4229a37e90
Scale the derivative such that computing the arc length of a unit quarter circle wil produce the expected result of PI/2.
2057 lines
62 KiB
C
2057 lines
62 KiB
C
/*
|
|
* Copyright © 2020 Benjamin Otte
|
|
*
|
|
* This library is free software; you can redistribute it and/or
|
|
* modify it under the terms of the GNU Lesser General Public
|
|
* License as published by the Free Software Foundation; either
|
|
* version 2.1 of the License, or (at your option) any later version.
|
|
*
|
|
* This library is distributed in the hope that it will be useful,
|
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
|
* Lesser General Public License for more details.
|
|
*
|
|
* You should have received a copy of the GNU Lesser General Public
|
|
* License along with this library. If not, see <http://www.gnu.org/licenses/>.
|
|
*
|
|
* Authors: Benjamin Otte <otte@gnome.org>
|
|
*/
|
|
|
|
#include "config.h"
|
|
|
|
#include "gskcurveprivate.h"
|
|
#include "gskboundingboxprivate.h"
|
|
|
|
/* GskCurve collects all the functionality we need for Bézier segments */
|
|
|
|
#define MIN_PROGRESS (1/1024.f)
|
|
|
|
typedef struct _GskCurveClass GskCurveClass;
|
|
|
|
struct _GskCurveClass
|
|
{
|
|
void (* init) (GskCurve *curve,
|
|
gskpathop op);
|
|
void (* init_foreach) (GskCurve *curve,
|
|
GskPathOperation op,
|
|
const graphene_point_t *pts,
|
|
gsize n_pts);
|
|
void (* print) (const GskCurve *curve,
|
|
GString *string);
|
|
gskpathop (* pathop) (const GskCurve *curve);
|
|
const graphene_point_t * (* get_start_point) (const GskCurve *curve);
|
|
const graphene_point_t * (* get_end_point) (const GskCurve *curve);
|
|
void (* get_start_tangent) (const GskCurve *curve,
|
|
graphene_vec2_t *tangent);
|
|
void (* get_end_tangent) (const GskCurve *curve,
|
|
graphene_vec2_t *tangent);
|
|
void (* get_point) (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *pos);
|
|
void (* get_tangent) (const GskCurve *curve,
|
|
float t,
|
|
graphene_vec2_t *tangent);
|
|
void (* reverse) (const GskCurve *curve,
|
|
GskCurve *reverse);
|
|
float (* get_curvature) (const GskCurve *curve,
|
|
float t);
|
|
void (* split) (const GskCurve *curve,
|
|
float progress,
|
|
GskCurve *result1,
|
|
GskCurve *result2);
|
|
void (* segment) (const GskCurve *curve,
|
|
float start,
|
|
float end,
|
|
GskCurve *segment);
|
|
gboolean (* decompose) (const GskCurve *curve,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data);
|
|
gboolean (* decompose_curve) (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data);
|
|
void (* get_bounds) (const GskCurve *curve,
|
|
GskBoundingBox *bounds);
|
|
void (* get_tight_bounds) (const GskCurve *curve,
|
|
GskBoundingBox *bounds);
|
|
void (* get_derivative) (const GskCurve *curve,
|
|
GskCurve *derivative);
|
|
int (* get_crossing) (const GskCurve *curve,
|
|
const graphene_point_t *point);
|
|
};
|
|
|
|
/* {{{ Utilities */
|
|
|
|
#define RAD_TO_DEG(r) ((r)*180.f/M_PI)
|
|
#define DEG_TO_RAD(d) ((d)*M_PI/180.f)
|
|
|
|
static void
|
|
get_tangent (const graphene_point_t *p0,
|
|
const graphene_point_t *p1,
|
|
graphene_vec2_t *t)
|
|
{
|
|
graphene_vec2_init (t, p1->x - p0->x, p1->y - p0->y);
|
|
graphene_vec2_normalize (t, t);
|
|
}
|
|
|
|
static int
|
|
line_intersection (const graphene_point_t *a,
|
|
const graphene_vec2_t *ta,
|
|
const graphene_point_t *c,
|
|
const graphene_vec2_t *tc,
|
|
graphene_point_t *p)
|
|
{
|
|
float a1 = graphene_vec2_get_y (ta);
|
|
float b1 = - graphene_vec2_get_x (ta);
|
|
float c1 = a1*a->x + b1*a->y;
|
|
|
|
float a2 = graphene_vec2_get_y (tc);
|
|
float b2 = - graphene_vec2_get_x (tc);
|
|
float c2 = a2*c->x+ b2*c->y;
|
|
|
|
float det = a1*b2 - a2*b1;
|
|
|
|
if (fabs (det) < 0.001)
|
|
{
|
|
p->x = NAN;
|
|
p->y = NAN;
|
|
return 0;
|
|
}
|
|
else
|
|
{
|
|
p->x = (b2*c1 - b1*c2) / det;
|
|
p->y = (a1*c2 - a2*c1) / det;
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
static int
|
|
line_get_crossing (const graphene_point_t *p,
|
|
const graphene_point_t *p1,
|
|
const graphene_point_t *p2)
|
|
{
|
|
if (p1->y <= p->y)
|
|
{
|
|
if (p2->y > p->y)
|
|
{
|
|
if ((p2->x - p1->x) * (p->y - p1->y) - (p->x - p1->x) * (p2->y - p1->y) > 0)
|
|
return 1;
|
|
}
|
|
}
|
|
else if (p2->y <= p->y)
|
|
{
|
|
if ((p2->x - p1->x) * (p->y - p1->y) - (p->x - p1->x) * (p2->y - p1->y) < 0)
|
|
return -1;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
static int
|
|
get_crossing_by_bisection (const GskCurve *curve,
|
|
const graphene_point_t *point)
|
|
{
|
|
GskBoundingBox bounds;
|
|
GskCurve c1, c2;
|
|
|
|
gsk_curve_get_bounds (curve, &bounds);
|
|
|
|
if (bounds.max.y < point->y || bounds.min.y > point->y || bounds.max.x < point->x)
|
|
return 0;
|
|
|
|
if (bounds.min.x > point->x)
|
|
return line_get_crossing (point, gsk_curve_get_start_point (curve), gsk_curve_get_end_point (curve));
|
|
|
|
if (graphene_point_distance (&bounds.min, &bounds.max, NULL, NULL) < 0.001)
|
|
return line_get_crossing (point, gsk_curve_get_start_point (curve), gsk_curve_get_end_point (curve));
|
|
|
|
gsk_curve_split (curve, 0.5, &c1, &c2);
|
|
|
|
return gsk_curve_get_crossing (&c1, point) + gsk_curve_get_crossing (&c2, point);
|
|
}
|
|
|
|
/* Replace a line by an equivalent quad,
|
|
* and a quad by an equivalent cubic.
