570 lines
20 KiB
C++
570 lines
20 KiB
C++
// This code is based off the Minkowski Portal Refinement algorithm by Gary Snethen in XenoCollide & Game Programming Gems 7.
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namespace mpr
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{
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struct CubePlanes
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{
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const clipplanes &p;
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CubePlanes(const clipplanes &p) : p(p) {}
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vec center() const { return p.o; }
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vec supportpoint(const vec &n) const
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{
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int besti = 7;
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float bestd = n.dot(p.v[7]);
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loopi(7)
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{
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float d = n.dot(p.v[i]);
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if(d > bestd) { besti = i; bestd = d; }
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}
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return p.v[besti];
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}
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};
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struct SolidCube
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{
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vec o;
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int size;
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SolidCube(float x, float y, float z, int size) : o(x, y, z), size(size) {}
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SolidCube(const vec &o, int size) : o(o), size(size) {}
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SolidCube(const ivec &o, int size) : o(o), size(size) {}
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vec center() const { return vec(o).add(size/2); }
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vec supportpoint(const vec &n) const
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{
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vec p(o);
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if(n.x > 0) p.x += size;
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if(n.y > 0) p.y += size;
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if(n.z > 0) p.z += size;
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return p;
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}
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};
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struct Ent
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{
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physent *ent;
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Ent(physent *ent) : ent(ent) {}
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vec center() const { return vec(ent->o.x, ent->o.y, ent->o.z + (ent->aboveeye - ent->eyeheight)/2); }
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};
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struct EntOBB : Ent
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{
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matrix3 orient;
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EntOBB(physent *ent) : Ent(ent)
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{
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orient.setyaw(ent->yaw*RAD);
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}
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vec contactface(const vec &wn, const vec &wdir) const
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{
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vec n = orient.transform(wn).div(vec(ent->xradius, ent->yradius, (ent->aboveeye + ent->eyeheight)/2)),
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dir = orient.transform(wdir),
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an(fabs(n.x), fabs(n.y), dir.z ? fabs(n.z) : 0),
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fn(0, 0, 0);
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if(an.x > an.y)
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{
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if(an.x > an.z) fn.x = n.x*dir.x < 0 ? (n.x > 0 ? 1 : -1) : 0;
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else if(an.z > 0) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
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}
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else if(an.y > an.z) fn.y = n.y*dir.y < 0 ? (n.y > 0 ? 1 : -1) : 0;
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else if(an.z > 0) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
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return orient.transposedtransform(fn);
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}
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vec localsupportpoint(const vec &ln) const
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{
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return vec(ln.x > 0 ? ent->xradius : -ent->xradius,
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ln.y > 0 ? ent->yradius : -ent->yradius,
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ln.z > 0 ? ent->aboveeye : -ent->eyeheight);
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}
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vec supportpoint(const vec &n) const
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{
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return orient.transposedtransform(localsupportpoint(orient.transform(n))).add(ent->o);
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}
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float supportcoordneg(const vec &p) const
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{
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return localsupportpoint(vec(p).neg()).dot(p);
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}
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float supportcoord(const vec &p) const
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{
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return localsupportpoint(p).dot(p);
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}
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float left() const { return supportcoordneg(orient.a) + ent->o.x; }
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float right() const { return supportcoord(orient.a) + ent->o.x; }
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float back() const { return supportcoordneg(orient.b) + ent->o.y; }
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float front() const { return supportcoord(orient.b) + ent->o.y; }
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float bottom() const { return ent->o.z - ent->eyeheight; }
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float top() const { return ent->o.z + ent->aboveeye; }
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};
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struct EntFuzzy : Ent
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{
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EntFuzzy(physent *ent) : Ent(ent) {}
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float left() const { return ent->o.x - ent->radius; }
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float right() const { return ent->o.x + ent->radius; }
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float back() const { return ent->o.y - ent->radius; }
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float front() const { return ent->o.y + ent->radius; }
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float bottom() const { return ent->o.z - ent->eyeheight; }
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float top() const { return ent->o.z + ent->aboveeye; }
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};
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struct EntCylinder : EntFuzzy
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{
