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Diffstat (limited to 'Opcode/OPC_TriTriOverlap.h')
| -rw-r--r-- | Opcode/OPC_TriTriOverlap.h | 279 |
1 files changed, 279 insertions, 0 deletions
diff --git a/Opcode/OPC_TriTriOverlap.h b/Opcode/OPC_TriTriOverlap.h new file mode 100644 index 0000000..ccc8161 --- /dev/null +++ b/Opcode/OPC_TriTriOverlap.h @@ -0,0 +1,279 @@ +
+//! 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)
+#define LOCAL_EPSILON 0.000001f
+
+//! sort so that a<=b
+#define SORT(a,b) \
+ if(a>b) \
+ { \
+ const float c=a; \
+ a=b; \
+ b=c; \
+ }
+
+//! Edge to edge test based on Franlin Antonio's gem: "Faster Line Segment Intersection", in Graphics Gems III, pp. 199-202
+#define EDGE_EDGE_TEST(V0, U0, U1) \
+ Bx = U0[i0] - U1[i0]; \
+ By = U0[i1] - U1[i1]; \
+ Cx = V0[i0] - U0[i0]; \
+ Cy = V0[i1] - U0[i1]; \
+ f = Ay*Bx - Ax*By; \
+ d = By*Cx - Bx*Cy; \
+ if((f>0.0f && d>=0.0f && d<=f) || (f<0.0f && d<=0.0f && d>=f)) \
+ { \
+ const float e=Ax*Cy - Ay*Cx; \
+ if(f>0.0f) \
+ { \
+ if(e>=0.0f && e<=f) return TRUE; \
+ } \
+ else \
+ { \
+ if(e<=0.0f && e>=f) return TRUE; \
+ } \
+ }
+
+//! TO BE DOCUMENTED
+#define EDGE_AGAINST_TRI_EDGES(V0, V1, U0, U1, U2) \
+{ \
+ float Bx,By,Cx,Cy,d,f; \
+ const float Ax = V1[i0] - V0[i0]; \
+ const float Ay = V1[i1] - V0[i1]; \
+ /* test edge U0,U1 against V0,V1 */ \
+ EDGE_EDGE_TEST(V0, U0, U1); \
+ /* test edge U1,U2 against V0,V1 */ \
+ EDGE_EDGE_TEST(V0, U1, U2); \
+ /* test edge U2,U1 against V0,V1 */ \
+ EDGE_EDGE_TEST(V0, U2, U0); \
+}
+
+//! TO BE DOCUMENTED
+#define POINT_IN_TRI(V0, U0, U1, U2) \
+{ \
+ /* is T1 completly inside T2? */ \
+ /* check if V0 is inside tri(U0,U1,U2) */ \
+ float a = U1[i1] - U0[i1]; \
+ float b = -(U1[i0] - U0[i0]); \
+ float c = -a*U0[i0] - b*U0[i1]; \
+ float d0 = a*V0[i0] + b*V0[i1] + c; \
+ \
+ a = U2[i1] - U1[i1]; \
+ b = -(U2[i0] - U1[i0]); \
+ c = -a*U1[i0] - b*U1[i1]; \
+ const float d1 = a*V0[i0] + b*V0[i1] + c; \
+ \
+ a = U0[i1] - U2[i1]; \
+ b = -(U0[i0] - U2[i0]); \
+ c = -a*U2[i0] - b*U2[i1]; \
+ const float d2 = a*V0[i0] + b*V0[i1] + c; \
+ if(d0*d1>0.0f) \
+ { \
+ if(d0*d2>0.0f) return TRUE; \
+ } \
+}
+
+//! TO BE DOCUMENTED
