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//! if OPC_TRITRI_EPSILON_TEST is true then we do a check (if |dv|<EPSILON then dv=0.0;) else no check is done (which is less robust, but faster)
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#define LOCAL_EPSILON 0.000001f
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//! Edge to edge test based on Franlin Antonio's gem: "Faster Line Segment Intersection", in Graphics Gems III, pp. 199-202
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#define EDGE_EDGE_TEST(V0, U0, U1) \
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Bx = U0[i0] - U1[i0]; \
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By = U0[i1] - U1[i1]; \
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Cx = V0[i0] - U0[i0]; \
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Cy = V0[i1] - U0[i1]; \
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if((f>0.0f && d>=0.0f && d<=f) || (f<0.0f && d<=0.0f && d>=f)) \
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const float e=Ax*Cy - Ay*Cx; \
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if(e>=0.0f && e<=f) return TRUE; \
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if(e<=0.0f && e>=f) return TRUE; \
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#define EDGE_AGAINST_TRI_EDGES(V0, V1, U0, U1, U2) \
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float Bx,By,Cx,Cy,d,f; \
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const float Ax = V1[i0] - V0[i0]; \
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const float Ay = V1[i1] - V0[i1]; \
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/* test edge U0,U1 against V0,V1 */ \
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EDGE_EDGE_TEST(V0, U0, U1); \
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/* test edge U1,U2 against V0,V1 */ \
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EDGE_EDGE_TEST(V0, U1, U2); \
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/* test edge U2,U1 against V0,V1 */ \
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EDGE_EDGE_TEST(V0, U2, U0); \
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#define POINT_IN_TRI(V0, U0, U1, U2) \
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/* is T1 completly inside T2? */ \
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/* check if V0 is inside tri(U0,U1,U2) */ \
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float a = U1[i1] - U0[i1]; \
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float b = -(U1[i0] - U0[i0]); \
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float c = -a*U0[i0] - b*U0[i1]; \
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float d0 = a*V0[i0] + b*V0[i1] + c; \
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a = U2[i1] - U1[i1]; \
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b = -(U2[i0] - U1[i0]); \
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c = -a*U1[i0] - b*U1[i1]; \
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const float d1 = a*V0[i0] + b*V0[i1] + c; \
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a = U0[i1] - U2[i1]; \
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b = -(U0[i0] - U2[i0]); \
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c = -a*U2[i0] - b*U2[i1]; \
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const float d2 = a*V0[i0] + b*V0[i1] + c; \
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if(d0*d2>0.0f) return TRUE; \
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BOOL CoplanarTriTri(const Point& n, const Point& v0, const Point& v1, const Point& v2, const Point& u0, const Point& u1, const Point& u2)
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/* first project onto an axis-aligned plane, that maximizes the area */
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/* of the triangles, compute indices: i0,i1. */
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i0=1; /* A[0] is greatest */
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i0=0; /* A[2] is greatest */
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i0=0; /* A[2] is greatest */
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i0=0; /* A[1] is greatest */
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/* test all edges of triangle 1 against the edges of triangle 2 */
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EDGE_AGAINST_TRI_EDGES(v0, v1, u0, u1, u2);
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EDGE_AGAINST_TRI_EDGES(v1, v2, u0, u1, u2);
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EDGE_AGAINST_TRI_EDGES(v2, v0, u0, u1, u2);
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/* finally, test if tri1 is totally contained in tri2 or vice versa */
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POINT_IN_TRI(v0, u0, u1, u2);
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POINT_IN_TRI(u0, v0, v1, v2);
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#define NEWCOMPUTE_INTERVALS(VV0, VV1, VV2, D0, D1, D2, D0D1, D0D2, A, B, C, X0, X1) \
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/* here we know that D0D2<=0.0 */ \
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/* that is D0, D1 are on the same side, D2 on the other or on the plane */ \
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A=VV2; B=(VV0 - VV2)*D2; C=(VV1 - VV2)*D2; X0=D2 - D0; X1=D2 - D1; \
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/* here we know that d0d1<=0.0 */ \
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A=VV1; B=(VV0 - VV1)*D1; C=(VV2 - VV1)*D1; X0=D1 - D0; X1=D1 - D2; \
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else if(D1*D2>0.0f || D0!=0.0f) \
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/* here we know that d0d1<=0.0 or that D0!=0.0 */ \
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A=VV0; B=(VV1 - VV0)*D0; C=(VV2 - VV0)*D0; X0=D0 - D1; X1=D0 - D2; \
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A=VV1; B=(VV0 - VV1)*D1; C=(VV2 - VV1)*D1; X0=D1 - D0; X1=D1 - D2; \
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A=VV2; B=(VV0 - VV2)*D2; C=(VV1 - VV2)*D2; X0=D2 - D0; X1=D2 - D1; \
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/* triangles are coplanar */ \
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return CoplanarTriTri(N1, V0, V1, V2, U0, U1, U2); \
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///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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* Triangle/triangle intersection test routine,
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* by Tomas Moller, 1997.
