axis, point, angle);
}
public static Transform3D GetRotationTransform(Point3D point, Vector3D startNormal, Vector3D endNormal)
{
var axis = startNormal.Cross(endNormal);
return GetRotationTransform(axis, point, startNormal, endNormal);
}
public static List<double> RayMeshIntersections(Point3D orig, Vector3D dir, MeshGeometry3D mesh, bool frontFacesOnly)
{
List<double> result = new List<double>();
if (mesh == null || !dir.IsValid())
return result;
double epsilon = 1E-9;
Int32Collection indices = mesh.TriangleIndices;
Point3DCollection positions = mesh.Positions;
for (int i = 0; i < indices.Count; i += 3)
{
Point3D vert0 = positions[indices[i]];
Point3D vert1 = positions[indices[i + 1]];
Point3D vert2 = positions[indices[i + 2]];
//--- find vectors for two edges sharing vert0
Vector3D edge1 = vert1 - vert0;
Vector3D edge2 = vert2 - vert0;
//--- begin calculating determinant also used to calculate U parameter
Vector3D pvec = dir.Cross(edge2);
//--- if determinant is near zero ray lies in plane of triangle
double det = edge1.Dot(pvec);
if (det < epsilon)
{
if (frontFacesOnly)
continue;
else if (det > -epsilon)
continue;
}
double inv_det = 1.0 / det;
//--- calculate distance from vert0 to ray origin
Vector3D tvec = orig - vert0;
//--- calculate U parameter and test bounds
double u = tvec.Dot(pvec) * inv_det;
if (u < 0.0 || u > 1.0)
continue;
//--- prepare to test V parameter
Vector3D qvec = tvec.Cross(edge1);
//--- calculate V parameter and test bounds
double v = dir.Dot(qvec) * inv_det;
if (v < 0.0 || u + v > 1.0)
continue;
//--- calculate t scale parameters, ray intersects triangle
double t = edge2.Dot(qvec) * inv_det;
result.Add(t);
}
return result;
}