/src/Geometry_GeometricTests/BPT_DynamicIntersectionTests.cpp

  1#include "BasicPrimitiveTests.h"
  2
  3bool BasicPrimitiveTests::IntersectingMovingSphereAgainstPlane(const BoundingSphere & sphere, const Plane & plane)
  4{
  5	/*
  6		Main Idea:
  7            -> Interpret the sphere center's movement as a line segment.
  8            -> Intersect the line segment with the plane using Section 5.3.1
  9                -> Displaced by sphere's radius.
 10
 11        Categorize the Sphere's movement:
 12            Since [...] indicates what side the plane the sphere is on
 13                -> dot(n, C) - d
 14
 15            Toward plane:
 16                -> dot(n, v) * dot(n, C-d) > 0
 17
 18            Away from plane:
 19                -> dot(n, v) * dot(n, C-d) < 0
 20
 21            Parallel to plane:
 22                -> dot(n, v) = 0
 23
 24        If Sphere is moving towards plane:
 25            -> Displace plane by sphere's radius towards sphere
 26            -> Interpret sphere center's movement as line segment.
 27                -> Intersect the line segment with plane.
 28                    -> Use Section 5.3.1
 29                    -> Insert movement segment as X into displaced plane equation.
 30                        -> Solve for "t"
 31	*/
 32	return false;
 33}
 34bool BasicPrimitiveTests::IntersectingMovingAABBAgainstPlane(const AABB & aabb, const Plane & plane)
 35{
 36	/*
 37		Main Idea:
 38            -> Separating axis test with plane normal "n" as sole axis.
 39            -> Reduce the test to a moving-sphere-against-plane test.
 40                -> By finding the projection radius of the AABB with respect to the plane's normal.
 41
 42        Let:
 43            Plane: 
 44                -> dot(n, X) = d
 45            AABB:
 46                -> Center:
 47                    -> C
 48                -> Local axis vectors:
 49                    -> u0, u1, u2
 50                -> Extents:
 51                    -> e0, e1, e2
 52
 53        Test:
 54            -> Get projection radius of ABB with respect to the plane's normal:
 55                -> r = e0 * |dot(u0,n)| + e1 * |dot(u1, n)| + e2 * |dot(u2, n)|
 56                
 57                -> Since u0, u1, u2 are axis-aligned and unit length:
 58                    -> r = e0 * |n.x| + e1 * |n.y| + e2 * |n.z|
 59
 60            Test for initial contact:
 61                -> length(dot(n, C) - d) <= r
 62           
 63            If AABB moving towards plane:
 64                -> Witness point for contact on AABB will be:
 65                    -> Q = C(t) - r * n
 66                        -> where C(t) = center location at time "t" during intersection.
 67
 68                    -> Q on place when:
 69                        -> dot(n, Q) = d
 70                            -> Solve for "t":
 71                                -> t = (    r + d - dot(n, C)    /    dot(n, v)    )
 72
 73	*/
 74	return false;
 75}
 76bool BasicPrimitiveTests::IntersectingMovingSphereAgainstSphere(const BoundingSphere & sphere_a, const BoundingSphere & sphere_b)
 77{
 78	/*
 79		Main Idea:
 80            Method 1:
 81                -> Get the displacement vector between sphere centers by expressing sphere movements as line segments.
 82                    -> Find the time when the spheres come into contact,
 83                        -> When the displacement vector's length = sum of their radii.
 84                        -> Requires quadratic formula.
 85            
 86            Method 2:
 87                -> Turn problem into moving sphere against stationary sphere 
 88                    -> subtract one velocity from both.
 89
 90                -> Turn problem into moving point (ray) against stationary sphere 
 91                    -> shrink radius of one and grow radius of the other.
 92                    -> Possible because spheres first come into contact when distance between them = radius_0 + radius_1
 93
 94                -> Solve with Section 5.3.2
 95
 96        Method 1 Details:
 97            Let:
 98                -> d(t) = displacement vector between sphere centers.
 99
100            Contact Condition:
101                -> dot(   d(t), d(t))   ) = exp( r0 + r1 , 2)
102                    -> where ri = radii.