|
|
*/
|
|
static void
|
|
gsk_curve_elevate (const GskCurve *curve,
|
|
GskCurve *elevated)
|
|
{
|
|
if (curve->op == GSK_PATH_LINE)
|
|
{
|
|
graphene_point_t p[3];
|
|
|
|
p[0] = curve->line.points[0];
|
|
graphene_point_interpolate (&curve->line.points[0],
|
|
&curve->line.points[1],
|
|
0.5,
|
|
&p[1]);
|
|
p[2] = curve->line.points[1];
|
|
gsk_curve_init (elevated, gsk_pathop_encode (GSK_PATH_QUAD, p));
|
|
}
|
|
else if (curve->op == GSK_PATH_QUAD)
|
|
{
|
|
graphene_point_t p[4];
|
|
|
|
p[0] = curve->quad.points[0];
|
|
graphene_point_interpolate (&curve->quad.points[0],
|
|
&curve->quad.points[1],
|
|
2/3.,
|
|
&p[1]);
|
|
graphene_point_interpolate (&curve->quad.points[2],
|
|
&curve->quad.points[1],
|
|
2/3.,
|
|
&p[2]);
|
|
p[3] = curve->quad.points[2];
|
|
gsk_curve_init (elevated, gsk_pathop_encode (GSK_PATH_CUBIC, p));
|
|
}
|
|
else
|
|
g_assert_not_reached ();
|
|
}
|
|
|
|
static inline void
|
|
_sincosf (float angle, float *s, float *c)
|
|
{
|
|
#ifdef HAVE_SINCOSF
|
|
sincosf (angle, s, c);
|
|
#else
|
|
*s = sinf (angle);
|
|
*c = cosf (angle);
|
|
#endif
|
|
}
|
|
|
|
/* }}} */
|
|
/* {{{ Line */
|
|
|
|
static void
|
|
gsk_line_curve_init_from_points (GskLineCurve *self,
|
|
GskPathOperation op,
|
|
const graphene_point_t *start,
|
|
const graphene_point_t *end)
|
|
{
|
|
self->op = op;
|
|
self->points[0] = *start;
|
|
self->points[1] = *end;
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_init (GskCurve *curve,
|
|
gskpathop op)
|
|
{
|
|
GskLineCurve *self = &curve->line;
|
|
const graphene_point_t *pts = gsk_pathop_points (op);
|
|
|
|
gsk_line_curve_init_from_points (self, gsk_pathop_op (op), &pts[0], &pts[1]);
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_init_foreach (GskCurve *curve,
|
|
GskPathOperation op,
|
|
const graphene_point_t *pts,
|
|
gsize n_pts)
|
|
{
|
|
GskLineCurve *self = &curve->line;
|
|
|
|
g_assert (n_pts == 2);
|
|
|
|
gsk_line_curve_init_from_points (self, op, &pts[0], &pts[1]);
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_print (const GskCurve *curve,
|
|
GString *string)
|
|
{
|
|
g_string_append_printf (string,
|
|
"M %g %g L %g %g",
|
|
curve->line.points[0].x, curve->line.points[0].y,
|
|
curve->line.points[1].x, curve->line.points[1].y);
|
|
}
|
|
|
|
static gskpathop
|
|
gsk_line_curve_pathop (const GskCurve *curve)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
|
|
return gsk_pathop_encode (self->op, self->points);
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_line_curve_get_start_point (const GskCurve *curve)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
|
|
return &self->points[0];
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_line_curve_get_end_point (const GskCurve *curve)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
|
|
return &self->points[1];
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_get_start_end_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
|
|
get_tangent (&self->points[0], &self->points[1], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_get_point (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *pos)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
|
|
graphene_point_interpolate (&self->points[0], &self->points[1], t, pos);
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_get_tangent (const GskCurve *curve,
|
|
float t,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
|
|
get_tangent (&self->points[0], &self->points[1], tangent);
|
|
}
|
|
|
|
static float
|
|
gsk_line_curve_get_curvature (const GskCurve *curve,
|
|
float t)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_reverse (const GskCurve *curve,
|
|
GskCurve *reverse)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
|
|
reverse->op = GSK_PATH_LINE;
|
|
reverse->line.points[0] = self->points[1];
|
|
reverse->line.points[1] = self->points[0];
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_split (const GskCurve *curve,
|
|
float progress,
|
|
GskCurve *start,
|
|
GskCurve *end)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
graphene_point_t point;
|
|
|
|
graphene_point_interpolate (&self->points[0], &self->points[1], progress, &point);
|
|
|
|
if (start)
|
|
gsk_line_curve_init_from_points (&start->line, GSK_PATH_LINE, &self->points[0], &point);
|
|
if (end)
|
|
gsk_line_curve_init_from_points (&end->line, GSK_PATH_LINE, &point, &self->points[1]);
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_segment (const GskCurve *curve,
|
|
float start,
|
|
float end,
|
|
GskCurve *segment)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
graphene_point_t start_point, end_point;
|
|
|
|
graphene_point_interpolate (&self->points[0], &self->points[1], start, &start_point);
|
|
graphene_point_interpolate (&self->points[0], &self->points[1], end, &end_point);
|
|
|
|
