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);
}
}
}
