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+// This code is based off the Minkowski Portal Refinement algorithm by Gary Snethen in XenoCollide & Game Programming Gems 7.
+
+namespace mpr
+{
+ struct CubePlanes
+ {
+ const clipplanes &p;
+
+ CubePlanes(const clipplanes &p) : p(p) {}
+
+ vec center() const { return p.o; }
+
+ vec supportpoint(const vec &n) const
+ {
+ int besti = 7;
+ float bestd = n.dot(p.v[7]);
+ loopi(7)
+ {
+ float d = n.dot(p.v[i]);
+ if(d > bestd) { besti = i; bestd = d; }
+ }
+ return p.v[besti];
+ }
+ };
+
+ struct SolidCube
+ {
+ vec o;
+ int size;
+
+ SolidCube(float x, float y, float z, int size) : o(x, y, z), size(size) {}
+ SolidCube(const vec &o, int size) : o(o), size(size) {}
+ SolidCube(const ivec &o, int size) : o(o), size(size) {}
+
+ vec center() const { return vec(o).add(size/2); }
+
+ vec supportpoint(const vec &n) const
+ {
+ vec p(o);
+ if(n.x > 0) p.x += size;
+ if(n.y > 0) p.y += size;
+ if(n.z > 0) p.z += size;
+ return p;
+ }
+ };
+
+ struct Ent
+ {
+ physent *ent;
+
+ Ent(physent *ent) : ent(ent) {}
+
+ vec center() const { return vec(ent->o.x, ent->o.y, ent->o.z + (ent->aboveeye - ent->eyeheight)/2); }
+ };
+
+ struct EntOBB : Ent
+ {
+ matrix3 orient;
+ float zmargin;
+
+ EntOBB(physent *ent, float zmargin = 0) : Ent(ent), zmargin(zmargin)
+ {
+ orient.setyaw(ent->yaw*RAD);
+ }
+
+ vec center() const { return vec(ent->o.x, ent->o.y, ent->o.z + (ent->aboveeye - ent->eyeheight - zmargin)/2); }
+
+ vec contactface(const vec &wn, const vec &wdir) const
+ {
+ vec n = orient.transform(wn).div(vec(ent->xradius, ent->yradius, (ent->aboveeye + ent->eyeheight + zmargin)/2)),
+ dir = orient.transform(wdir),
+ an(fabs(n.x), fabs(n.y), dir.z ? fabs(n.z) : 0),
+ fn(0, 0, 0);
+ if(an.x > an.y)
+ {
+ if(an.x > an.z) fn.x = n.x*dir.x < 0 ? (n.x > 0 ? 1 : -1) : 0;
+ else if(an.z > 0) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
+ }
+ else if(an.y > an.z) fn.y = n.y*dir.y < 0 ? (n.y > 0 ? 1 : -1) : 0;
+ else if(an.z > 0) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
+ return orient.transposedtransform(fn);
+ }
+
+ vec localsupportpoint(const vec &ln) const
+ {
+ return vec(ln.x > 0 ? ent->xradius : -ent->xradius,
+ ln.y > 0 ? ent->yradius : -ent->yradius,
+ ln.z > 0 ? ent->aboveeye : -ent->eyeheight - zmargin);
+ }
+
+ vec supportpoint(const vec &n) const
+ {
+ return orient.transposedtransform(localsupportpoint(orient.transform(n))).add(ent->o);
+ }
+
+ float supportcoordneg(float a, float b, float c) const
+ {
+ return localsupportpoint(vec(-a, -b, -c)).dot(vec(a, b, c));
+ }
+ float supportcoord(float a, float b, float c) const
+ {
+ return localsupportpoint(vec(a, b, c)).dot(vec(a, b, c));
+ }
+
+ float left() const { return supportcoordneg(orient.a.x, orient.b.x, orient.c.x) + ent->o.x; }
+ float right() const { return supportcoord(orient.a.x, orient.b.x, orient.c.x) + ent->o.x; }
+ float back() const { return supportcoordneg(orient.a.y, orient.b.y, orient.c.y) + ent->o.y; }
+ float front() const { return supportcoord(orient.a.y, orient.b.y, orient.c.y) + ent->o.y; }
+ float bottom() const { return ent->o.z - ent->eyeheight - zmargin; }
+ float top() const { return ent->o.z + ent->aboveeye; }