gsk_line_curve_init_from_points (&segment->line, GSK_PATH_LINE, &start_point, &end_point);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_line_curve_decompose (const GskCurve *curve,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
|
|
return add_line_func (&self->points[0], &self->points[1], 0.0f, 1.0f, GSK_CURVE_LINE_REASON_STRAIGHT, user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_line_curve_decompose_curve (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
|
|
return add_curve_func (GSK_PATH_LINE, self->points, 2, user_data);
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_get_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
const graphene_point_t *pts = self->points;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[1]);
|
|
}
|
|
|
|
static void
|
|
gsk_line_curve_get_derivative (const GskCurve *curve,
|
|
GskCurve *deriv)
|
|
{
|
|
const GskLineCurve *self = &curve->line;
|
|
graphene_point_t p;
|
|
|
|
p.x = self->points[1].x - self->points[0].x;
|
|
p.y = self->points[1].y - self->points[0].y;
|
|
|
|
gsk_line_curve_init_from_points (&deriv->line, GSK_PATH_LINE, &p, &p);
|
|
}
|
|
|
|
static int
|
|
gsk_line_curve_get_crossing (const GskCurve *curve,
|
|
const graphene_point_t *point)
|
|
{
|
|
return line_get_crossing (point, gsk_curve_get_start_point (curve), gsk_curve_get_end_point (curve));
|
|
}
|
|
|
|
static const GskCurveClass GSK_LINE_CURVE_CLASS = {
|
|
gsk_line_curve_init,
|
|
gsk_line_curve_init_foreach,
|
|
gsk_line_curve_print,
|
|
gsk_line_curve_pathop,
|
|
gsk_line_curve_get_start_point,
|
|
gsk_line_curve_get_end_point,
|
|
gsk_line_curve_get_start_end_tangent,
|
|
gsk_line_curve_get_start_end_tangent,
|
|
gsk_line_curve_get_point,
|
|
gsk_line_curve_get_tangent,
|
|
gsk_line_curve_reverse,
|
|
gsk_line_curve_get_curvature,
|
|
gsk_line_curve_split,
|
|
gsk_line_curve_segment,
|
|
gsk_line_curve_decompose,
|
|
gsk_line_curve_decompose_curve,
|
|
gsk_line_curve_get_bounds,
|
|
gsk_line_curve_get_bounds,
|
|
gsk_line_curve_get_derivative,
|
|
gsk_line_curve_get_crossing,
|
|
};
|
|
|
|
/* }}} */
|
|
/* {{{ Quadratic */
|
|
|
|
static void
|
|
gsk_quad_curve_ensure_coefficients (const GskQuadCurve *curve)
|
|
{
|
|
GskQuadCurve *self = (GskQuadCurve *) curve;
|
|
const graphene_point_t *pts = self->points;
|
|
|
|
if (self->has_coefficients)
|
|
return;
|
|
|
|
self->coeffs[2] = pts[0];
|
|
self->coeffs[1] = GRAPHENE_POINT_INIT (2 * (pts[1].x - pts[0].x),
|
|
2 * (pts[1].y - pts[0].y));
|
|
self->coeffs[0] = GRAPHENE_POINT_INIT (pts[2].x - 2 * pts[1].x + pts[0].x,
|
|
pts[2].y - 2 * pts[1].y + pts[0].y);
|
|
|
|
self->has_coefficients = TRUE;
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_init_from_points (GskQuadCurve *self,
|
|
const graphene_point_t pts[3])
|
|
{
|
|
self->op = GSK_PATH_QUAD;
|
|
self->has_coefficients = FALSE;
|
|
memcpy (self->points, pts, sizeof (graphene_point_t) * 3);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_init (GskCurve *curve,
|
|
gskpathop op)
|
|
{
|
|
GskQuadCurve *self = &curve->quad;
|
|
|
|
gsk_quad_curve_init_from_points (self, gsk_pathop_points (op));
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_init_foreach (GskCurve *curve,
|
|
GskPathOperation op,
|
|
const graphene_point_t *pts,
|
|
gsize n_pts)
|
|
{
|
|
GskQuadCurve *self = &curve->quad;
|
|
|
|
g_assert (n_pts == 3);
|
|
|
|
gsk_quad_curve_init_from_points (self, pts);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_print (const GskCurve *curve,
|
|
GString *string)
|
|
{
|
|
g_string_append_printf (string,
|
|
"M %g %g Q %g %g %g %g",
|
|
curve->quad.points[0].x, curve->quad.points[0].y,
|
|
curve->quad.points[1].x, curve->cubic.points[1].y,
|
|
curve->quad.points[2].x, curve->cubic.points[2].y);
|
|
}
|
|
|
|
static gskpathop
|
|
gsk_quad_curve_pathop (const GskCurve *curve)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
return gsk_pathop_encode (self->op, self->points);
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_quad_curve_get_start_point (const GskCurve *curve)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
return &self->points[0];
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_quad_curve_get_end_point (const GskCurve *curve)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
return &self->points[2];
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_start_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
get_tangent (&self->points[0], &self->points[1], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_end_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
get_tangent (&self->points[1], &self->points[2], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_point (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *pos)
|
|
{
|
|
GskQuadCurve *self = (GskQuadCurve *) &curve->quad;
|
|
const graphene_point_t *c = self->coeffs;
|
|
|
|
gsk_quad_curve_ensure_coefficients (self);