103                    -> This equation is squared on both sides to avoid square roots.
104
105                -> Solve for "t"
106                    -> Encounters quadratic equation in "t".
107                        -> t = (    -b [plus/minus] sqrt(b*b - a*c)    /    a    )
108                            -> where a = dot(v, v)
109                            -> where b = dot(v, s)
110                            -> where c = dot(s, s) - r*r
111
112                        -> Number of real roots => number of intersections.
113                            -> For two real root, first contact at smaller "t" then separation at larger "t".
114	*/
115	return false;
116}
117bool BasicPrimitiveTests::IntersectingMovingSphereAgainstTriangle(const BoundingSphere & sphere, const Triangle & triangle)
118{
119	/*
120		Main Idea:
121            -> Both methods model the movement of the first point on the sphere (not sphere center) to come in contact with the polygon's plane as a line segment.
122                -> Call this line segment L.
123
124            -> Both methods split the test into two cases:
125                -> If the intersection is within the polygon.
126                -> If the intersection is not inside the polygon.
127
128        Movement of first point of sphere to make contact:
129            -> L(t) = D + t * v.
130                -> where v = sphere velocity.
131                -> where D = C - r * n
132                    -> where r = sphere radius
133                    -> where n = plane normal
134
135        Method 1:
136            -> Intersect L with polygon's plane, then test if intersection is within polygon.
137                -> If inside, intersects.
138
139                -> If outside, must check if sphere later intersects polygon at different point.
140                    -> If if it does, it will be at point Q on that triangle/polygon that is closest to L's interesction with the plane.
141                        -> Test if sphere hits Q by shooting a ray in verse from Q towards sphere.
142                            -> Ray: Q - t * v
143
144        Method 2:
145
146            Main Idea:
147                -> Ray test against the Minkowsky sum of Sphere and Triangle.
148
149            -> Intersect L with polygon's plane, then test if intersection is within polygon.
150                -> If inside, intersects.
151                -> If outside, continue.
152
153            -> Test moving sphere against each triangle edge.
154                -> Turn this into a test between the ray of the sphere's movement against the edges turned into cylinders with sphere's radius.
155                -> If no intersection, continue.
156
157            -> Test moving sphere with each vertex.
158                -> Equivalent to testing ray with vertices with sphere's radius.
159	*/
160	return false;
161}
162bool BasicPrimitiveTests::IntersectingMovingSphereAgainstAABB(const BoundingSphere & sphere, const AABB & aabb)
163{
164	/*
165		Main Idea:
166                -> Ray test with Minkowsky sum of Sphere and AABB   
167                    -> Minkowsky sum will be the box with faces expanded outwards by sphere's radius WITH corners beveled.
168
169        Let:
170            -> E = Minkowsky sum of sphere and AABB, without the beveled corners.
171                -> In other words, E = AABB with faces expanded outwards by sphere's radius.
172            
173            -> L = Line Segment representing sphere center's movement.
174
175        Procedure:
176            -> Intersect L with E.
177            -> If intersect,
178                -> Must split test into 3 cases based on if intersection is in face, vertex, or edge Voronoi region of AABB.
179
180                    Face Voronoi region:
181                        -> Intersects.
182
183                    Edge Voronoi region:
184                        -> Must intersect with the capsule of sphere's radius determined by the edge.
185
186                    Vertex Vornoi region:
187                        -> Must test for intersection with capsules of sphere's radius from all three edges coincident to the vertex.
188
189                            Potential speed-up:
190                                -> Before testing the three capsules,
191                                    -> Test L with vertex with sphere's radius.
192                                        -> If intersects, then test ends with this intersection.
193                                        -> If no intersection, continue testing the three edge capsules.
194	*/
195	return false;
196}
197bool BasicPrimitiveTests::IntersectingMovingAABBAgainstAABB(const AABB & aabb_a, const AABB & aabb_b)
198{
199	/*
200		Main Idea:
201            -> Moving Separating-Axis test using the three principle axes.
202	*/
203	return false;
204}