// reduces a polynomial with respect to a set of polynomials F
Polynomial *normal_form(Polynomial **set, Polynomial *orig,
int index, int num_polys, int *reduced){
Polynomial *res, *temp;
// we must try all quotient and remainders
Polynomial **quots = (Polynomial **) malloc(sizeof(Polynomial *) * num_polys);
Polynomial **rems = (Polynomial **) malloc(sizeof(Polynomial *) * num_polys);
res = copy_poly(orig);
*reduced = 0;
printf("computing some reduction\n");
// try to divide using all things in the set
for (int i = 0; i < num_polys; i++){
if (i == index) continue;
divide_polys(orig, set[i], &(quots[i]), &(rems[i]));
}
printf("wtf tried to divide everything\n");
// nothing divided out completely the first time
// keep trying to divide out stuff recursively
for (int i = 0; i < num_polys; i++){
if (i == index) continue;
// remainder is 0, return this right away
if (rems[i]->terms[0].coeff.num == 0){
free(res);
res = copy_poly(rems[i]);
break;
}
// try to divide recursively
else if (quots[i]->terms[0].coeff.num != 0){
temp = normal_form(set, rems[i], index, num_polys, reduced);
free(res);
// it reduced all the way
if (temp->terms[0].coeff.num == 0){
res = copy_poly(temp);
break;
}
else{
res = copy_poly(rems[i]);
}
free(temp);
}
}
// free all this stuff
for (int i = 0; i < num_polys; i++) {
if (i == index) continue;
free(quots[i]);
free(rems[i]);
}
free(quots);
free(rems);
return res;
}
/* draw an angle from the current point to b and then to c,
* with a rounded corner of the given radius.
*/
static void
rounded_corner (cairo_t * cr,
gdouble bx, gdouble by,
gdouble cx, gdouble cy, gdouble radius)
{
gdouble ax, ay;
gdouble n1x, n1y, d1;
gdouble n2x, n2y, d2;
gdouble pd1, pd2;
gdouble ix, iy;
gdouble dist1, dist2;
gdouble nx, ny, d;
gdouble a1x, a1y, c1x, c1y;
gdouble phi1, phi2;
cairo_get_current_point (cr, &ax, &ay);
#ifdef KBDRAW_DEBUG
printf (" current point: (%f, %f), radius %f:\n", ax, ay,
radius);
#endif
/* make sure radius is not too large */
dist1 = length (bx - ax, by - ay);
dist2 = length (cx - bx, cy - by);
radius = MIN (radius, MIN (dist1, dist2));
/* construct normal forms of the lines */
normal_form (ax, ay, bx, by, &n1x, &n1y, &d1);
normal_form (bx, by, cx, cy, &n2x, &n2y, &d2);
/* find which side of the line a,b the point c is on */
if (point_line_distance (cx, cy, n1x, n1y) < d1)
pd1 = d1 - radius;
else
pd1 = d1 + radius;
/* find which side of the line b,c the point a is on */
if (point_line_distance (ax, ay, n2x, n2y) < d2)
pd2 = d2 - radius;
else
pd2 = d2 + radius;
/* intersect the parallels to find the center of the arc */
intersect (n1x, n1y, pd1, n2x, n2y, pd2, &ix, &iy);
nx = (bx - ax) / dist1;
ny = (by - ay) / dist1;
d = point_line_distance (ix, iy, nx, ny);
/* a1 is the point on the line a-b where the arc starts */
intersect (n1x, n1y, d1, nx, ny, d, &a1x, &a1y);
nx = (cx - bx) / dist2;
ny = (cy - by) / dist2;
d = point_line_distance (ix, iy, nx, ny);
/* c1 is the point on the line b-c where the arc ends */
intersect (n2x, n2y, d2, nx, ny, d, &c1x, &c1y);
/* determine the first angle */
if (a1x - ix == 0)
phi1 = (a1y - iy > 0) ? M_PI_2 : 3 * M_PI_2;
else if (a1x - ix > 0)
phi1 = atan ((a1y - iy) / (a1x - ix));
else
phi1 = M_PI + atan ((a1y - iy) / (a1x - ix));
/* determine the second angle */
if (c1x - ix == 0)
phi2 = (c1y - iy > 0) ? M_PI_2 : 3 * M_PI_2;
else if (c1x - ix > 0)
phi2 = atan ((c1y - iy) / (c1x - ix));
else
phi2 = M_PI + atan ((c1y - iy) / (c1x - ix));
/* compute the difference between phi2 and phi1 mod 2pi */
d = phi2 - phi1;
while (d < 0)
d += 2 * M_PI;
while (d > 2 * M_PI)
d -= 2 * M_PI;
#ifdef KBDRAW_DEBUG
printf (" line 1 to: (%f, %f):\n", a1x, a1y);
#endif
if (!(isnan (a1x) || isnan (a1y)))
cairo_line_to (cr, a1x, a1y);
/* pick the short arc from phi1 to phi2 */
if (d < M_PI)
cairo_arc (cr, ix, iy, radius, phi1, phi2);
else
cairo_arc_negative (cr, ix, iy, radius, phi1, phi2);
#ifdef KBDRAW_DEBUG
printf (" line 2 to: (%f, %f):\n", cx, cy);
#endif
cairo_line_to (cr, cx, cy);
}