|
|
|
|
*pos = GRAPHENE_POINT_INIT ((c[0].x * t + c[1].x) * t + c[2].x,
|
|
(c[0].y * t + c[1].y) * t + c[2].y);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_tangent (const GskCurve *curve,
|
|
float t,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
GskQuadCurve *self = (GskQuadCurve *) &curve->quad;
|
|
const graphene_point_t *c = self->coeffs;
|
|
|
|
gsk_quad_curve_ensure_coefficients (self);
|
|
|
|
graphene_vec2_init (tangent,
|
|
2.0f * c[0].x * t + c[1].x,
|
|
2.0f * c[0].y * t + c[1].y);
|
|
graphene_vec2_normalize (tangent, tangent);
|
|
}
|
|
|
|
|
|
static float gsk_cubic_curve_get_curvature (const GskCurve *curve,
|
|
float t);
|
|
|
|
static float
|
|
gsk_quad_curve_get_curvature (const GskCurve *curve,
|
|
float t)
|
|
{
|
|
return gsk_cubic_curve_get_curvature (curve, t);
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_reverse (const GskCurve *curve,
|
|
GskCurve *reverse)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
reverse->op = GSK_PATH_QUAD;
|
|
reverse->cubic.points[0] = self->points[2];
|
|
reverse->cubic.points[1] = self->points[1];
|
|
reverse->cubic.points[2] = self->points[0];
|
|
reverse->cubic.has_coefficients = FALSE;
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_split (const GskCurve *curve,
|
|
float progress,
|
|
GskCurve *start,
|
|
GskCurve *end)
|
|
{
|
|
GskQuadCurve *self = (GskQuadCurve *) &curve->quad;
|
|
const graphene_point_t *pts = self->points;
|
|
graphene_point_t ab, bc;
|
|
graphene_point_t final;
|
|
|
|
graphene_point_interpolate (&pts[0], &pts[1], progress, &ab);
|
|
graphene_point_interpolate (&pts[1], &pts[2], progress, &bc);
|
|
graphene_point_interpolate (&ab, &bc, progress, &final);
|
|
|
|
if (start)
|
|
gsk_quad_curve_init_from_points (&start->quad, (graphene_point_t[3]) { pts[0], ab, final });
|
|
if (end)
|
|
gsk_quad_curve_init_from_points (&end->quad, (graphene_point_t[3]) { final, bc, pts[2] });
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_segment (const GskCurve *curve,
|
|
float start,
|
|
float end,
|
|
GskCurve *segment)
|
|
{
|
|
GskCurve tmp;
|
|
|
|
gsk_quad_curve_split (curve, start, NULL, &tmp);
|
|
gsk_quad_curve_split (&tmp, (end - start) / (1.0f - start), segment, NULL);
|
|
}
|
|
|
|
/* taken from Skia, including the very descriptive name */
|
|
static gboolean
|
|
gsk_quad_curve_too_curvy (const GskQuadCurve *self,
|
|
float tolerance)
|
|
{
|
|
const graphene_point_t *pts = self->points;
|
|
float dx, dy;
|
|
|
|
dx = fabs (pts[1].x / 2 - (pts[0].x + pts[2].x) / 4);
|
|
dy = fabs (pts[1].y / 2 - (pts[0].y + pts[2].y) / 4);
|
|
|
|
return MAX (dx, dy) > tolerance;
|
|
}
|
|
|
|
static gboolean
|
|
gsk_quad_curve_decompose_step (const GskCurve *curve,
|
|
float start_progress,
|
|
float end_progress,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
GskCurve left, right;
|
|
float mid_progress;
|
|
|
|
if (!gsk_quad_curve_too_curvy (self, tolerance))
|
|
return add_line_func (&self->points[0], &self->points[2], start_progress, end_progress, GSK_CURVE_LINE_REASON_STRAIGHT, user_data);
|
|
if (end_progress - start_progress <= MIN_PROGRESS)
|
|
return add_line_func (&self->points[0], &self->points[2], start_progress, end_progress, GSK_CURVE_LINE_REASON_SHORT, user_data);
|
|
|
|
gsk_quad_curve_split ((const GskCurve *) self, 0.5, &left, &right);
|
|
mid_progress = (start_progress + end_progress) / 2;
|
|
|
|
return gsk_quad_curve_decompose_step (&left, start_progress, mid_progress, tolerance, add_line_func, user_data)
|
|
&& gsk_quad_curve_decompose_step (&right, mid_progress, end_progress, tolerance, add_line_func, user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_quad_curve_decompose (const GskCurve *curve,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
return gsk_quad_curve_decompose_step (curve, 0.0, 1.0, tolerance, add_line_func, user_data);
|
|
}
|
|
|
|
typedef struct
|
|
{
|
|
GskCurveAddCurveFunc add_curve;
|
|
gpointer user_data;
|
|
} AddLineData;
|
|
|
|
static gboolean
|
|
gsk_curve_add_line_cb (const graphene_point_t *from,
|
|
const graphene_point_t *to,
|
|
float from_progress,
|
|
float to_progress,
|
|
GskCurveLineReason reason,
|
|
gpointer user_data)
|
|
{
|
|
AddLineData *data = user_data;
|
|
graphene_point_t p[2] = { *from, *to };
|
|
|
|
return data->add_curve (GSK_PATH_LINE, p, 2, data->user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_quad_curve_decompose_curve (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
|
|
if (flags & GSK_PATH_FOREACH_ALLOW_QUAD)
|
|
return add_curve_func (GSK_PATH_QUAD, self->points, 3, user_data);
|
|
else if (flags & GSK_PATH_FOREACH_ALLOW_CUBIC)
|
|
{
|
|
GskCurve c;
|
|
|
|
gsk_curve_elevate (curve, &c);
|
|
return add_curve_func (GSK_PATH_CUBIC, c.cubic.points, 4, user_data);
|
|
}
|
|
else
|
|
{
|
|
return gsk_quad_curve_decompose (curve,