+ };
+
+ struct EntFuzzy : Ent
+ {
+ EntFuzzy(physent *ent) : Ent(ent) {}
+
+ float left() const { return ent->o.x - ent->radius; }
+ float right() const { return ent->o.x + ent->radius; }
+ float back() const { return ent->o.y - ent->radius; }
+ float front() const { return ent->o.y + ent->radius; }
+ float bottom() const { return ent->o.z - ent->eyeheight; }
+ float top() const { return ent->o.z + ent->aboveeye; }
+ };
+
+ struct EntCylinder : EntFuzzy
+ {
+ float zmargin;
+
+ EntCylinder(physent *ent, float zmargin = 0) : EntFuzzy(ent), zmargin(zmargin) {}
+
+ vec center() const { return vec(ent->o.x, ent->o.y, ent->o.z + (ent->aboveeye - ent->eyeheight - zmargin)/2); }
+
+ float bottom() const { return ent->o.z - ent->eyeheight - zmargin; }
+
+ vec contactface(const vec &n, const vec &dir) const
+ {
+ float dxy = n.dot2(n)/(ent->radius*ent->radius), dz = n.z*n.z*4/(ent->aboveeye + ent->eyeheight + zmargin);
+ vec fn(0, 0, 0);
+ if(dz > dxy && dir.z) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
+ else if(n.dot2(dir) < 0)
+ {
+ fn.x = n.x;
+ fn.y = n.y;
+ fn.normalize();
+ }
+ return fn;
+ }
+
+ vec supportpoint(const vec &n) const
+ {
+ vec p(ent->o);
+ if(n.z > 0) p.z += ent->aboveeye;
+ else p.z -= ent->eyeheight + zmargin;
+ if(n.x || n.y)
+ {
+ float r = ent->radius / n.magnitude2();
+ p.x += n.x*r;
+ p.y += n.y*r;
+ }
+ return p;
+ }
+ };
+
+ struct EntCapsule : EntFuzzy
+ {
+ EntCapsule(physent *ent) : EntFuzzy(ent) {}
+
+ vec supportpoint(const vec &n) const
+ {
+ vec p(ent->o);
+ if(n.z > 0) p.z += ent->aboveeye - ent->radius;
+ else p.z -= ent->eyeheight - ent->radius;
+ p.add(vec(n).mul(ent->radius / n.magnitude()));
+ return p;
+ }
+ };
+
+ struct EntEllipsoid : EntFuzzy
+ {
+ EntEllipsoid(physent *ent) : EntFuzzy(ent) {}
+
+ vec supportpoint(const vec &dir) const
+ {
+ vec p(ent->o), n = vec(dir).normalize();
+ p.x += ent->radius*n.x;
+ p.y += ent->radius*n.y;
+ p.z += (ent->aboveeye + ent->eyeheight)/2*(1 + n.z) - ent->eyeheight;
+ return p;
+ }
+ };
+
+ struct Model
+ {
+ vec o, radius;
+ matrix3 orient;
+
+ Model(const vec &ent, const vec &center, const vec &radius, int yaw) : o(ent), radius(radius)
+ {
+ orient.setyaw(yaw*RAD);
+ o.add(orient.transposedtransform(center));
+ }
+
+ vec center() const { return o; }
+ };
+
+ struct ModelOBB : Model
+ {
+ ModelOBB(const vec &ent, const vec &center, const vec &radius, int yaw) :
+ Model(ent, center, radius, yaw)
+ {}
+
+ vec contactface(const vec &wn, const vec &wdir) const
+ {
+ vec n = orient.transform(wn).div(radius), dir = orient.transform(wdir),
+ an(fabs(n.x), fabs(n.y), dir.z ? fabs(n.z) : 0),
+ fn(0, 0, 0);
+ if(an.x > an.y)
+ {
+ if(an.x > an.z) fn.x = n.x*dir.x < 0 ? (n.x > 0 ? 1 : -1) : 0;
+ else if(an.z > 0) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
+ }
+ else if(an.y > an.z) fn.y = n.y*dir.y < 0 ? (n.y > 0 ? 1 : -1) : 0;
+ else if(an.z > 0) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
+ return orient.transposedtransform(fn);
+ }
+
+ vec supportpoint(const vec &n) const
+ {
+ vec ln = orient.transform(n), p(0, 0, 0);
+ if(ln.x > 0) p.x += radius.x;
+ else p.x -= radius.x;
+ if(ln.y > 0) p.y += radius.y;
