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curve: Move some curve apis to gskcurve.c

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Some of this will be reused elsewhere, so move
it out of gskpathstroke.c.
This commit is contained in:
Matthias Clasen
2022-03-20 23:08:47 -04:00
parent cf793f94ac
commit 5eb79b3b01
3 changed files with 152 additions and 143 deletions
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144
gsk/gskcurve.c
View File

@@ -1802,3 +1802,147 @@ gsk_curve_get_curvature (const GskCurve *curve,
return k;
}
static void
align_points (const graphene_point_t *p,
const graphene_point_t *a,
const graphene_point_t *b,
graphene_point_t *q,
int n)
{
graphene_vec2_t n1;
float angle;
float s, c;
get_tangent (a, b, &n1);
angle = - atan2 (graphene_vec2_get_y (&n1), graphene_vec2_get_x (&n1));
sincosf (angle, &s, &c);
for (int i = 0; i < n; i++)
{
q[i].x = (p[i].x - a->x) * c - (p[i].y - a->y) * s;
q[i].y = (p[i].x - a->x) * s + (p[i].y - a->y) * c;
}
}
/* find solutions for at^2 + bt + c = 0 */
static int
solve_quadratic (float a, float b, float c, float t[2])
{
float d;
int n = 0;
if (fabs (a) > 0.0001)
{
if (b*b > 4*a*c)
{
d = sqrt (b*b - 4*a*c);
t[n++] = (-b + d)/(2*a);
t[n++] = (-b - d)/(2*a);
}
else
{
t[n++] = -b / (2*a);
}
}
else if (fabs (b) > 0.0001)
{
t[n++] = -c / b;
}
return n;
}
static int
filter_allowable (float t[3],
int n)
{
float g[3];
int j = 0;
for (int i = 0; i < n; i++)
if (0 < t[i] && t[i] < 1)
g[j++] = t[i];
for (int i = 0; i < j; i++)
t[i] = g[i];
return j;
}
/* Get the points where the curvature of curve is
* zero, or a maximum or minimum, inside the open
* interval from 0 to 1.
*/
int
gsk_curve_get_curvature_points (const GskCurve *curve,
float t[3])
{
const graphene_point_t *pts = curve->curve.points;
graphene_point_t p[4];
float a, b, c, d;
float x, y, z;
int n;
align_points (pts, &pts[0], &pts[3], p, 4);
a = p[2].x * p[1].y;
b = p[3].x * p[1].y;
c = p[1].x * p[2].y;
d = p[3].x * p[2].y;
x = - 3*a + 2*b + 3*c - d;
y = 3*a - b - 3*c;
z = c - a;
n = solve_quadratic (x, y, z, t);
return filter_allowable (t, n);
}
/* Find cusps inside the open interval from 0 to 1. According
* to Stone & deRose, A Geometric Characterization of Parametric
* Cubic curves, a necessary and sufficient condition is that
* the first derivative vanishes.
*/
int
gsk_curve_get_cusps (const GskCurve *curve,
float t[2])
{
const graphene_point_t *pts = curve->curve.points;
graphene_point_t p[3];
float ax, bx, cx;
float ay, by, cy;
float tx[3];
int nx;
int n = 0;
if (curve->op != GSK_PATH_CURVE)
return 0;
p[0].x = 3 * (pts[1].x - pts[0].x);
p[0].y = 3 * (pts[1].y - pts[0].y);
p[1].x = 3 * (pts[2].x - pts[1].x);
p[1].y = 3 * (pts[2].y - pts[1].y);
p[2].x = 3 * (pts[3].x - pts[2].x);
p[2].y = 3 * (pts[3].y - pts[2].y);
ax = p[0].x - 2 * p[1].x + p[2].x;
bx = - 2 * p[0].x + 2 * p[1].x;
cx = p[0].x;
nx = solve_quadratic (ax, bx, cx, tx);
nx = filter_allowable (tx, nx);
ay = p[0].y - 2 * p[1].y + p[2].y;
by = - 2 * p[0].y + 2 * p[1].y;
cy = p[0].y;
for (int i = 0; i < nx; i++)
{
float ti = tx[i];
if (0 < ti && ti < 1 &&
fabs (ay * ti * ti + by * ti + cy) < 0.001)
t[n++] = ti;
}
return n;
}

6
gsk/gskcurveprivate.h
View File

@@ -149,6 +149,12 @@ float gsk_curve_get_curvature (const GskCurve
float t,
graphene_point_t *center);
int gsk_curve_get_curvature_points (const GskCurve *curve,
float t[3]);
int gsk_curve_get_cusps (const GskCurve *curve,
float t[2]);
G_END_DECLS
#endif /* __GSK_CURVE_PRIVATE_H__ */

