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cameo: consider inside/outside also when checking corner points

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This commit is contained in:
Werner Almesberger 2012-03-20 20:07:29 -03:00
parent 7a61482a04
commit 340fb2cf8b
2 changed files with 187 additions and 16 deletions
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81
cameo/above.fig Normal file
View File

@ -0,0 +1,81 @@
#FIG 3.2 Produced by xfig version 3.2.5b
Landscape
Center
Metric
A4
100.00
Single
-2
1200 2
5 1 1 2 14 7 68 -1 -1 6.000 0 0 0 0 5398.867 4722.104 8550 5535 8467 5807 7512 7197
6 7605 5715 7965 5985
2 1 0 1 4 7 50 -1 0 4.000 0 0 -1 1 0 2
1 1 1.00 30.00 30.00
7650 5760 7920 5760
4 1 4 50 -1 18 15 0.0000 4 135 300 7785 5985 na\001
-6
1 3 0 2 0 7 50 -1 0 0.000 1 0.0000 5625 6750 45 45 5625 6750 5670 6750
1 3 0 2 0 7 50 -1 0 0.000 1 0.0000 8100 6525 45 45 8100 6525 8145 6525
1 3 0 2 0 7 50 -1 0 0.000 1 0.0000 8550 7425 45 45 8550 7425 8595 7425
1 3 0 2 0 7 50 -1 0 0.000 1 0.0000 5400 4725 45 45 5400 4725 5445 4725
1 3 0 2 0 7 50 -1 0 0.000 1 0.0000 9315 4365 45 45 9315 4365 9360 4365
1 3 0 2 0 7 50 -1 0 0.000 1 0.0000 7053 5826 45 45 7053 5826 7098 5826
2 1 1 2 0 7 45 -1 0 6.000 0 0 -1 1 0 2
0 0 2.00 150.00 180.00
8100 6525 5400 4725
2 1 0 2 0 7 45 -1 0 0.000 0 0 -1 0 0 2
5625 6750 9315 4365
2 1 0 2 1 7 55 -1 0 0.000 0 0 -1 1 0 2
0 0 2.00 150.00 180.00
5635 6763 8100 6525
2 1 0 2 1 7 55 -1 0 0.000 0 0 -1 1 0 2
0 0 2.00 150.00 180.00
8100 6525 8550 7425
2 1 0 2 4 7 60 -1 0 0.000 0 0 -1 1 0 2
0 0 2.00 150.00 180.00
8100 6525 7965 4995
2 1 0 2 4 7 60 -1 0 0.000 0 0 -1 1 0 2
0 0 2.00 150.00 180.00
8100 6525 9450 5850
2 1 1 2 1 7 55 -1 0 6.000 0 0 -1 0 0 2
8550 7425 8775 8550
2 1 1 2 1 7 55 -1 0 6.000 0 0 -1 0 0 2
5625 6750 4275 7200
2 3 0 0 1 7 70 -1 44 0.000 0 0 -1 0 0 6
4500 7155 5625 6750 8100 6525 8550 7425 8730 8325 4500 7155
2 1 0 2 14 7 55 -1 0 0.000 0 0 -1 1 0 2
0 0 2.00 150.00 180.00
2925 4725 5400 4725
2 1 0 1 4 7 50 -1 0 4.000 0 0 -1 1 0 2
1 1 1.00 30.00 30.00
8595 6435 8865 6435
2 1 0 1 0 7 50 -1 0 4.000 0 0 -1 1 0 2
1 1 1.00 30.00 30.00
4185 4950 4500 4950
2 1 0 1 0 7 50 -1 0 4.000 0 0 -1 1 0 2
1 1 1.00 30.00 30.00
4140 5400 4500 5400
2 1 0 1 0 7 50 -1 0 4.000 0 0 -1 1 0 2
1 1 1.00 30.00 30.00
4365 5850 4680 5850
2 1 0 2 4 7 60 -1 0 0.000 0 0 -1 1 0 2
0 0 2.00 150.00 180.00
7974 5013 9324 4338
2 1 0 2 4 7 60 -1 0 0.000 0 0 -1 1 0 2
0 0 2.00 150.00 180.00
9450 5850 9315 4320
4 0 0 50 -1 18 15 0.0000 4 180 180 5355 6660 A\001
4 0 0 50 -1 18 15 0.0000 4 180 180 8685 7515 C\001
4 1 4 50 -1 18 15 0.0000 4 180 300 8730 6660 nb\001
4 0 0 50 -1 18 15 0.0000 4 180 180 8145 6345 B\001
4 1 14 50 -1 18 15 0.0000 4 180 165 5400 4590 P\001
4 1 0 50 -1 18 15 0.0000 4 195 195 6750 5445 Q\001
4 0 0 50 -1 18 15 0.0000 4 195 1470 3150 5175 Q = A+u*AM\001
4 0 0 50 -1 18 15 0.0000 4 195 1425 3150 5625 P = B+v*BQ\001
4 0 0 50 -1 18 15 0.0000 4 195 1650 3150 6075 Q = B+1/v*BP\001