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EntCylinder(physent *ent) : EntFuzzy(ent) {}
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vec contactface(const vec &n, const vec &dir) const
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{
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float dxy = n.dot2(n)/(ent->radius*ent->radius), dz = n.z*n.z*4/(ent->aboveeye + ent->eyeheight);
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vec fn(0, 0, 0);
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if(dz > dxy && dir.z) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
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else if(n.dot2(dir) < 0)
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{
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fn.x = n.x;
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fn.y = n.y;
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fn.normalize();
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}
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return fn;
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}
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vec supportpoint(const vec &n) const
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{
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vec p(ent->o);
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if(n.z > 0) p.z += ent->aboveeye;
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else p.z -= ent->eyeheight;
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if(n.x || n.y)
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{
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float r = ent->radius / n.magnitude2();
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p.x += n.x*r;
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p.y += n.y*r;
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}
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return p;
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}
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};
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struct EntCapsule : EntFuzzy
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{
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EntCapsule(physent *ent) : EntFuzzy(ent) {}
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vec supportpoint(const vec &n) const
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{
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vec p(ent->o);
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if(n.z > 0) p.z += ent->aboveeye - ent->radius;
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else p.z -= ent->eyeheight - ent->radius;
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p.add(vec(n).mul(ent->radius / n.magnitude()));
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return p;
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}
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};
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struct EntEllipsoid : EntFuzzy
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{
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EntEllipsoid(physent *ent) : EntFuzzy(ent) {}
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vec supportpoint(const vec &dir) const
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{
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vec p(ent->o), n = vec(dir).normalize();
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p.x += ent->radius*n.x;
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p.y += ent->radius*n.y;
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p.z += (ent->aboveeye + ent->eyeheight)/2*(1 + n.z) - ent->eyeheight;
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return p;
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}
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};
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struct Model
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{
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vec o, radius;
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matrix3 orient;
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Model(const vec &ent, const vec ¢er, const vec &radius, int yaw, int pitch, int roll) : o(ent), radius(radius)
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{
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orient.identity();
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if(roll) orient.rotate_around_y(sincosmod360(roll));
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if(pitch) orient.rotate_around_x(sincosmod360(-pitch));
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if(yaw) orient.rotate_around_z(sincosmod360(-yaw));
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o.add(orient.transposedtransform(center));
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}
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vec center() const { return o; }
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};
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struct ModelOBB : Model
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{
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ModelOBB(const vec &ent, const vec ¢er, const vec &radius, int yaw, int pitch, int roll) :
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Model(ent, center, radius, yaw, pitch, roll)
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{}
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vec contactface(const vec &wn, const vec &wdir) const
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{
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vec n = orient.transform(wn).div(radius), dir = orient.transform(wdir),
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an(fabs(n.x), fabs(n.y), dir.z ? fabs(n.z) : 0),
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fn(0, 0, 0);
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if(an.x > an.y)
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{
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if(an.x > an.z) fn.x = n.x*dir.x < 0 ? (n.x > 0 ? 1 : -1) : 0;
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else if(an.z > 0) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
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}
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else if(an.y > an.z) fn.y = n.y*dir.y < 0 ? (n.y > 0 ? 1 : -1) : 0;
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else if(an.z > 0) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
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return orient.transposedtransform(fn);
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}
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vec supportpoint(const vec &n) const
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{
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vec ln = orient.transform(n), p(0, 0, 0);
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if(ln.x > 0) p.x += radius.x;
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else p.x -= radius.x;
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if(ln.y > 0) p.y += radius.y;
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else p.y -= radius.y;
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if(ln.z > 0) p.z += radius.z;
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else p.z -= radius.z;
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return orient.transposedtransform(p).add(o);
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}
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};
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struct ModelEllipse : Model
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{
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ModelEllipse(const vec &ent, const vec ¢er, const vec &radius, int yaw, int pitch, int roll) :
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Model(ent, center, radius, yaw, pitch, roll)
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{}
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vec contactface(const vec &wn, const vec &wdir) const
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{
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vec n = orient.transform(wn).div(radius), dir = orient.transform(wdir);