+ else p.y -= radius.y;
+ if(ln.z > 0) p.z += radius.z;
+ else p.z -= radius.z;
+ return orient.transposedtransform(p).add(o);
+ }
+ };
+
+ struct ModelEllipse : Model
+ {
+ ModelEllipse(const vec &ent, const vec &center, const vec &radius, int yaw) :
+ Model(ent, center, radius, yaw)
+ {}
+
+ vec contactface(const vec &wn, const vec &wdir) const
+ {
+ vec n = orient.transform(wn).div(radius), dir = orient.transform(wdir);
+ float dxy = n.dot2(n), dz = n.z*n.z;
+ vec fn(0, 0, 0);
+ if(dz > dxy && dir.z) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
+ else if(n.dot2(dir) < 0)
+ {
+ fn.x = n.x*radius.y;
+ fn.y = n.y*radius.x;
+ fn.normalize();
+ }
+ return orient.transposedtransform(fn);
+ }
+
+ vec supportpoint(const vec &n) const
+ {
+ vec ln = orient.transform(n), p(0, 0, 0);
+ if(ln.z > 0) p.z += radius.z;
+ else p.z -= radius.z;
+ if(ln.x || ln.y)
+ {
+ float r = ln.magnitude2();
+ p.x += ln.x*radius.x/r;
+ p.y += ln.y*radius.y/r;
+ }
+ return orient.transposedtransform(p).add(o);
+ }
+ };
+
+ const float boundarytolerance = 1e-3f;
+
+ template<class T, class U>
+ bool collide(const T &p1, const U &p2)
+ {
+ // v0 = center of Minkowski difference
+ vec v0 = p2.center().sub(p1.center());
+ if(v0.iszero()) return true; // v0 and origin overlap ==> hit
+
+ // v1 = support in direction of origin
+ vec n = vec(v0).neg();
+ vec v1 = p2.supportpoint(n).sub(p1.supportpoint(vec(n).neg()));
+ if(v1.dot(n) <= 0) return false; // origin outside v1 support plane ==> miss
+
+ // v2 = support perpendicular to plane containing origin, v0 and v1
+ n.cross(v1, v0);
+ if(n.iszero()) return true; // v0, v1 and origin colinear (and origin inside v1 support plane) == > hit
+ vec v2 = p2.supportpoint(n).sub(p1.supportpoint(vec(n).neg()));
+ if(v2.dot(n) <= 0) return false; // origin outside v2 support plane ==> miss
+
+ // v3 = support perpendicular to plane containing v0, v1 and v2
+ n.cross(v0, v1, v2);
+
+ // If the origin is on the - side of the plane, reverse the direction of the plane
+ if(n.dot(v0) > 0)
+ {
+ swap(v1, v2);
+ n.neg();
+ }
+
+ ///
+ // Phase One: Find a valid portal
+
+ loopi(100)
+ {
+ // Obtain the next support point
+ vec v3 = p2.supportpoint(n).sub(p1.supportpoint(vec(n).neg()));
+ if(v3.dot(n) <= 0) return false; // origin outside v3 support plane ==> miss
+
+ // If origin is outside (v1,v0,v3), then portal is invalid -- eliminate v2 and find new support outside face
+ vec v3xv0;
+ v3xv0.cross(v3, v0);
+ if(v1.dot(v3xv0) < 0)
+ {
+ v2 = v3;
+ n.cross(v0, v1, v3);
+ continue;
+ }
+
+ // If origin is outside (v3,v0,v2), then portal is invalid -- eliminate v1 and find new support outside face
+ if(v2.dot(v3xv0) > 0)
+ {
+ v1 = v3;
+ n.cross(v0, v3, v2);
+ continue;
+ }
+
+ ///
+ // Phase Two: Refine the portal
+
+ for(int j = 0;; j++)
+ {
+ // Compute outward facing normal of the portal
+ n.cross(v1, v2, v3);
+
+ // If the origin is inside the portal, we have a hit
+ if(n.dot(v1) >= 0) return true;
+
+ n.normalize();
+
+ // Find the support point in the direction of the portal's normal
+ vec v4 = p2.supportpoint(n).sub(p1.supportpoint(vec(n).neg()));
+
+ // If the origin is outside the support plane or the boundary is thin enough, we have a miss