4 0 0 50 -1 18 15 0.0000 4 180 1695 2925 4635 Tool direction\001
4 0 0 50 -1 18 15 0.0000 4 240 1890 5715 7785 Polygon, inside\001
4 0 0 50 -1 18 15 0.0000 4 180 975 3150 7020 v >= 0 ?\001
4 0 0 50 -1 18 15 0.0000 4 225 1590 3150 6660 u in [0, 1] &&\001
4 0 0 50 -1 18 15 0.0000 4 180 210 9225 4275 M\001
4 0 0 50 -1 18 15 0.0000 4 240 2115 7155 4005 Midpoint, outside\001

122
cameo/area.c
View File

@ -25,7 +25,7 @@
#include "area.h" #include "area.h"
#define EPSILON 0.0001 #define EPSILON 1e-6
static int bbox(const struct path *path, static int bbox(const struct path *path,
@ -107,13 +107,14 @@ static int cramer2(double a, double b, double c, double d, double e, double f,
/* /*
* Solve * Solve
* ax+na*bx = cx+nb*dx *
* ay+na*by = cy+nb*dy * ax + na*bx = cx + nb*dx
* ay + na*by = cy + nb*dy
* *
* which is * which is
* *
* na*bx + nb*-dx = cx-ax * na*bx + nb*-dx = cx - ax
* na*by + nb*-dy = cy-ay * na*by + nb*-dy = cy - ay
*/ */
static int intersect(double ax, double ay, double bx, double by, static int intersect(double ax, double ay, double bx, double by,
@ -123,6 +124,55 @@ static int intersect(double ax, double ay, double bx, double by,
} }
/*
* See above.fig. The equation we solve is
*
* Q = A+u*(AM)
* Q = B+v*(BP)
*
* equals
*
* ax + u*(mx-ax) = bx + v*(px-bx)
* ay + u*(my-ay) = by + v*(py-by)
*
* equals
*
* u*(mx-ax) + v*(bx-px) = bx - ax
* u*(my-ay) + v*(by-py) = by - ay
*
* For BC, the equation becomes
*
* Q = C+u*(CM)
* Q = B+v*(BP)
*/
static int above(const struct point *a, const struct point *b,
const struct point *c, double px, double py)
{
double ab, bc;
double mx, my;
double u, v;
ab = hypot(a->x-b->x, a->y-b->y);
bc = hypot(b->x-c->x, b->y-c->y);
if (fabs(ab) < EPSILON || fabs(bc) < EPSILON)
return 0;
mx = b->x-(b->y-a->y)/ab-(c->y-b->y)/bc;
my = b->y+(b->x-a->x)/ab+(c->x-b->x)/bc;
if (cramer2(mx-a->x, b->x-px, my-a->y, b->y-py, b->x-a->x, b->y-a->y,
&u, &v))
if (u >= 0 && u <= 1 && v >= 0)
return 1;
if (cramer2(mx-c->x, b->x-px, my-c->y, b->y-py, b->x-c->x, b->y-c->y,
&u, &v))
if (u >= 0 && u <= 1 && v >= 0)
return 1;
return 0;
}
/* /*
* Solve * Solve
* *
@ -131,7 +181,7 @@ static int intersect(double ax, double ay, double bx, double by,
* http://en.wikipedia.org/wiki/Quadratic_equation * http://en.wikipedia.org/wiki/Quadratic_equation
*/ */
static int touch(double ax, double ay, double bx, double by, static int touch_solve(double ax, double ay, double bx, double by,
double cx, double cy, double r, int enter, double *n) double cx, double cy, double r, int enter, double *n)
{ {
double dx = cx-ax; double dx = cx-ax;
@ -153,9 +203,42 @@ static int touch(double ax, double ay, double bx, double by,
} }
/*
* The points A, B, and C are (if the path is left-handed):
*
* - A: the beginning of the segment leading into the corner
* - B: the corner point
* - C: the beginning of the segment leading out of the corner
*
* If the path is right-handed, we swap A and C, making it left-handed.