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float dxy = n.dot2(n), dz = n.z*n.z;
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vec fn(0, 0, 0);
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if(dz > dxy && dir.z) fn.z = n.z*dir.z < 0 ? (n.z > 0 ? 1 : -1) : 0;
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else if(n.dot2(dir) < 0)
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{
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fn.x = n.x*radius.y;
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fn.y = n.y*radius.x;
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fn.normalize();
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}
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return orient.transposedtransform(fn);
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}
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vec supportpoint(const vec &n) const
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{
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vec ln = orient.transform(n), p(0, 0, 0);
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if(ln.z > 0) p.z += radius.z;
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else p.z -= radius.z;
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if(ln.x || ln.y)
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{
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float r = ln.magnitude2();
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p.x += ln.x*radius.x/r;
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p.y += ln.y*radius.y/r;
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}
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return orient.transposedtransform(p).add(o);
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}
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};
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const float boundarytolerance = 1e-3f;
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template<class T, class U>
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bool collide(const T &p1, const U &p2)
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{
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// v0 = center of Minkowski difference
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vec v0 = p2.center().sub(p1.center());
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if(v0.iszero()) return true; // v0 and origin overlap ==> hit
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// v1 = support in direction of origin
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vec n = vec(v0).neg();
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vec v1 = p2.supportpoint(n).sub(p1.supportpoint(vec(n).neg()));
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if(v1.dot(n) <= 0) return false; // origin outside v1 support plane ==> miss
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// v2 = support perpendicular to plane containing origin, v0 and v1
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n.cross(v1, v0);
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if(n.iszero()) return true; // v0, v1 and origin colinear (and origin inside v1 support plane) == > hit
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vec v2 = p2.supportpoint(n).sub(p1.supportpoint(vec(n).neg()));
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if(v2.dot(n) <= 0) return false; // origin outside v2 support plane ==> miss
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// v3 = support perpendicular to plane containing v0, v1 and v2
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n.cross(v0, v1, v2);
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// If the origin is on the - side of the plane, reverse the direction of the plane
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if(n.dot(v0) > 0)
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{
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swap(v1, v2);
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n.neg();
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}
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///
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// Phase One: Find a valid portal
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loopi(100)
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{
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// Obtain the next support point
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vec v3 = p2.supportpoint(n).sub(p1.supportpoint(vec(n).neg()));
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if(v3.dot(n) <= 0) return false; // origin outside v3 support plane ==> miss
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// If origin is outside (v1,v0,v3), then portal is invalid -- eliminate v2 and find new support outside face
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vec v3xv0;
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v3xv0.cross(v3, v0);
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if(v1.dot(v3xv0) < 0)
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{
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v2 = v3;
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n.cross(v0, v1, v3);
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continue;
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}
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// If origin is outside (v3,v0,v2), then portal is invalid -- eliminate v1 and find new support outside face
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if(v2.dot(v3xv0) > 0)
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{
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v1 = v3;
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n.cross(v0, v3, v2);
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continue;
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}
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///
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// Phase Two: Refine the portal
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for(int j = 0;; j++)
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{
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// Compute outward facing normal of the portal
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n.cross(v1, v2, v3);
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// If the origin is inside the portal, we have a hit
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if(n.dot(v1) >= 0) return true;
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n.normalize();
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// Find the support point in the direction of the portal's normal
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vec v4 = p2.supportpoint(n).sub(p1.supportpoint(vec(n).neg()));
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// If the origin is outside the support plane or the boundary is thin enough, we have a miss
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if(v4.dot(n) <= 0 || vec(v4).sub(v3).dot(n) <= boundarytolerance || j > 100) return false;
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// Test origin against the three planes that separate the new portal candidates: (v1,v4,v0) (v2,v4,v0) (v3,v4,v0)
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// Note: We're taking advantage of the triple product identities here as an optimization
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// (v1 % v4) * v0 == v1 * (v4 % v0) > 0 if origin inside (v1, v4, v0)
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// (v2 % v4) * v0 == v2 * (v4 % v0) > 0 if origin inside (v2, v4, v0)
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// (v3 % v4) * v0 == v3 * (v4 % v0) > 0 if origin inside (v3, v4, v0)
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vec v4xv0;
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v4xv0.cross(v4, v0);
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if(v1.dot(v4xv0) > 0)
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{
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if(v2.dot(v4xv0) > 0) v1 = v4; // Inside v1 & inside v2 ==> eliminate v1
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else v3 = v4; // Inside v1 & outside v2 ==> eliminate v3
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}