+BOOL CoplanarTriTri(const IcePoint& n, const IcePoint& v0, const IcePoint& v1, const IcePoint& v2, const IcePoint& u0, const IcePoint& u1, const IcePoint& u2)
+{
+ float A[3];
+ short i0,i1;
+ /* first project onto an axis-aligned plane, that maximizes the area */
+ /* of the triangles, compute indices: i0,i1. */
+ A[0] = fabsf(n[0]);
+ A[1] = fabsf(n[1]);
+ A[2] = fabsf(n[2]);
+ if(A[0]>A[1])
+ {
+ if(A[0]>A[2])
+ {
+ i0=1; /* A[0] is greatest */
+ i1=2;
+ }
+ else
+ {
+ i0=0; /* A[2] is greatest */
+ i1=1;
+ }
+ }
+ else /* A[0]<=A[1] */
+ {
+ if(A[2]>A[1])
+ {
+ i0=0; /* A[2] is greatest */
+ i1=1;
+ }
+ else
+ {
+ i0=0; /* A[1] is greatest */
+ i1=2;
+ }
+ }
+
+ /* test all edges of triangle 1 against the edges of triangle 2 */
+ EDGE_AGAINST_TRI_EDGES(v0, v1, u0, u1, u2);
+ EDGE_AGAINST_TRI_EDGES(v1, v2, u0, u1, u2);
+ EDGE_AGAINST_TRI_EDGES(v2, v0, u0, u1, u2);
+
+ /* finally, test if tri1 is totally contained in tri2 or vice versa */
+ POINT_IN_TRI(v0, u0, u1, u2);
+ POINT_IN_TRI(u0, v0, v1, v2);
+
+ return FALSE;
+}
+
+//! TO BE DOCUMENTED
+#define NEWCOMPUTE_INTERVALS(VV0, VV1, VV2, D0, D1, D2, D0D1, D0D2, A, B, C, X0, X1) \
+{ \
+ if(D0D1>0.0f) \
+ { \
+ /* here we know that D0D2<=0.0 */ \
+ /* that is D0, D1 are on the same side, D2 on the other or on the plane */ \
+ A=VV2; B=(VV0 - VV2)*D2; C=(VV1 - VV2)*D2; X0=D2 - D0; X1=D2 - D1; \
+ } \
+ else if(D0D2>0.0f) \
+ { \
+ /* here we know that d0d1<=0.0 */ \
+ A=VV1; B=(VV0 - VV1)*D1; C=(VV2 - VV1)*D1; X0=D1 - D0; X1=D1 - D2; \
+ } \
+ else if(D1*D2>0.0f || D0!=0.0f) \
+ { \
+ /* here we know that d0d1<=0.0 or that D0!=0.0 */ \
+ A=VV0; B=(VV1 - VV0)*D0; C=(VV2 - VV0)*D0; X0=D0 - D1; X1=D0 - D2; \
+ } \
+ else if(D1!=0.0f) \
+ { \
+ A=VV1; B=(VV0 - VV1)*D1; C=(VV2 - VV1)*D1; X0=D1 - D0; X1=D1 - D2; \
+ } \
+ else if(D2!=0.0f) \
+ { \
+ A=VV2; B=(VV0 - VV2)*D2; C=(VV1 - VV2)*D2; X0=D2 - D0; X1=D2 - D1; \
+ } \
+ else \
+ { \
+ /* triangles are coplanar */ \
+ return CoplanarTriTri(N1, V0, V1, V2, U0, U1, U2); \
+ } \
+}
+
+///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+/**
+ * Triangle/triangle intersection test routine,
+ * by Tomas Moller, 1997.
+ * See article "A Fast Triangle-Triangle Intersection Test",
+ * Journal of Graphics Tools, 2(2), 1997
+ *
+ * Updated June 1999: removed the divisions -- a little faster now!
