bool BicubicPatch::intersect_subpatch(const BasicRay &ray, const TripleVector3d& V1, const DBL uu[3], const DBL vv[3], DBL *Depth, Vector3d& P, Vector3d& N, DBL *u, DBL *v) const
{
DBL squared_b0, squared_b1;
DBL d, n, a, b, r;
Vector3d Q;
Vector3d T1;
Matrix3x3 B, IB;
Vector3d NN[3];
B[0] = V1[1] - V1[0];
B[1] = V1[2] - V1[0];
B[2] = cross(B[0], B[1]);
d = B[2].lengthSqr();
squared_b0 = B[0].lengthSqr();
squared_b1 = B[1].lengthSqr();
if (d <= (BEZIER_EPSILON * squared_b1 * squared_b0))
{
return false;
}
d = 1.0 / sqrt(d);
B[2] *= d;
/* Degenerate triangle. */
if (!MInvers3(B, IB))
{
return false;
}
d = dot(ray.Direction, IB[2]);
if (fabs(d) < BEZIER_EPSILON)
{
return false;
}
Q = V1[0] - ray.Origin;
n = dot(Q, IB[2]);
*Depth = n / d;
if (*Depth < BEZIER_TOLERANCE)
{
return false;
}
T1 = ray.Direction * (*Depth);
P = ray.Origin + T1;
Q = P - V1[0];
a = dot(Q, IB[0]);
b = dot(Q, IB[1]);
if ((a < 0.0) || (b < 0.0) || (a + b > 1.0))
{
return false;
}
r = 1.0 - a - b;
bezier_value(&Control_Points, uu[0], vv[0], T1, NN[0]);
bezier_value(&Control_Points, uu[1], vv[1], T1, NN[1]);
bezier_value(&Control_Points, uu[2], vv[2], T1, NN[2]);
N = NN[0] * r
+ NN[1] * a
+ NN[2] * b;
*u = r * uu[0] + a * uu[1] + b * uu[2];
*v = r * vv[0] + a * vv[1] + b * vv[2];
d = N.lengthSqr();
if (d > BEZIER_EPSILON)
{
d = 1.0 / sqrt(d);
N *= d;
}
else
{
N = Vector3d(1.0, 0.0, 0.0);
}
return true;
}
static int intersect_subpatch(BICUBIC_PATCH *Shape, RAY *ray, VECTOR V1[3], DBL uu[3], DBL vv[3], DBL *Depth, VECTOR P, VECTOR N, DBL *u, DBL *v)
{
DBL squared_b0, squared_b1;
DBL d, n, a, b, r;
VECTOR Q, T1;
VECTOR B[3], IB[3], NN[3];
VSub(B[0], V1[1], V1[0]);
VSub(B[1], V1[2], V1[0]);
VCross(B[2], B[0], B[1]);
VDot(d, B[2], B[2]);
squared_b0 = VSumSqr(B[0]);
squared_b1 = VSumSqr(B[1]);
if (d <= (BEZIER_EPSILON * squared_b1 * squared_b0))
{
return (0);
}
d = 1.0 / sqrt(d);
VScaleEq(B[2], d);
/* Degenerate triangle. */
if (!MInvers3(B, IB))
{
return (0);
}
VDot(d, ray->Direction, IB[2]);
if (fabs(d) < BEZIER_EPSILON)
{
return (0);
}
VSub(Q, V1[0], ray->Initial);
VDot(n, Q, IB[2]);
*Depth = n / d;
if (*Depth < BEZIER_TOLERANCE)
{
return (0);
}
VScale(T1, ray->Direction, *Depth);
VAdd(P, ray->Initial, T1);
VSub(Q, P, V1[0]);
VDot(a, Q, IB[0]);
VDot(b, Q, IB[1]);
if ((a < 0.0) || (b < 0.0) || (a + b > 1.0))
{
return (0);
}
r = 1.0 - a - b;
Make_Vector(N, 0.0, 0.0, 0.0);
bezier_value((VECTOR(*)[4][4])&Shape->Control_Points, uu[0], vv[0], T1, NN[0]);
bezier_value((VECTOR(*)[4][4])&Shape->Control_Points, uu[1], vv[1], T1, NN[1]);
bezier_value((VECTOR(*)[4][4])&Shape->Control_Points, uu[2], vv[2], T1, NN[2]);
VScale(T1, NN[0], r); VAddEq(N, T1);
VScale(T1, NN[1], a); VAddEq(N, T1);
VScale(T1, NN[2], b); VAddEq(N, T1);
*u = r * uu[0] + a * uu[1] + b * uu[2];
*v = r * vv[0] + a * vv[1] + b * vv[2];
VDot(d, N, N);
if (d > BEZIER_EPSILON)
{
d = 1.0 / sqrt(d);
VScaleEq(N, d);
}
else
{
Make_Vector(N, 1, 0, 0);
}
return (1);
}