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else
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{
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if(v3.dot(v4xv0) > 0) v2 = v4; // Outside v1 & inside v3 ==> eliminate v2
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else v1 = v4; // Outside v1 & outside v3 ==> eliminate v1
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}
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}
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}
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return false;
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}
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template<class T, class U>
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bool collide(const T &p1, const U &p2, vec *contactnormal, vec *contactpoint1, vec *contactpoint2)
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{
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// v0 = center of Minkowski sum
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vec v01 = p1.center();
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vec v02 = p2.center();
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vec v0 = vec(v02).sub(v01);
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// Avoid case where centers overlap -- any direction is fine in this case
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if(v0.iszero()) v0 = vec(0, 0, 1e-5f);
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// v1 = support in direction of origin
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vec n = vec(v0).neg();
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vec v11 = p1.supportpoint(vec(n).neg());
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vec v12 = p2.supportpoint(n);
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vec v1 = vec(v12).sub(v11);
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if(v1.dot(n) <= 0)
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{
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if(contactnormal) *contactnormal = n;
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return false;
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}
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// v2 - support perpendicular to v1,v0
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n.cross(v1, v0);
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if(n.iszero())
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{
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n = vec(v1).sub(v0);
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n.normalize();
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if(contactnormal) *contactnormal = n;
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if(contactpoint1) *contactpoint1 = v11;
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if(contactpoint2) *contactpoint2 = v12;
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return true;
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}
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vec v21 = p1.supportpoint(vec(n).neg());
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vec v22 = p2.supportpoint(n);
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vec v2 = vec(v22).sub(v21);
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if(v2.dot(n) <= 0)
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{
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if(contactnormal) *contactnormal = n;
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return false;
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}
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// Determine whether origin is on + or - side of plane (v1,v0,v2)
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n.cross(v0, v1, v2);
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assert( !n.iszero() );
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// If the origin is on the - side of the plane, reverse the direction of the plane
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if(n.dot(v0) > 0)
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{
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swap(v1, v2);
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swap(v11, v21);
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swap(v12, v22);
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n.neg();
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}
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///
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// Phase One: Identify a portal
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loopi(100)
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{
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// Obtain the support point in a direction perpendicular to the existing plane
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// Note: This point is guaranteed to lie off the plane
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vec v31 = p1.supportpoint(vec(n).neg());
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vec v32 = p2.supportpoint(n);
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vec v3 = vec(v32).sub(v31);
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if(v3.dot(n) <= 0)
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{
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if(contactnormal) *contactnormal = n;
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return false;
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}
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// If origin is outside (v1,v0,v3), then eliminate v2 and loop
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vec v3xv0;
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v3xv0.cross(v3, v0);
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if(v1.dot(v3xv0) < 0)
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{
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v2 = v3;
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v21 = v31;
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v22 = v32;
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n.cross(v0, v1, v3);
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continue;
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}
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// If origin is outside (v3,v0,v2), then eliminate v1 and loop
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if(v2.dot(v3xv0) > 0)
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{
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v1 = v3;
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v11 = v31;
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v12 = v32;
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n.cross(v0, v3, v2);
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continue;
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}
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bool hit = false;
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///
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// Phase Two: Refine the portal
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// We are now inside of a wedge...
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for(int j = 0;; j++)
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{
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// Compute normal of the wedge face
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n.cross(v1, v2, v3);
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// Can this happen??? Can it be handled more cleanly?
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if(n.iszero())
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{
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assert(false);
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return true;
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}
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n.normalize();
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// If the origin is inside the wedge, we have a hit
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if(n.dot(v1) >= 0 && !hit)
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{
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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;
|
|
}
|
|
}
|
|
|