FORCEINLINE bool Intersect_BBox_Dir(const BoundingBox& bbox, const BBoxVector3d& origin, const BBoxVector3d& invdir, BBoxScalar mind, BBoxScalar maxd) { BBoxScalar tmin, tmax, tymin, tymax, tzmin, tzmax; BBoxVector3d bounds[2]; Make_min_max_from_BBox(bounds[0], bounds[1], bbox); tmin = (bounds[BX][X] - origin[X]) * invdir[X]; tmax = (bounds[1 - BX][X] - origin[X]) * invdir[X]; tymin = (bounds[BY][Y] - origin[Y]) * invdir[Y]; tymax = (bounds[1 - BY][Y] - origin[Y]) * invdir[Y]; if((tmin > tymax) || (tymin > tmax)) return false; if(tymin > tmin) tmin = tymin; if(tymax < tmax) tmax = tymax; tzmin = (bounds[BZ][Z] - origin[Z]) * invdir[Z]; tzmax = (bounds[1 - BZ][Z] - origin[Z]) * invdir[Z]; if((tmin > tzmax) || (tzmin > tmax)) return false; if(tzmin > tmin) tmin = tzmin; if(tzmax < tmax) tmax = tzmax; return ((tmin < maxd) && (tmax > mind)); }
void Compute_Quadric_BBox(QUADRIC *Quadric, VECTOR ClipMin, VECTOR ClipMax) { DBL A, B, C, D, E, F, G, H, I, J; DBL a, b, c, d; DBL rx, ry, rz, rx1, rx2, ry1, ry2, rz1, rz2, x, y, z; DBL New_Volume, Old_Volume; VECTOR Min, Max, TmpMin, TmpMax, NewMin, NewMax, T1; BBOX Old; OBJECT *Sib; /* * Check for 'normal' form. If the quadric isn't in it's normal form * we can't do anything (we could, but that would be to tedious! * Diagonalising the quadric's 4x4 matrix, i.e. finding its eigenvalues * and eigenvectors -> solving a 4th order polynom). */ /* Get quadrics coefficients. */ A = Quadric->Square_Terms[X]; E = Quadric->Square_Terms[Y]; H = Quadric->Square_Terms[Z]; B = Quadric->Mixed_Terms[X] / 2.0; C = Quadric->Mixed_Terms[Y] / 2.0; F = Quadric->Mixed_Terms[Z] / 2.0; D = Quadric->Terms[X] / 2.0; G = Quadric->Terms[Y] / 2.0; I = Quadric->Terms[Z] / 2.0; J = Quadric->Constant; /* Set small values to 0. */ if (fabs(A) < EPSILON) A = 0.0; if (fabs(B) < EPSILON) B = 0.0; if (fabs(C) < EPSILON) C = 0.0; if (fabs(D) < EPSILON) D = 0.0; if (fabs(E) < EPSILON) E = 0.0; if (fabs(F) < EPSILON) F = 0.0; if (fabs(G) < EPSILON) G = 0.0; if (fabs(H) < EPSILON) H = 0.0; if (fabs(I) < EPSILON) I = 0.0; if (fabs(J) < EPSILON) J = 0.0; /* Non-zero mixed terms --> return */ if ((B != 0.0) || (C != 0.0) || (F != 0.0)) { return; } /* Non-zero linear terms --> get translation vector */ if ((D != 0.0) || (G != 0.0) || (I != 0.0)) { if (A != 0.0) { T1[X] = -D / A; } else { if (D != 0.0) { T1[X] = J / (2.0 * D); } else { T1[X] = 0.0; } } if (E != 0.0) { T1[Y] = -G / E; } else { if (G != 0.0) { T1[Y] = J / (2.0 * G); } else { T1[Y] = 0.0; } } if (H != 0.0) { T1[Z] = -I / H; } else { if (I != 0.0) { T1[Z] = J / (2.0 * I); } else { T1[Z] = 