int InCircle(const Point2d& a, const Point2d& b,
const Point2d& c, const Point2d& d)
// Returns TRUE if the point d is inside the circle defined by the
// points a, b, c. See Guibas and Stolfi (1985) p.107.
{
return (a.x*a.x + a.y*a.y) * TriArea(b, c, d) -
(b.x*b.x + b.y*b.y) * TriArea(a, c, d) +
(c.x*c.x + c.y*c.y) * TriArea(a, b, d) -
(d.x*d.x + d.y*d.y) * TriArea(a, b, c) > 0;
}
void CalcUVMapPolygon(Object *obj, Vec3 *P, double *u, double *v)
{
PolygonData *p = obj->data.polygon;
double area, a1, a2, a3, pu, pv;
float *P1, *P2, *P3;
int A, B;
/*
* Project the triangle vertices to the 2D plane
* that is most perpendicular to the plane normal.
* We use the triangle formed by the first three vertices
* of the polygon.
*/
switch(p->axis )
{
case X_AXIS:
A = 1;
B = 2;
pu = P->y;
pv = P->z;
break;
case Y_AXIS:
A = 0;
B = 2;
pu = P->x;
pv = P->z;
break;
default: /* Z_AXIS. */
A = 0;
B = 1;
pu = P->x;
pv = P->y;
break;
}
P1 = p->pts;
P2 = &p->pts[3];
P3 = &p->pts[6];
/* Determine barycentric coordinates of point... */
area = TriArea(P1[A], P1[B], P2[A], P2[B], P3[A], P3[B]);
a1 = TriArea(pu, pv, P2[A], P2[B], P3[A], P3[B]) / area;
a2 = TriArea(P1[A], P1[B], pu, pv, P3[A], P3[B]) / area;
a3 = 1.0 - a1 - a2;
/*
* ...and use them to interpolate between the UV coordinates
* for each vertex to get actual UV position.
*/
*u = 1.0 - a1;
*v = a3;
}
static void TriDlDx(double dldx[][2], double const_term[],
const double p0[], const double p1[], const double p2[]){
const double area = TriArea(p0,p1,p2);
const double tmp1 = 0.5 / area;
const_term[0] = tmp1*(p1[0]*p2[1]-p2[0]*p1[1]);
const_term[1] = tmp1*(p2[0]*p0[1]-p0[0]*p2[1]);
const_term[2] = tmp1*(p0[0]*p1[1]-p1[0]*p0[1]);
dldx[0][0] = tmp1*(p1[1]-p2[1]);
dldx[1][0] = tmp1*(p2[1]-p0[1]);
dldx[2][0] = tmp1*(p0[1]-p1[1]);
dldx[0][1] = tmp1*(p2[0]-p1[0]);
dldx[1][1] = tmp1*(p0[0]-p2[0]);
dldx[2][1] = tmp1*(p1[0]-p0[0]);
}
int ccw(const Point2d& a, const Point2d& b, const Point2d& c)
// Returns TRUE if the points a, b, c are in a counterclockwise order
{
return (TriArea(a, b, c) > 0);
}
