; -------------------------------------------------------------------------------------------------------------------
; This function returns TRUE if a ray intersects a triangle.
; It also calculates the UV coordinates of said colision as part of the intersection test,
; but does not return them.
;
; V0xyz, V1xyz, and V2xyz are the locations of the three vertices of the triangle.
;
; These vertices should be wound in CLOCKWISE order. By clockwise I mean that if you face the front side of the
; trianngle, the vertcies go around the trangle from V0 to V1 to V2 in a clockwise direction. This is the same
; as Blitz, so just pass the vertcies for a triangle in the same order that Blitz does.
;
; The UV's generated by the function are set up as follows:
; V0 is the location of UV(0,0)
; V1 is the location of UV(0,1)
; V2 is the location of UV(1,0)
;
; This is useful to know if you want to know the exact location in texture space of the collision.
; You can easily modify the function to return the values of T#, U#, and V#.
;
; Pxyz is a the start of the line.
; Triangles which are "behind" this point are ignored.
; "Behind" is defined as the direction opposite that which Dxyz points in.
;
; Dxyz is a vector providing the slope of the line.
; Dxyz does not have to be normalized.
;
; If Extend_To_Infinity is set to false, then the length of Dxyz is how far the ray extends.
; So if you want an endpoint on your ray beyond which no triangles will be detected, subtract the position
; of Pxyz from your endpoint's position, and pass that ato the function as Dxyz. Ie: (Dx = P2x-P1x)
;
; If Cull_Backfaces is set to true, then if the specified ray passes through the triangle from it's back side, then
; it will not register that it hit that triangle.
; -------------------------------------------------------------------------------------------------------------------
Function Ray_Intersect_Triangle(Px#, Py#, Pz#, Dx#, Dy#, Dz#, V0x#, V0y#, V0z#, V1x#, V1y#, V1z#, V2x#, V2y#, V2z#, Extend_To_Infinity=True, Cull_Backfaces=False)
; crossproduct(b,c) =
; ax = (by * cz) - (cy * bz)
; ay = (bz * cx) - (cz * bx)
; az = (bx * cy) - (cx * by)
; dotproduct(v,q) =
; (vx * qx) + (vy * qy) + (vz * qz)
; DP = 1 = Vectors point in same direction. ( 0 degrees of seperation)
; DP = 0 = Vectors are perpendicular to one another. ( 90 degrees of seperation)
; DP = -1 = Vectors point in opposite directions. (180 degrees of seperation)
;
; The dot product is also reffered to as "the determinant" or "the inner product"
; Calculate the vector that represents the first side of the triangle.
E1x# = V2x# - V0x#
E1y# = V2y# - V0y#
E1z# = V2z# - V0z#
; Calculate the vector that represents the second side of the triangle.
E2x# = V1x# - V0x#
E2y# = V1y# - V0y#
E2z# = V1z# - V0z#
; Calculate a vector which is perpendicular to the vector between point 0 and point 1,
; and the direction vector for the ray.
; Hxyz = Crossproduct(Dxyz, E2xyz)
Hx# = (Dy# * E2z#) - (E2y# * Dz#)
Hy# = (Dz# * E2x#) - (E2z# * Dx#)
Hz# = (Dx# * E2y#) - (E2x# * Dy#)
; Calculate the dot product of the above vector and the vector between point 0 and point 2.
A# = (E1x# * Hx#) + (E1y# * Hy#) + (E1z# * Hz#)
; If we should ignore triangles the ray passes through the back side of,
; and the ray points in the same direction as the normal of the plane,
; then the ray passed through the back side of the plane,
; and the ray does not intersect the plane the triangle lies in.
If (Cull_Backfaces = True) And (A# >= 0) Then Return False
; If the ray is almost parralel to the plane,
; then the ray does not intersect the plane the triangle lies in.
If (A# > -0.00001) And (A# < 0.00001) Then Return False
; Inverse Determinant. (Dot Product)
; (Scaling factor for UV's?)
F# = 1.0 / A#
; Calculate a vector between the starting point of our ray, and the first point of the triangle,
; which is at UV(0,0)
Sx# = Px# - V0x#
Sy# = Py# - V0y#
Sz# = Pz# - V0z#
; Calculate the U coordinate of the intersection point.
;
; Sxyz is the vector between the start of our ray and the first point of the triangle.
; Hxyz is the normal of our triangle.
;
; U# = F# * (DotProduct(Sxyz, Hxyz))
U# = F# * ((Sx# * Hx#) + (Sy# * Hy#) + (Sz# * Hz#))
; Is the U coordinate outside the range of values inside the triangle?
If (U# < 0.0) Or (U# > 1.0)
; The ray has intersected the plane outside the triangle.