*/
static int touch(double ax, double ay, double bx, double by,
const struct point *a, const struct point *b, const struct point *c,
double r, int enter, int left, double *n)
{
double px, py;
if (!touch_solve(ax, ay, bx, by, b->x, b->y, r, enter, n))
return 0;
px = ax+*n*bx;
py = ay+*n*by;
return above(a, b, c, px, py) == left;
}
/*
* Here, the points A, B, C, and D are:
*
* - A: before the beginning of the current segment
* - B: the beginning
* - C: the end
* - D: the next point beyond the end
*/
static int hit_segment(double fx, double fy, double tx, double ty, static int hit_segment(double fx, double fy, double tx, double ty,
const struct point *a, const struct point *b, double r, int enter, const struct point *a, const struct point *b, const struct point *c,
int left, double *n) const struct point *d, double r, int enter, int left, double *n)
{ {
double dx, dy, nx, ny, nn; double dx, dy, nx, ny, nn;
double px, py; double px, py;
@ -164,8 +247,8 @@ static int hit_segment(double fx, double fy, double tx, double ty,
tx -= fx; tx -= fx;
ty -= fy; ty -= fy;
dx = b->x-a->x; dx = c->x-b->x;
dy = b->y-a->y; dy = c->y-b->y;
if (left) { if (left) {
nx = dx; nx = dx;
@ -181,17 +264,17 @@ static int hit_segment(double fx, double fy, double tx, double ty,
nn = hypot(nx, ny); nn = hypot(nx, ny);
px = a->x-ny/nn*r; px = b->x-ny/nn*r;
py = a->y+nx/nn*r; py = b->y+nx/nn*r;
if (!intersect(fx, fy, tx, ty, px, py, dx, dy, &na, &nb)) if (!intersect(fx, fy, tx, ty, px, py, dx, dy, &na, &nb))
return 0; return 0;
if (nb <= 0) { if (nb <= 0) {
if (!touch(fx, fy, tx, ty, a->x, a->y, r, enter, &na)) if (!touch(fx, fy, tx, ty, a, b, c, r, enter, left, &na))
return 0; return 0;
} }
if (nb >= 1) { if (nb >= 1) {
if (!touch(fx, fy, tx, ty, b->x, b->y, r, enter, &na)) if (!touch(fx, fy, tx, ty, b, c, d, r, enter, left, &na))
return 0; return 0;
} }
if (na <= 0 || na >= 1) if (na <= 0 || na >= 1)
@ -204,21 +287,28 @@ static int hit_segment(double fx, double fy, double tx, double ty,
static int hit_path(double fx, double fy, double tx, double ty, static int hit_path(double fx, double fy, double tx, double ty,
const struct path *path, int inside, int enter, double r, double *x) const struct path *path, int inside, int enter, double r, double *x)
{ {
const struct point *p; const struct point *p, *last, *next2;
int left; int left;
double nx, tmp; double nx, tmp;
int found = 0; int found = 0;
/*
* @@@ We don't wrap around the ends properly and create a zero-sized
* imaginary segment between path->first and path->last.
*/
left = path_tool_is_left(path); left = path_tool_is_left(path);
if (inside) if (inside)
left = !left; left = !left;
last = path->last;
for (p = path->first; p != path->last; p = p->next) { for (p = path->first; p != path->last; p = p->next) {
if (hit_segment(fx, fy, tx, ty, p, p->next, next2 = p->next->next ? p->next->next : path->first;
if (hit_segment(fx, fy, tx, ty, last, p, p->next, next2,
r, enter, left, &tmp)) { r, enter, left, &tmp)) {
if (!found || nx > tmp) if (!found || nx > tmp)
nx = tmp; nx = tmp;
found = 1; found = 1;
} }
last = p;
} }
if (found) if (found)
*x = fx+nx*(tx-fx); *x = fx+nx*(tx-fx);