+ if(v4.dot(n) <= 0 || vec(v4).sub(v3).dot(n) <= boundarytolerance || j > 100) return false;
+
+ // Test origin against the three planes that separate the new portal candidates: (v1,v4,v0) (v2,v4,v0) (v3,v4,v0)
+ // Note: We're taking advantage of the triple product identities here as an optimization
+ // (v1 % v4) * v0 == v1 * (v4 % v0) > 0 if origin inside (v1, v4, v0)
+ // (v2 % v4) * v0 == v2 * (v4 % v0) > 0 if origin inside (v2, v4, v0)
+ // (v3 % v4) * v0 == v3 * (v4 % v0) > 0 if origin inside (v3, v4, v0)
+ vec v4xv0;
+ v4xv0.cross(v4, v0);
+ if(v1.dot(v4xv0) > 0)
+ {
+ if(v2.dot(v4xv0) > 0) v1 = v4; // Inside v1 & inside v2 ==> eliminate v1
+ else v3 = v4; // Inside v1 & outside v2 ==> eliminate v3
+ }
+ else
+ {
+ if(v3.dot(v4xv0) > 0) v2 = v4; // Outside v1 & inside v3 ==> eliminate v2
+ else v1 = v4; // Outside v1 & outside v3 ==> eliminate v1
+ }
+ }
+ }
+ return false;
+ }
+
+ template<class T, class U>
+ bool collide(const T &p1, const U &p2, vec *contactnormal, vec *contactpoint1, vec *contactpoint2)
+ {
+ // v0 = center of Minkowski sum
+ vec v01 = p1.center();
+ vec v02 = p2.center();
+ vec v0 = vec(v02).sub(v01);
+
+ // Avoid case where centers overlap -- any direction is fine in this case
+ if(v0.iszero()) v0 = vec(0, 0, 1e-5f);
+
+ // v1 = support in direction of origin
+ vec n = vec(v0).neg();
+ vec v11 = p1.supportpoint(vec(n).neg());
+ vec v12 = p2.supportpoint(n);
+ vec v1 = vec(v12).sub(v11);
+ if(v1.dot(n) <= 0)
+ {
+ if(contactnormal) *contactnormal = n;
+ return false;
+ }
+
+ // v2 - support perpendicular to v1,v0
+ n.cross(v1, v0);
+ if(n.iszero())
+ {
+ n = vec(v1).sub(v0);
+ n.normalize();
+ if(contactnormal) *contactnormal = n;
+ if(contactpoint1) *contactpoint1 = v11;
+ if(contactpoint2) *contactpoint2 = v12;
+ return true;
+ }
+ vec v21 = p1.supportpoint(vec(n).neg());
+ vec v22 = p2.supportpoint(n);
+ vec v2 = vec(v22).sub(v21);
+ if(v2.dot(n) <= 0)
+ {
+ if(contactnormal) *contactnormal = n;
+ return false;
+ }
+
+ // Determine whether origin is on + or - side of plane (v1,v0,v2)
+ n.cross(v0, v1, v2);
+ ASSERT( !n.iszero() );
+ // If the origin is on the - side of the plane, reverse the direction of the plane
+ if(n.dot(v0) > 0)
+ {
+ swap(v1, v2);
+ swap(v11, v21);
+ swap(v12, v22);
+ n.neg();
+ }
+
+ ///
+ // Phase One: Identify a portal
+
+ loopi(100)
+ {
+ // Obtain the support point in a direction perpendicular to the existing plane
+ // Note: This point is guaranteed to lie off the plane
+ vec v31 = p1.supportpoint(vec(n).neg());
+ vec v32 = p2.supportpoint(n);
+ vec v3 = vec(v32).sub(v31);
+ if(v3.dot(n) <= 0)
+ {
+ if(contactnormal) *contactnormal = n;
+ return false;
+ }
+
+ // If origin is outside (v1,v0,v3), then eliminate v2 and loop
+ vec v3xv0;
+ v3xv0.cross(v3, v0);
+ if(v1.dot(v3xv0) < 0)
+ {
+ v2 = v3;
+ v21 = v31;
+ v22 = v32;
+ n.cross(v0, v1, v3);
+ continue;
+ }
+
+ // If origin is outside (v3,v0,v2), then eliminate v1 and loop
+ if(v2.dot(v3xv0) > 0)
+ {
+ v1 = v3;
+ v11 = v31;
+ v12 = v32;
+ n.cross(v0, v3, v2);
+ continue;
+ }
+
+ bool hit = false;
+
+ ///
+ // Phase Two: Refine the portal
+
+ // We are now inside of a wedge...