+ * Updated October 1999: added {} to CROSS and SUB macros
+ *
+ * int NoDivTriTriIsect(float V0[3],float V1[3],float V2[3],
+ * float U0[3],float U1[3],float U2[3])
+ *
+ * \param V0 [in] triangle 0, vertex 0
+ * \param V1 [in] triangle 0, vertex 1
+ * \param V2 [in] triangle 0, vertex 2
+ * \param U0 [in] triangle 1, vertex 0
+ * \param U1 [in] triangle 1, vertex 1
+ * \param U2 [in] triangle 1, vertex 2
+ * \return true if triangles overlap
+ */
+///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+inline_ BOOL AABBTreeCollider::TriTriOverlap(const IcePoint& V0, const IcePoint& V1, const IcePoint& V2, const IcePoint& U0, const IcePoint& U1, const IcePoint& U2)
+{
+ // Stats
+ mNbPrimPrimTests++;
+
+ // Compute plane equation of triangle(V0,V1,V2)
+ IcePoint E1 = V1 - V0;
+ IcePoint E2 = V2 - V0;
+ const IcePoint N1 = E1 ^ E2;
+ const float d1 =-N1 | V0;
+ // Plane equation 1: N1.X+d1=0
+
+ // Put U0,U1,U2 into plane equation 1 to compute signed distances to the plane
+ float du0 = (N1|U0) + d1;
+ float du1 = (N1|U1) + d1;
+ float du2 = (N1|U2) + d1;
+
+ // Coplanarity robustness check
+#ifdef OPC_TRITRI_EPSILON_TEST
+ if(fabsf(du0)<LOCAL_EPSILON) du0 = 0.0f;
+ if(fabsf(du1)<LOCAL_EPSILON) du1 = 0.0f;
+ if(fabsf(du2)<LOCAL_EPSILON) du2 = 0.0f;
+#endif
+ const float du0du1 = du0 * du1;
+ const float du0du2 = du0 * du2;
+
+ if(du0du1>0.0f && du0du2>0.0f) // same sign on all of them + not equal 0 ?
+ return FALSE; // no intersection occurs
+
+ // Compute plane of triangle (U0,U1,U2)
+ E1 = U1 - U0;
+ E2 = U2 - U0;
+ const IcePoint N2 = E1 ^ E2;
+ const float d2=-N2 | U0;
+ // plane equation 2: N2.X+d2=0
+
+ // put V0,V1,V2 into plane equation 2
+ float dv0 = (N2|V0) + d2;
+ float dv1 = (N2|V1) + d2;
+ float dv2 = (N2|V2) + d2;
+
+#ifdef OPC_TRITRI_EPSILON_TEST
+ if(fabsf(dv0)<LOCAL_EPSILON) dv0 = 0.0f;
+ if(fabsf(dv1)<LOCAL_EPSILON) dv1 = 0.0f;
+ if(fabsf(dv2)<LOCAL_EPSILON) dv2 = 0.0f;
+#endif
+
+ const float dv0dv1 = dv0 * dv1;
+ const float dv0dv2 = dv0 * dv2;
+
+ if(dv0dv1>0.0f && dv0dv2>0.0f) // same sign on all of them + not equal 0 ?
+ return FALSE; // no intersection occurs
+
+ // Compute direction of intersection line
+ const IcePoint D = N1^N2;
+
+ // Compute and index to the largest component of D
+ float max=fabsf(D[0]);
+ short index=0;
+ float bb=fabsf(D[1]);
+ float cc=fabsf(D[2]);
+ if(bb>max) max=bb,index=1;
+ if(cc>max) max=cc,index=2;
+
+ // This is the simplified projection onto L
+ const float vp0 = V0[index];
+ const float vp1 = V1[index];
+ const float vp2 = V2[index];
+
+ const float up0 = U0[index];
+ const float up1 = U1[index];
+ const float up2 = U2[index];
+
+ // Compute interval for triangle 1
+ float a,b,c,x0,x1;
+ NEWCOMPUTE_INTERVALS(vp0,vp1,vp2,dv0,dv1,dv2,dv0dv1,dv0dv2,a,b,c,x0,x1);
+
+ // Compute interval for triangle 2
+ float d,e,f,y0,y1;
+ NEWCOMPUTE_INTERVALS(up0,up1,up2,du0,du1,du2,du0du1,du0du2,d,e,f,y0,y1);
+
+ const float xx=x0*x1;
+ const float yy=y0*y1;
+ const float xxyy=xx*yy;
+
+ float isect1[2], isect2[2];
+
+ float tmp=a*xxyy;
+ isect1[0]=tmp+b*x1*yy;
+ isect1[1]=tmp+c*x0*yy;
+
+ tmp=d*xxyy;
+ isect2[0]=tmp+e*xx*y1;
+ isect2[1]=tmp+f*xx*y0;
+
+ SORT(isect1[0],isect1[1]);
+ SORT(isect2[0],isect2[1]);
+
+ if(isect1[1]<isect2[0] || isect2[1]<isect1[0]) return FALSE;
+ return TRUE;
+}
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