0.0; } } /* Recalculate coefficients. */ D += A * T1[X]; G += E * T1[Y]; I += H * T1[Z]; J -= T1[X]*(A*T1[X] + 2.0*D) + T1[Y]*(E*T1[Y] + 2.0*G) + T1[Z]*(H*T1[Z] + 2.0*I); } else { Make_Vector(T1, 0.0, 0.0, 0.0); } /* Get old bounding box. */ Old = Quadric->BBox; /* Init new bounding box. */ NewMin[X] = NewMin[Y] = NewMin[Z] = -BOUND_HUGE/2; NewMax[X] = NewMax[Y] = NewMax[Z] = BOUND_HUGE/2; /* Get the bounding box of the clipping object. */ if (Quadric->Clip != NULL) { Min[X] = Min[Y] = Min[Z] = -BOUND_HUGE; Max[X] = Max[Y] = Max[Z] = BOUND_HUGE; /* Intersect the members bounding boxes. */ for (Sib = Quadric->Clip; Sib != NULL; Sib = Sib->Sibling) { if (!Test_Flag(Sib, INVERTED_FLAG)) { if (Sib->Methods == &Plane_Methods) { Compute_Plane_Min_Max((PLANE *)Sib, TmpMin, TmpMax); } else { Make_min_max_from_BBox(TmpMin, TmpMax, Sib->BBox); } Min[X] = max(Min[X], TmpMin[X]); Min[Y] = max(Min[Y], TmpMin[Y]); Min[Z] = max(Min[Z], TmpMin[Z]); Max[X] = min(Max[X], TmpMax[X]); Max[Y] = min(Max[Y], TmpMax[Y]); Max[Z] = min(Max[Z], TmpMax[Z]); } } Assign_Vector(ClipMin, Min); Assign_Vector(ClipMax, Max); } /* Translate clipping box. */ VSubEq(ClipMin, T1); VSubEq(ClipMax, T1); /* We want A to be non-negative. */ if (A < 0.0) { A = -A; D = -D; E = -E; G = -G; H = -H; I = -I; J = -J; } /* * * Check for ellipsoid. * * x*x y*y z*z * ----- + ----- + ----- - 1 = 0 * a*a b*b c*c * */ if ((A > 0.0) && (E > 0.0) && (H > 0.0) && (J < 0.0)) { a = sqrt(-J/A); b = sqrt(-J/E); c = sqrt(-J/H); NewMin[X] = -a; NewMin[Y] = -b; NewMin[Z] = -c; NewMax[X] = a; NewMax[Y] = b; NewMax[Z] = c; } /* * * Check for cylinder (x-axis). * * y*y z*z * ----- + ----- - 1 = 0 * b*b c*c * */ if ((A == 0.0) && (E > 0.0) && (H > 0.0) && (J < 0.0)) { b = sqrt(-J/E); c = sqrt(-J/H); NewMin[Y] = -b; NewMin[Z] = -c; NewMax[Y] = b; NewMax[Z] = c; } /* * * Check for cylinder (y-axis). * * x*x z*z * ----- + ----- - 1 = 0 * a*a c*c * */ if ((A > 0.0) && (E == 0.0) && (H > 0.0) && (J < 0.0)) { a = sqrt(-J/A); c = sqrt(-J/H); NewMin[X] = -a; NewMin[Z] = -c; NewMax[X] = a; NewMax[Z] = c; } /* * * Check for cylinder (z-axis). * * x*x y*y * ----- + ----- - 1 = 0 * a*a b*b * */ if ((A > 0.0) && (E > 0.0) && (H == 0.0) && (J < 0.0)) { a = sqrt(-J/A); b = sqrt(-J/E); NewMin[X] = -a; NewMin[Y] = -b; NewMax[X] = a; NewMax[Y] = b; } /* * * Check for cone (x-axis). * * x*x y*y z*z * ----- - ----- - ----- = 0 * a*a b*b c*c * */ if ((A > 0.0) && (E < 0.0) && (H < 0.0) && (J == 0.0)) { a = sqrt(1.0/A); b = sqrt(-1.0/E); c = sqrt(-1.0/H); /* Get radii for lower x value. */ x = ClipMin[X]; ry1 = fabs(x * b / a); rz1 = fabs(x * c / a); /* Get radii for upper x value. */ x = ClipMax[X]; ry2 = fabs(x * b / a); rz2 = fabs(x * c / a); ry = max(ry1, ry2); rz = max(rz1, rz2); NewMin[Y] = -ry; NewMin[Z] = -rz; NewMax[Y] = ry; NewMax[Z] = rz; } /* * * Check for cone (y-axis). * * x*x y*y z*z * ----- - ----- + ----- = 0 * a*a b*b c*c * */ if ((A > 0.0) && (E < 0.0) && (H > 0.0) && (J == 0.0)) { a = sqrt(1.0/A); b = sqrt(-1.0/E); c = sqrt(1.0/H); /* Get radii for lower y value. */ y = ClipMin[Y]; rx1 = fabs(y * a / b); rz1 = fabs(y * c / b); /* Get radii for upper y value. */ y = ClipMax[Y]; rx2 = fabs(y * a / b); rz2 = fabs(y * c / b); rx = max(rx1, rx2); rz = max(rz1, rz2); NewMin[X] = -rx; NewMin[Z] = -rz; NewMax[X] = rx; NewMax[Z] = rz; } /* * * Check for cone (z-axis). * * x*x y*y z*z * ----- + ----- - ----- = 0 * a*a b*b c*c * */ if ((A > 0.0) && (E > 0.0) && (H < 0.0) && (J == 0.0)) { a = sqrt(1.0/A); b = sqrt(1.0/E); c = sqrt(-1.0/H); /* Get radii for lower z value. */ z = ClipMin[Z]; rx1 = fabs(z * a / c); ry1 = fabs(z * b / c); /* Get radii for upper z value. */ z = ClipMax[Z]; rx2 = fabs(z * a / c); ry2 = fabs(z * b / c); rx = max(rx1, rx2); ry = max(ry1, ry2); NewMin[X] = -rx; NewMin[Y] = -ry; NewMax[X] = rx; NewMax[Y] = ry; } /* * * Check for hyperboloid (x-axis). * * x*x y*y z*z * ----- - ----- - ----- + 1 = 0 * a*a b*b c*c * */ if ((A > 0.0) && (E < 0.0) && (H < 0.0) && (J > 0.0)) { /* Get radii for lower x value. */ x = ClipMin[X]; d = 1.0 + A * Sqr(x); ry1 = sqrt(-d / E); rz1 = sqrt(-d / H); /* Get radii for upper x value. */ x = ClipMax[X]; d = 1.0 + A * Sqr(x); ry2 = sqrt(-d / E); rz2 = sqrt(-d / H); ry = max(ry1, ry2); rz = max(rz1, rz2); NewMin[Y] = -ry; NewMin[Z] = -rz; NewMax[Y] = ry; NewMax[Z] = rz; } /* * * Check for hyperboloid (y-axis). * * x*x y*y z*z * ----- - ----- + ----- - 1 = 0 * a*a b*b c*c * */ if ((A > 0.0) && (E < 0.0) && (H > 0.0) && (J < 0.0)) { /* Get radii for lower y value. */ y = ClipMin[Y]; d = 1.0 - E * Sqr(y); rx1 = sqrt(d / A); rz1 = sqrt(d / H); /* Get radii for upper y value. */ y = ClipMax[Y]; d = 1.0 - E * Sqr(y); rx2 = sqrt(d / A); rz2 = sqrt(d / H); rx = max(rx1, rx2); rz = max(rz1, rz2); NewMin[X] = -rx; NewMin[Z] = -rz; NewMax[X] = rx; NewMax[Z] = rz; } /* * * Check for hyperboloid (z-axis). * * x*x y*y z*z * ----- + ----- - ----- - 1 = 0 * a*a b*b c*c * */ if ((A > 0.0) && (E > 0.0) && (H < 0.0) && (J < 0.0)) { /* Get radii for lower z value. */ z = ClipMin[Z]; d = 1.0 - H * Sqr(z); rx1 = sqrt(d / A); ry1 = sqrt(d / E); /* Get radii for upper z value. */ z = ClipMax[Z]; d = 1.0 - H * Sqr(z); rx2 = sqrt(d / A); ry2 = sqrt(d / E); rx = max(rx1, rx2); ry = max(ry1, ry2); NewMin[X] = -rx; NewMin[Y] = -ry; NewMax[X] = rx; NewMax[Y] = ry; } /* * * Check for paraboloid (x-axis). * * y*y z*z * x - ----- - ----- = 0 * b*b c*c * */ if ((A == 0.0) && (D != 0.0) && (E != 0.0) && (H != 0.0) && (J == 0.0)) { /* Get radii for lower x value. */ x = ClipMin[X]; ry1 = sqrt(fabs(2.0 * D * x / E)); rz1 = sqrt(fabs(2.0 * D * x / H)); /* Get radii for upper x value. */ x = ClipMax[X]; ry2 = sqrt(fabs(2.0 * D * x / E)); rz2 = sqrt(fabs(2.0 * D * x / H)); ry = max(ry1, ry2); rz = max(rz1, rz2); NewMin[Y] = -ry; NewMin[Z] = -rz; NewMax[Y] = ry; NewMax[Z] = rz; } /* * * Check for paraboloid (y-axis). * * x*x z*z * y - ----- - ----- = 0 * a*a c*c * */ if ((E == 0.0) && (G != 0.0) && (A != 0.0) && (H != 0.0) && (J == 0.0)) { /* Get radii for lower y-value. */ y = ClipMin[Y]; rx1 = sqrt(fabs(2.0 * G * y / A)); rz1 = sqrt(fabs(2.0 * G * y / H)); /* Get radii for upper y value. */ y = ClipMax[Y]; rx2 = sqrt(fabs(2.0 * G * y / A)); rz2 = sqrt(fabs(2.0 * G * y / H)); rx = max(rx1, rx2); rz = max(rz1, rz2); NewMin[X] = -rx; NewMin[Z] = -rz; NewMax[X] = rx; NewMax[Z] = rz; } /* * * Check for paraboloid (z-axis). * * x*x y*y * z - ----- - ----- = 0 * a*a b*b * */ if ((H == 0.0) && (I != 0.0) && (A != 0.0) && (E != 0.0) && (J == 0.0)) { /* Get radii for lower z-value. */ z = ClipMin[Z]; rx1 = sqrt(fabs(2.0 * I * z / A)); ry1 = sqrt(fabs(2.0 * I * z / E)); /* Get radii for upper z value. */ z = ClipMax[Z]; rx2 = sqrt(fabs(2.0 * I * z / A)); ry2 = sqrt(fabs(2.0 * I * z / E)); rx = max(rx1, rx2); ry = max(ry1, ry2); NewMin[X] = -rx; NewMin[Y] = -ry; NewMax[X] = rx; NewMax[Y] = ry; } /* Intersect clipping object's and quadric's bounding boxes */ NewMin[X] = max(NewMin[X], ClipMin[X]); NewMin[Y] = max(NewMin[Y], ClipMin[Y]); NewMin[Z] = max(NewMin[Z], ClipMin[Z]); NewMax[X] = min(NewMax[X], ClipMax[X]); NewMax[Y] = min(NewMax[Y], ClipMax[Y]); NewMax[Z] = min(NewMax[Z], ClipMax[Z]); /* Use old or new bounding box? */ New_Volume = (NewMax[X] - NewMin[X]) * (NewMax[Y] - NewMin[Y]) * (NewMax[Z] - NewMin[Z]); BOUNDS_VOLUME(Old_Volume, Old); if (New_Volume < Old_Volume) { /* Add translation. */ Quadric->Automatic_Bounds = true; VAddEq(NewMin, T1); VAddEq(NewMax, T1); Make_BBox_from_min_max(Quadric->BBox, NewMin, NewMax); /* Beware of bounding boxes to large. */ if ((Quadric->BBox.Lengths[X] > CRITICAL_LENGTH) || (Quadric->BBox.Lengths[Y] > CRITICAL_LENGTH) || (Quadric->BBox.Lengths[Z] > CRITICAL_LENGTH)) { Make_BBox(Quadric->BBox, -BOUND_HUGE/2, -BOUND_HUGE/2, -BOUND_HUGE/2, BOUND_HUGE, BOUND_HUGE, BOUND_HUGE); } } }