+ for(int j = 0;; j++)
+ {
+ // Compute normal of the wedge face
+ n.cross(v1, v2, v3);
+
+ // Can this happen??? Can it be handled more cleanly?
+ if(n.iszero())
+ {
+ ASSERT(0);
+ return true;
+ }
+
+ n.normalize();
+
+ // If the origin is inside the wedge, we have a hit
+ if(n.dot(v1) >= 0 && !hit)
+ {
+ if(contactnormal) *contactnormal = n;
+
+ // Compute the barycentric coordinates of the origin
+ if(contactpoint1 || contactpoint2)
+ {
+ float b0 = v3.scalartriple(v1, v2),
+ b1 = v0.scalartriple(v3, v2),
+ b2 = v3.scalartriple(v0, v1),
+ b3 = v0.scalartriple(v2, v1),
+ sum = b0 + b1 + b2 + b3;
+ if(sum <= 0)
+ {
+ b0 = 0;
+ b1 = n.scalartriple(v2, v3);
+ b2 = n.scalartriple(v3, v1);
+ b3 = n.scalartriple(v1, v2);
+ sum = b1 + b2 + b3;
+ }
+ if(contactpoint1)
+ *contactpoint1 = (vec(v01).mul(b0).add(vec(v11).mul(b1)).add(vec(v21).mul(b2)).add(vec(v31).mul(b3))).mul(1.0f/sum);
+ if(contactpoint2)
+ *contactpoint2 = (vec(v02).mul(b0).add(vec(v12).mul(b1)).add(vec(v22).mul(b2)).add(vec(v32).mul(b3))).mul(1.0f/sum);
+ }
+
+ // HIT!!!
+ hit = true;
+ }
+
+ // Find the support point in the direction of the wedge face
+ vec v41 = p1.supportpoint(vec(n).neg());
+ vec v42 = p2.supportpoint(n);
+ vec v4 = vec(v42).sub(v41);
+
+ // If the boundary is thin enough or the origin is outside the support plane for the newly discovered vertex, then we can terminate
+ if(v4.dot(n) <= 0 || vec(v4).sub(v3).dot(n) <= boundarytolerance || j > 100)
+ {
+ if(contactnormal) *contactnormal = n;
+ return hit;
+ }
+
+ // Test origin against the three planes that separate the new portal candidates: (v1,v4,v0) (v2,v4,v0) (v3,v4,v0)
+ // Note: We're taking advantage of the triple product identities here as an optimization
+ // (v1 % v4) * v0 == v1 * (v4 % v0) > 0 if origin inside (v1, v4, v0)
+ // (v2 % v4) * v0 == v2 * (v4 % v0) > 0 if origin inside (v2, v4, v0)
+ // (v3 % v4) * v0 == v3 * (v4 % v0) > 0 if origin inside (v3, v4, v0)
+ vec v4xv0;
+ v4xv0.cross(v4, v0);
+ if(v1.dot(v4xv0) > 0) // Compute the tetrahedron dividing face d1 = (v4,v0,v1)
+ {
+ if(v2.dot(v4xv0) > 0) // Compute the tetrahedron dividing face d2 = (v4,v0,v2)
+ {
+ // Inside d1 & inside d2 ==> eliminate v1
+ v1 = v4;
+ v11 = v41;
+ v12 = v42;
+ }
+ else
+ {
+ // Inside d1 & outside d2 ==> eliminate v3
+ v3 = v4;
+ v31 = v41;
+ v32 = v42;
+ }
+ }
+ else
+ {
+ if(v3.dot(v4xv0) > 0) // Compute the tetrahedron dividing face d3 = (v4,v0,v3)
+ {
+ // Outside d1 & inside d3 ==> eliminate v2
+ v2 = v4;
+ v21 = v41;
+ v22 = v42;
+ }
+ else
+ {
+ // Outside d1 & outside d3 ==> eliminate v1
+ v1 = v4;
+ v11 = v41;
+ v12 = v42;
+ }
+ }
+ }
+ }
+ return false;
+ }
+}
+
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