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* See article "A Fast Triangle-Triangle Intersection Test",
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* Journal of Graphics Tools, 2(2), 1997
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* Updated June 1999: removed the divisions -- a little faster now!
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* Updated October 1999: added {} to CROSS and SUB macros
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* int NoDivTriTriIsect(float V0[3],float V1[3],float V2[3],
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* float U0[3],float U1[3],float U2[3])
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* \param V0 [in] triangle 0, vertex 0
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* \param V1 [in] triangle 0, vertex 1
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* \param V2 [in] triangle 0, vertex 2
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* \param U0 [in] triangle 1, vertex 0
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* \param U1 [in] triangle 1, vertex 1
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* \param U2 [in] triangle 1, vertex 2
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* \return true if triangles overlap
178
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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inline_ BOOL AABBTreeCollider::TriTriOverlap(const Point& V0, const Point& V1, const Point& V2, const Point& U0, const Point& U1, const Point& U2)
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// Compute plane equation of triangle(V0,V1,V2)
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const Point N1 = E1 ^ E2;
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const float d1 =-N1 | V0;
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// Plane equation 1: N1.X+d1=0
191
// Put U0,U1,U2 into plane equation 1 to compute signed distances to the plane
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float du0 = (N1|U0) + d1;
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float du1 = (N1|U1) + d1;
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float du2 = (N1|U2) + d1;
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// Coplanarity robustness check
197
#ifdef OPC_TRITRI_EPSILON_TEST
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if(fabsf(du0)<LOCAL_EPSILON) du0 = 0.0f;
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if(fabsf(du1)<LOCAL_EPSILON) du1 = 0.0f;
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if(fabsf(du2)<LOCAL_EPSILON) du2 = 0.0f;
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const float du0du1 = du0 * du1;
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const float du0du2 = du0 * du2;
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if(du0du1>0.0f && du0du2>0.0f) // same sign on all of them + not equal 0 ?
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return FALSE; // no intersection occurs
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// Compute plane of triangle (U0,U1,U2)
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const Point N2 = E1 ^ E2;
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const float d2=-N2 | U0;
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// plane equation 2: N2.X+d2=0
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// put V0,V1,V2 into plane equation 2
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float dv0 = (N2|V0) + d2;
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float dv1 = (N2|V1) + d2;
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float dv2 = (N2|V2) + d2;
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#ifdef OPC_TRITRI_EPSILON_TEST
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if(fabsf(dv0)<LOCAL_EPSILON) dv0 = 0.0f;
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if(fabsf(dv1)<LOCAL_EPSILON) dv1 = 0.0f;
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if(fabsf(dv2)<LOCAL_EPSILON) dv2 = 0.0f;
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const float dv0dv1 = dv0 * dv1;
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const float dv0dv2 = dv0 * dv2;
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if(dv0dv1>0.0f && dv0dv2>0.0f) // same sign on all of them + not equal 0 ?
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return FALSE; // no intersection occurs
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// Compute direction of intersection line
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const Point D = N1^N2;
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// Compute and index to the largest component of D
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float max=fabsf(D[0]);
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float bb=fabsf(D[1]);
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float cc=fabsf(D[2]);
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if(bb>max) max=bb,index=1;
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if(cc>max) max=cc,index=2;
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// This is the simplified projection onto L
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const float vp0 = V0[index];
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const float vp1 = V1[index];
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const float vp2 = V2[index];
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const float up0 = U0[index];
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const float up1 = U1[index];
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const float up2 = U2[index];
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// Compute interval for triangle 1
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NEWCOMPUTE_INTERVALS(vp0,vp1,vp2,dv0,dv1,dv2,dv0dv1,dv0dv2,a,b,c,x0,x1);
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// Compute interval for triangle 2
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NEWCOMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,d,e,f,y0,y1);
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const float xx=x0*x1;
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const float yy=y0*y1;
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const float xxyy=xx*yy;
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float isect1[2], isect2[2];
267
isect1[0]=tmp+b*x1*yy;
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isect1[1]=tmp+c*x0*yy;
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isect2[0]=tmp+e*xx*y1;
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isect2[1]=tmp+f*xx*y0;
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SORT(isect1[0],isect1[1]);
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SORT(isect2[0],isect2[1]);
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if(isect1[1]<isect2[0] || isect2[1]<isect1[0]) return FALSE;
added
removed
ode-0.5/OPCODE/OPC_TriTriOverlap.h