Return False
EndIf
; Not sure what this is, but it's definitely NOT the intersection point.
;
; Sxyz is the vector from the starting point of the ray to the first corner of the triangle.
; E1xyz is the vector which represents the first side of the triangle.
; The crossproduct of these two would be a vector which is perpendicular to both.
;
; Qxyz = CrossProduct(Sxyz, E1xyz)
Qx# = (Sy# * E1z#) - (E1y# * Sz#)
Qy# = (Sz# * E1x#) - (E1z# * Sx#)
Qz# = (Sx# * E1y#) - (E1x# * Sy#)
; Calculate the V coordinate of the intersection point.
;
; Dxyz is the vector which represents the direction the ray is pointing in.
; Qxyz is the intersection point I think?
;
; V# = F# * DotProduct(Dxyz, Qxyz)
V# = F# * ((Dx# * Qx#) + (Dy# * Qy#) + (Dz# * Qz#))
; Is the V coordinate outside the range of values inside the triangle?
; Does U+V exceed 1.0?
If (V# < 0.0) Or ((U# + V#) > 1.0)
; The ray has intersected the plane outside the triangle.
Return False
; The reason we check U+V is because if you imagine the triangle as half a square, U=1 V=1 would
; be in the lower left hand corner which would be in the lower left triangle making up the square.
; We are looking for the upper right triangle, and if you think about it, U+V will always be less
; than or equal to 1.0 if the point is in the upper right of the triangle.
EndIf
; Calculate the distance of the intersection point from the starting point of the ray, Pxyz.
; This distance is scaled so that at Pxyz, the start of the ray, T=0, and at Dxyz, the end of the ray, T=1.
; If the intersection point is behind Pxyz, then T will be negative, and if the intersection point is
; beyond Dxyz then T will be greater than 1.
T# = F# * ((E2x# * Qx#) + (E2y# * Qy#) + (E2z# * Qz#))
; If the triangle is behind Pxyz, ignore this intersection.
; We want a directional ray, which only intersects triangles in the direction it points.
If (T# < 0) Then Return False
; If the plane is beyond Dxyz, amd we do not want the ray to extend to infinity, then ignore this intersection.
If (Extend_To_Infinity = False) And (T# > 1) Return False
; The ray intersects the triangle!
Return True
End Function
; -------------------------------------------------------------------------------------------------------------------
; This function returns true if a ray intersects a mesh.
;
; This function differs from LinePick in that the specified mesh does not need to have a pickmode set,
; and this function can optionally ignore backfacing polygons in the mesh. So if you do a pick from
; inside a mesh, it will not register a hit.
; -------------------------------------------------------------------------------------------------------------------
Function Ray_Intersect_Mesh(Mesh, Px#, Py#, Pz#, Dx#, Dy#, Dz#, Extend_To_Infinity=True, Cull_Backfaces=False)
Surfaces = CountSurfaces(Mesh)
; Make sure there's a surface, because the mesh might be empty.
If Surfaces > 0
For SurfaceLoop = 1 To Surfaces
Surface = GetSurface(Mesh, SurfaceLoop)
; Examine all triangles in this surface.
Tris = CountTriangles(Surface)
For TriLoop = 0 To Tris-1
V0 = TriangleVertex(Surface, TriLoop, 0)
V1 = TriangleVertex(Surface, TriLoop, 1)
V2 = TriangleVertex(Surface, TriLoop, 2)
V0x# = VertexX#(Surface, V0)
V0y# = VertexY#(Surface, V0)
V0z# = VertexZ#(Surface, V0)
V1x# = VertexX#(Surface, V1)
V1y# = VertexY#(Surface, V1)
V1z# = VertexZ#(Surface, V1)
V2x# = VertexX#(Surface, V2)
V2y# = VertexY#(Surface, V2)
V2z# = VertexZ#(Surface, V2)
TFormPoint V0x#, V0y#, V0z#, Mesh, 0
V0x# = TFormedX#()
V0y# = TFormedY#()
V0z# = TFormedZ#()
TFormPoint V1x#, V1y#, V1z#, Mesh, 0
V1x# = TFormedX#()
V1y# = TFormedY#()
V1z# = TFormedZ#()
TFormPoint V2x#, V2y#, V2z#, Mesh, 0
V2x# = TFormedX#()
V2y# = TFormedY#()
V2z# = TFormedZ#()
Intersected = Ray_Intersect_Triangle(Px#, Py#, Pz#, Dx#, Dy#, Dz#, V0x#, V0y#, V0z#, V1x#, V1y#, V1z#, V2x#, V2y#, V2z#, Extend_To_Infinity, Cull_Backfaces)
If Intersected Then Return True
Next
Next
EndIf
Return False
End Function