|
|
tolerance,
|
|
gsk_curve_add_line_cb,
|
|
&(AddLineData) { add_curve_func, user_data });
|
|
}
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
const graphene_point_t *pts = self->points;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[2]);
|
|
gsk_bounding_box_expand (bounds, &pts[1]);
|
|
}
|
|
|
|
/* Solve P' = 0 where P is
|
|
* P = (1-t)^2*pa + 2*t*(1-t)*pb + t^2*pc
|
|
*/
|
|
static int
|
|
get_quadratic_extrema (float pa, float pb, float pc, float t[1])
|
|
{
|
|
float d = pa - 2 * pb + pc;
|
|
|
|
if (fabs (d) > 0.0001)
|
|
{
|
|
t[0] = (pa - pb) / d;
|
|
return 1;
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_tight_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
const graphene_point_t *pts = self->points;
|
|
float t[4];
|
|
int n;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[2]);
|
|
|
|
n = 0;
|
|
n += get_quadratic_extrema (pts[0].x, pts[1].x, pts[2].x, &t[n]);
|
|
n += get_quadratic_extrema (pts[0].y, pts[1].y, pts[2].y, &t[n]);
|
|
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
graphene_point_t p;
|
|
|
|
gsk_quad_curve_get_point (curve, t[i], &p);
|
|
gsk_bounding_box_expand (bounds, &p);
|
|
}
|
|
}
|
|
|
|
static void
|
|
gsk_quad_curve_get_derivative (const GskCurve *curve,
|
|
GskCurve *deriv)
|
|
{
|
|
const GskQuadCurve *self = &curve->quad;
|
|
graphene_point_t p[2];
|
|
|
|
p[0].x = 2.f * (self->points[1].x - self->points[0].x);
|
|
p[0].y = 2.f * (self->points[1].y - self->points[0].y);
|
|
p[1].x = 2.f * (self->points[2].x - self->points[1].x);
|
|
p[1].y = 2.f * (self->points[2].y - self->points[1].y);
|
|
|
|
gsk_line_curve_init_from_points (&deriv->line, GSK_PATH_LINE, &p[0], &p[1]);
|
|
}
|
|
|
|
static int
|
|
gsk_quad_curve_get_crossing (const GskCurve *curve,
|
|
const graphene_point_t *point)
|
|
{
|
|
return get_crossing_by_bisection (curve, point);
|
|
}
|
|
|
|
static const GskCurveClass GSK_QUAD_CURVE_CLASS = {
|
|
gsk_quad_curve_init,
|
|
gsk_quad_curve_init_foreach,
|
|
gsk_quad_curve_print,
|
|
gsk_quad_curve_pathop,
|
|
gsk_quad_curve_get_start_point,
|
|
gsk_quad_curve_get_end_point,
|
|
gsk_quad_curve_get_start_tangent,
|
|
gsk_quad_curve_get_end_tangent,
|
|
gsk_quad_curve_get_point,
|
|
gsk_quad_curve_get_tangent,
|
|
gsk_quad_curve_reverse,
|
|
gsk_quad_curve_get_curvature,
|
|
gsk_quad_curve_split,
|
|
gsk_quad_curve_segment,
|
|
gsk_quad_curve_decompose,
|
|
gsk_quad_curve_decompose_curve,
|
|
gsk_quad_curve_get_bounds,
|
|
gsk_quad_curve_get_tight_bounds,
|
|
gsk_quad_curve_get_derivative,
|
|
gsk_quad_curve_get_crossing,
|
|
};
|
|
|
|
/* }}} */
|
|
/* {{{ Cubic */
|
|
|
|
static void
|
|
gsk_cubic_curve_ensure_coefficients (const GskCubicCurve *curve)
|
|
{
|
|
GskCubicCurve *self = (GskCubicCurve *) curve;
|
|
const graphene_point_t *pts = &self->points[0];
|
|
|
|
if (self->has_coefficients)
|
|
return;
|
|
|
|
self->coeffs[0] = GRAPHENE_POINT_INIT (pts[3].x - 3.0f * pts[2].x + 3.0f * pts[1].x - pts[0].x,
|
|
pts[3].y - 3.0f * pts[2].y + 3.0f * pts[1].y - pts[0].y);
|
|
self->coeffs[1] = GRAPHENE_POINT_INIT (3.0f * pts[2].x - 6.0f * pts[1].x + 3.0f * pts[0].x,
|
|
3.0f * pts[2].y - 6.0f * pts[1].y + 3.0f * pts[0].y);
|
|
self->coeffs[2] = GRAPHENE_POINT_INIT (3.0f * pts[1].x - 3.0f * pts[0].x,
|
|
3.0f * pts[1].y - 3.0f * pts[0].y);
|
|
self->coeffs[3] = pts[0];
|
|
|
|
self->has_coefficients = TRUE;
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_init_from_points (GskCubicCurve *self,
|
|
const graphene_point_t pts[4])
|
|
{
|
|
self->op = GSK_PATH_CUBIC;
|
|
self->has_coefficients = FALSE;
|
|
memcpy (self->points, pts, sizeof (graphene_point_t) * 4);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_init (GskCurve *curve,
|
|
gskpathop op)
|
|
{
|
|
GskCubicCurve *self = &curve->cubic;
|
|
|
|
gsk_cubic_curve_init_from_points (self, gsk_pathop_points (op));
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_init_foreach (GskCurve *curve,
|
|
GskPathOperation op,
|
|
const graphene_point_t *pts,
|
|
gsize n_pts)
|
|
{
|
|
GskCubicCurve *self = &curve->cubic;
|
|
|
|
g_assert (n_pts == 4);
|
|
|
|
gsk_cubic_curve_init_from_points (self, pts);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_print (const GskCurve *curve,
|
|
GString *string)
|
|
{
|
|
g_string_append_printf (string,
|
|
"M %f %f C %f %f %f %f %f %f",
|
|
curve->cubic.points[0].x, curve->cubic.points[0].y,
|
|
curve->cubic.points[1].x, curve->cubic.points[1].y,
|
|
curve->cubic.points[2].x, curve->cubic.points[2].y,
|
|
curve->cubic.points[3].x, curve->cubic.points[3].y);
|
|
}
|
|
|
|
static gskpathop
|
|
gsk_cubic_curve_pathop (const GskCurve *curve)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
return gsk_pathop_encode (self->op, self->points);
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_cubic_curve_get_start_point (const GskCurve *curve)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
