Adaptive Sampling of Parametric Curves

.1
Adaptive Sampling of
Parametric Curves
Luiz Henrique de Figueiredo
IMPA, Instituto de Matematica Pura e Aplicada
Rio de Janeiro, Brasil
Introduction
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typedef struct point { double t,x,y,z; } Point;
#define
#define
#define
#define
T(p)
X(p)
Y(p)
Z(p)
((p)->t)
((p)->x)
((p)->y)
((p)->z)
extern void gamma(Point* p);
extern void line(Point* p, Point* q);
/* user supplied */
/* user supplied */
static void sample(Point* p, Point* q)
{
Point rr, *r=&rr;
double t = 0.45 + 0.1 * (rand()/(double) RAND_MAX);
T(r) = T(p) + t*(T(q)-T(p));
gamma(r);
if (flat(p,q,r)) line(p,q); else { sample(p,r); sample(r,q); }
}
static int flat(Point* p, Point* q, Point* r)
{
extern double tol;
/* user supplied
double xp = X(p)-X(r); double yp = Y(p)-Y(r); double zp
double xq = X(q)-X(r); double yq = Y(q)-Y(r); double zq
double x = yp*zq-yq*zp;
double y = xp*zq-xq*zp;
double z = xp*yq-xq*yp;
return (x*x+y*y+z*z) < tol;
/* |pr x qr|^2 <
}
void aspc(double a, double b)
{
Point pp, *p = &pp;
Point qq, *q = &qq;
srand(time(0));
T(p)= a; gamma(p); T(q)=b; gamma(q);
sample(p,q);
}
*/
= Z(p)-Z(r);
= Z(q)-Z(r);
/* entry point */
/* randomize */
/* set up */
/* sample */
tol */
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Bibliography
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Adaptive Sampling of Parametric Curves

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