145
gsk/gskpathstroke.c
View File

@@ -573,147 +573,6 @@ conic_is_degenerate (const GskCurve *curve)
return FALSE;
}
static void
align_points (const graphene_point_t *p,
const graphene_point_t *a,
const graphene_point_t *b,
graphene_point_t *q,
int n)
{
graphene_vec2_t n1;
float angle;
float s, c;
get_tangent (a, b, &n1);
angle = - atan2 (graphene_vec2_get_y (&n1), graphene_vec2_get_x (&n1));
sincosf (angle, &s, &c);
for (int i = 0; i < n; i++)
{
q[i].x = (p[i].x - a->x) * c - (p[i].y - a->y) * s;
q[i].y = (p[i].x - a->x) * s + (p[i].y - a->y) * c;
}
}
/* find solutions for at^2 + bt + c = 0 */
static int
solve_quadratic (float a, float b, float c, float t[2])
{
float d;
int n = 0;
if (fabs (a) > 0.0001)
{
if (b*b > 4*a*c)
{
d = sqrt (b*b - 4*a*c);
t[n++] = (-b + d)/(2*a);
t[n++] = (-b - d)/(2*a);
}
else
{
t[n++] = -b / (2*a);
}
}
else if (fabs (b) > 0.0001)
{
t[n++] = -c / b;
}
return n;
}
static int
filter_allowable (float t[3],
int n)
{
float g[3];
int j = 0;
for (int i = 0; i < n; i++)
if (0 < t[i] && t[i] < 1)
g[j++] = t[i];
for (int i = 0; i < j; i++)
t[i] = g[i];
return j;
}
/* Get the points where the curvature of curve is
* zero, or a maximum or minimum, inside the open
* interval from 0 to 1.
*/
static int
cubic_curvature_points (const GskCurve *curve,
float t[3])
{
const graphene_point_t *pts = curve->curve.points;
graphene_point_t p[4];
float a, b, c, d;
float x, y, z;
int n;
align_points (pts, &pts[0], &pts[3], p, 4);
a = p[2].x * p[1].y;
b = p[3].x * p[1].y;
c = p[1].x * p[2].y;
d = p[3].x * p[2].y;
x = - 3*a + 2*b + 3*c - d;
y = 3*a - b - 3*c;
z = c - a;
n = solve_quadratic (x, y, z, t);
return filter_allowable (t, n);
}
/* Find cusps inside the open interval from 0 to 1. According
* to Stone & deRose, A Geometric Characterization of Parametric
* Cubic curves, a necessary and sufficient condition is that
* the first derivative vanishes.
*/
static int
find_cusps (const GskCurve *curve,
float t[2])
{
const graphene_point_t *pts = curve->curve.points;
graphene_point_t p[3];
float ax, bx, cx;
float ay, by, cy;
float tx[3];
int nx;
int n = 0;
p[0].x = 3 * (pts[1].x - pts[0].x);
p[0].y = 3 * (pts[1].y - pts[0].y);
p[1].x = 3 * (pts[2].x - pts[1].x);
p[1].y = 3 * (pts[2].y - pts[1].y);
p[2].x = 3 * (pts[3].x - pts[2].x);
p[2].y = 3 * (pts[3].y - pts[2].y);
ax = p[0].x - 2 * p[1].x + p[2].x;
bx = - 2 * p[0].x + 2 * p[1].x;
cx = p[0].x;
nx = solve_quadratic (ax, bx, cx, tx);
nx = filter_allowable (tx, nx);
ay = p[0].y - 2 * p[1].y + p[2].y;
by = - 2 * p[0].y + 2 * p[1].y;
cy = p[0].y;
for (int i = 0; i < nx; i++)
{
float ti = tx[i];
if (0 < ti && ti < 1 &&
fabs (ay * ti * ti + by * ti + cy) < 0.001)
t[n++] = ti;
}
return n;
}
/* }}} */
/* {{{ Stroke helpers */
@@ -1761,7 +1620,7 @@ subdivide_and_add_curve (const GskCurve *curve,
add_curve_cb (curve, force_round_join, data);
else if (level < MAX_SUBDIVISION && cubic_is_simple (curve))
add_curve_cb (curve, force_round_join, data);
else if (level == MAX_SUBDIVISION && (n = find_cusps (curve, t)) > 0)
else if (level == MAX_SUBDIVISION && (n = gsk_curve_get_cusps (curve, t)) > 0)
{
t[n++] = 0;
t[n++] = 1;
@@ -1783,7 +1642,7 @@ subdivide_and_add_curve (const GskCurve *curve,
if (level == MAX_SUBDIVISION)
{
n += cubic_curvature_points (curve, &t[n]);
n += gsk_curve_get_curvature_points (curve, &t[n]);
qsort (t, n, sizeof (float), cmpfloat);
}