return &self->points[0];
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_cubic_curve_get_end_point (const GskCurve *curve)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
return &self->points[3];
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_start_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
if (graphene_point_near (&self->points[0], &self->points[1], 0.0001))
|
|
{
|
|
if (graphene_point_near (&self->points[0], &self->points[2], 0.0001))
|
|
get_tangent (&self->points[0], &self->points[3], tangent);
|
|
else
|
|
get_tangent (&self->points[0], &self->points[2], tangent);
|
|
}
|
|
else
|
|
get_tangent (&self->points[0], &self->points[1], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_end_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
if (graphene_point_near (&self->points[2], &self->points[3], 0.0001))
|
|
{
|
|
if (graphene_point_near (&self->points[1], &self->points[3], 0.0001))
|
|
get_tangent (&self->points[0], &self->points[3], tangent);
|
|
else
|
|
get_tangent (&self->points[1], &self->points[3], tangent);
|
|
}
|
|
else
|
|
get_tangent (&self->points[2], &self->points[3], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_point (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *pos)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
const graphene_point_t *c = self->coeffs;
|
|
|
|
gsk_cubic_curve_ensure_coefficients (self);
|
|
|
|
*pos = GRAPHENE_POINT_INIT (((c[0].x * t + c[1].x) * t +c[2].x) * t + c[3].x,
|
|
((c[0].y * t + c[1].y) * t +c[2].y) * t + c[3].y);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_tangent (const GskCurve *curve,
|
|
float t,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
const graphene_point_t *c = self->coeffs;
|
|
|
|
gsk_cubic_curve_ensure_coefficients (self);
|
|
|
|
graphene_vec2_init (tangent,
|
|
(3.0f * c[0].x * t + 2.0f * c[1].x) * t + c[2].x,
|
|
(3.0f * c[0].y * t + 2.0f * c[1].y) * t + c[2].y);
|
|
graphene_vec2_normalize (tangent, tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_reverse (const GskCurve *curve,
|
|
GskCurve *reverse)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
reverse->op = GSK_PATH_CUBIC;
|
|
reverse->cubic.points[0] = self->points[3];
|
|
reverse->cubic.points[1] = self->points[2];
|
|
reverse->cubic.points[2] = self->points[1];
|
|
reverse->cubic.points[3] = self->points[0];
|
|
reverse->cubic.has_coefficients = FALSE;
|
|
}
|
|
|
|
static inline float
|
|
cross (const graphene_vec2_t *v1,
|
|
const graphene_vec2_t *v2)
|
|
{
|
|
return graphene_vec2_get_x (v1) * graphene_vec2_get_y (v2)
|
|
- graphene_vec2_get_y (v1) * graphene_vec2_get_x (v2);
|
|
}
|
|
|
|
static inline float
|
|
pow3 (float w)
|
|
{
|
|
return w * w * w;
|
|
}
|
|
|
|
static void gsk_cubic_curve_get_derivative (const GskCurve *curve,
|
|
GskCurve *deriv);
|
|
|
|
static float
|
|
gsk_cubic_curve_get_curvature (const GskCurve *curve,
|
|
float t)
|
|
{
|
|
GskCurve c1, c2;
|
|
graphene_point_t p, pp;
|
|
graphene_vec2_t d, dd;
|
|
float num, denom;
|
|
|
|
gsk_cubic_curve_get_derivative (curve, &c1);
|
|
gsk_quad_curve_get_derivative (&c1, &c2);
|
|
|
|
gsk_curve_get_point (&c1, t, &p);
|
|
gsk_curve_get_point (&c2, t, &pp);
|
|
|
|
graphene_vec2_init (&d, p.x, p.y);
|
|
graphene_vec2_init (&dd, pp.x, pp.y);
|
|
|
|
num = cross (&d, &dd);
|
|
if (num == 0)
|
|
return 0;
|
|
|
|
denom = pow3 (graphene_vec2_length (&d));
|
|
if (denom == 0)
|
|
return 0;
|
|
|
|
return num / denom;
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_split (const GskCurve *curve,
|
|
float progress,
|
|
GskCurve *start,
|
|
GskCurve *end)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
const graphene_point_t *pts = self->points;
|
|
graphene_point_t ab, bc, cd;
|
|
graphene_point_t abbc, bccd;
|
|
graphene_point_t final;
|
|
|
|
graphene_point_interpolate (&pts[0], &pts[1], progress, &ab);
|
|
graphene_point_interpolate (&pts[1], &pts[2], progress, &bc);
|
|
graphene_point_interpolate (&pts[2], &pts[3], progress, &cd);
|
|
graphene_point_interpolate (&ab, &bc, progress, &abbc);
|
|
graphene_point_interpolate (&bc, &cd, progress, &bccd);
|
|
graphene_point_interpolate (&abbc, &bccd, progress, &final);
|
|
|
|
if (start)
|
|
gsk_cubic_curve_init_from_points (&start->cubic, (graphene_point_t[4]) { pts[0], ab, abbc, final });
|
|
if (end)
|
|
gsk_cubic_curve_init_from_points (&end->cubic, (graphene_point_t[4]) { final, bccd, cd, pts[3] });
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_segment (const GskCurve *curve,
|
|
float start,
|
|
float end,
|
|
GskCurve *segment)
|
|
{
|
|
GskCurve tmp;
|
|
|
|
gsk_cubic_curve_split (curve, start, NULL, &tmp);
|
|
gsk_cubic_curve_split (&tmp, (end - start) / (1.0f - start), segment, NULL);
|
|
}
|
|
|
|
/* taken from Skia, including the very descriptive name */
|
|
static gboolean
|
|
gsk_cubic_curve_too_curvy (const GskCubicCurve *self,
|
|
float tolerance)
|
|
{
|
|
const graphene_point_t *pts = self->points;
|
|
graphene_point_t p;
|
|
|
|
graphene_point_interpolate (&pts[0], &pts[3], 1.0f / 3, &p);
|
|
if (MAX (ABS (p.x - pts[1].x), ABS (p.y - pts[1].y)) > tolerance)
|
|
return TRUE;
|
|
|
|
graphene_point_interpolate (&pts[0], &pts[3], 2.0f / 3, &p);
|
|
if (MAX (ABS (p.x - pts[2].x), ABS (p.y - pts[2].y)) > tolerance)
|
|
return TRUE;
|
|
|
|
return FALSE;
|
|
}
|
|
|
|
static gboolean
|
|
gsk_cubic_curve_decompose_step (const GskCurve *curve,
|
|
float start_progress,
|
|
float end_progress,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
GskCurve left, right;
|
|
float mid_progress;
|
|
|
|
if (!gsk_cubic_curve_too_curvy (self, tolerance))
|
|
return add_line_func (&self->points[0], &self->points[3], start_progress, end_progress, GSK_CURVE_LINE_REASON_STRAIGHT, user_data);
|
|
if (end_progress - start_progress <= MIN_PROGRESS)
|
|
return add_line_func (&self->points[0], &self->points[3], start_progress, end_progress, GSK_CURVE_LINE_REASON_SHORT, user_data);
|
|
|
|
gsk_cubic_curve_split ((const GskCurve *) self, 0.5, &left, &right);
|
|
mid_progress = (start_progress + end_progress) / 2;
|
|
|
|
return gsk_cubic_curve_decompose_step (&left, start_progress, mid_progress, tolerance, add_line_func, user_data)
|
|
&& gsk_cubic_curve_decompose_step (&right, mid_progress, end_progress, tolerance, add_line_func, user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_cubic_curve_decompose (const GskCurve *curve,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
return gsk_cubic_curve_decompose_step (curve, 0.0, 1.0, tolerance, add_line_func, user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_cubic_curve_decompose_curve (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
|
|
if (flags & GSK_PATH_FOREACH_ALLOW_CUBIC)
|
|
return add_curve_func (GSK_PATH_CUBIC, self->points, 4, user_data);
|
|
|
|
/* FIXME: Quadratic or arc approximation */
|
|
return gsk_cubic_curve_decompose (curve,
|
|
tolerance,
|
|
gsk_curve_add_line_cb,
|
|
&(AddLineData) { add_curve_func, user_data });
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
const graphene_point_t *pts = self->points;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[3]);
|
|
gsk_bounding_box_expand (bounds, &pts[1]);
|
|
gsk_bounding_box_expand (bounds, &pts[2]);
|
|
}
|
|
|
|
static inline gboolean
|
|
acceptable (float t)
|
|
{
|
|
return 0 <= t && t <= 1;
|
|
}
|
|
|
|
/* Solve P' = 0 where P is
|
|
* P = (1-t)^3*pa + 3*t*(1-t)^2*pb + 3*t^2*(1-t)*pc + t^3*pd
|
|
*/
|
|
static int
|
|
get_cubic_extrema (float pa, float pb, float pc, float pd, float t[2])
|
|
{
|
|
float a, b, c;
|
|
float d, tt;
|
|
int n = 0;
|
|
|
|
a = 3 * (pd - 3*pc + 3*pb - pa);
|
|
b = 6 * (pc - 2*pb + pa);
|
|
c = 3 * (pb - pa);
|
|
|
|
if (fabs (a) > 0.0001)
|
|
{
|
|
if (b*b > 4*a*c)
|
|
{
|
|
d = sqrt (b*b - 4*a*c);
|
|
tt = (-b + d)/(2*a);
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
tt = (-b - d)/(2*a);
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
}
|
|
else
|
|
{
|
|
tt = -b / (2*a);
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
}
|
|
}
|
|
else if (fabs (b) > 0.0001)
|
|
{
|
|
tt = -c / b;
|
|
if (acceptable (tt))
|
|
t[n++] = tt;
|
|
}
|
|
|
|
return n;
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_tight_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
const graphene_point_t *pts = self->points;
|
|
float t[4];
|
|
int n;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[3]);
|
|
|
|
n = 0;
|
|
n += get_cubic_extrema (pts[0].x, pts[1].x, pts[2].x, pts[3].x, &t[n]);
|
|
n += get_cubic_extrema (pts[0].y, pts[1].y, pts[2].y, pts[3].y, &t[n]);
|
|
|
|
for (int i = 0; i < n; i++)
|
|
{
|
|
graphene_point_t p;
|
|
|
|
gsk_cubic_curve_get_point (curve, t[i], &p);
|
|
gsk_bounding_box_expand (bounds, &p);
|
|
}
|
|
}
|
|
|
|
static void
|
|
gsk_cubic_curve_get_derivative (const GskCurve *curve,
|
|
GskCurve *deriv)
|
|
{
|
|
const GskCubicCurve *self = &curve->cubic;
|
|
graphene_point_t p[3];
|
|
|
|
p[0].x = 3.f * (self->points[1].x - self->points[0].x);
|
|
p[0].y = 3.f * (self->points[1].y - self->points[0].y);
|
|
p[1].x = 3.f * (self->points[2].x - self->points[1].x);
|
|
p[1].y = 3.f * (self->points[2].y - self->points[1].y);
|
|
p[2].x = 3.f * (self->points[3].x - self->points[2].x);
|
|
p[2].y = 3.f * (self->points[3].y - self->points[2].y);
|
|
|
|
gsk_quad_curve_init_from_points (&deriv->quad, p);
|
|
}
|
|
|
|
static int
|
|
gsk_cubic_curve_get_crossing (const GskCurve *curve,
|
|
const graphene_point_t *point)
|
|
{
|
|
return get_crossing_by_bisection (curve, point);
|
|
}
|
|
|
|
static const GskCurveClass GSK_CUBIC_CURVE_CLASS = {
|
|
gsk_cubic_curve_init,
|
|
gsk_cubic_curve_init_foreach,
|
|
gsk_cubic_curve_print,
|
|
gsk_cubic_curve_pathop,
|
|
gsk_cubic_curve_get_start_point,
|
|
gsk_cubic_curve_get_end_point,
|
|
gsk_cubic_curve_get_start_tangent,
|
|
gsk_cubic_curve_get_end_tangent,
|
|
gsk_cubic_curve_get_point,
|
|
gsk_cubic_curve_get_tangent,
|
|
gsk_cubic_curve_reverse,
|
|
gsk_cubic_curve_get_curvature,
|
|
gsk_cubic_curve_split,
|
|
gsk_cubic_curve_segment,
|
|
gsk_cubic_curve_decompose,
|
|
gsk_cubic_curve_decompose_curve,
|
|
gsk_cubic_curve_get_bounds,
|
|
gsk_cubic_curve_get_tight_bounds,
|
|
gsk_cubic_curve_get_derivative,
|
|
gsk_cubic_curve_get_crossing,
|
|
};
|
|
|
|
/* }}} */
|
|
/* {{{ Arc */
|
|
|
|
static void
|
|
gsk_arc_curve_ensure_matrix (const GskArcCurve *curve)
|
|
{
|
|
GskArcCurve *self = (GskArcCurve *)curve;
|
|
const graphene_point_t *pts = self->points;
|
|
graphene_matrix_t m1, m2, m3, tmp;
|
|
|
|
if (self->has_matrix)
|
|
return;
|
|
|
|
/* Compute a matrix that maps (1, 0), (1, 1), (0, 1) to pts[0..2] */
|
|
graphene_matrix_init_from_2d (&m1, 1, 0, 0, 1, -1, -1);
|
|
graphene_matrix_init_from_2d (&m2, -pts[2].x + pts[1].x, -pts[2].y + pts[1].y,
|
|
-pts[0].x + pts[1].x, -pts[0].y + pts[1].y,
|
|
0, 0);
|
|
graphene_matrix_init_from_2d (&m3, 1, 0, 0, 1, pts[1].x, pts[1].y);
|
|
|
|
graphene_matrix_multiply (&m1, &m2, &tmp);
|
|
graphene_matrix_multiply (&tmp, &m3, &self->m);
|
|
|
|
self->has_matrix = TRUE;
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_init_from_points (GskArcCurve *self,
|
|
const graphene_point_t pts[3])
|
|
{
|
|
self->op = GSK_PATH_ARC;
|
|
self->has_matrix = FALSE;
|
|
|
|
memcpy (self->points, pts, sizeof (graphene_point_t) * 3);
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_init (GskCurve *curve,
|
|
gskpathop op)
|
|
{
|
|
GskArcCurve *self = &curve->arc;
|
|
|
|
gsk_arc_curve_init_from_points (self, gsk_pathop_points (op));
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_init_foreach (GskCurve *curve,
|
|
GskPathOperation op,
|
|
const graphene_point_t *pts,
|
|
gsize n_pts)
|
|
{
|
|
GskArcCurve *self = &curve->arc;
|
|
|
|
g_assert (n_pts == 3);
|
|
|
|
gsk_arc_curve_init_from_points (self, pts);
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_print (const GskCurve *curve,
|
|
GString *string)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
|
|
g_string_append_printf (string,
|
|
"M %g %g E %g %g %g %g",
|
|
self->points[0].x, self->points[0].y,
|
|
self->points[1].x, self->points[1].y,
|
|
self->points[2].x, self->points[2].y);
|
|
}
|
|
|
|
static gskpathop
|
|
gsk_arc_curve_pathop (const GskCurve *curve)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
|
|
return gsk_pathop_encode (self->op, self->points);
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_arc_curve_get_start_point (const GskCurve *curve)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
|
|
return &self->points[0];
|
|
}
|
|
|
|
static const graphene_point_t *
|
|
gsk_arc_curve_get_end_point (const GskCurve *curve)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
|
|
return &self->points[2];
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_get_start_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
|
|
get_tangent (&self->points[0], &self->points[1], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_get_end_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
|
|
get_tangent (&self->points[1], &self->points[2], tangent);
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_get_point (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *pos)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
float s, c;
|
|
|
|
gsk_arc_curve_ensure_matrix (self);
|
|
|
|
_sincosf (t * M_PI_2, &s, &c);
|
|
graphene_matrix_transform_point (&self->m, &GRAPHENE_POINT_INIT (c, s), pos);
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_get_tangent (const GskCurve *curve,
|
|
float t,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
graphene_vec3_t tmp, tmp2;
|
|
float s, c;
|
|
|
|
gsk_arc_curve_ensure_matrix (self);
|
|
|
|
_sincosf (t * M_PI_2, &s, &c);
|
|
graphene_matrix_transform_vec3 (&self->m, graphene_vec3_init (&tmp, -s, c, 0), &tmp2);
|
|
graphene_vec2_init (tangent, graphene_vec3_get_x (&tmp2), graphene_vec3_get_y (&tmp2));
|
|
graphene_vec2_normalize (tangent, tangent);
|
|
}
|
|
|
|
static float
|
|
gsk_arc_curve_get_curvature (const GskCurve *curve,
|
|
float t)
|
|
{
|
|
float t2;
|
|
graphene_point_t p, p2, q;
|
|
graphene_vec2_t tan, tan2;
|
|
|
|
if (t < 1)
|
|
t2 = CLAMP (t + 0.05, 0, 1);
|
|
else
|
|
t2 = CLAMP (t - 0.05, 0, 1);
|
|
|
|
gsk_arc_curve_get_point (curve, t, &p);
|
|
gsk_arc_curve_get_tangent (curve, t, &tan);
|
|
gsk_arc_curve_get_point (curve, t2, &p2);
|
|
gsk_arc_curve_get_tangent (curve, t2, &tan2);
|
|
|
|
graphene_vec2_init (&tan, - graphene_vec2_get_y (&tan), graphene_vec2_get_x (&tan));
|
|
graphene_vec2_init (&tan2, - graphene_vec2_get_y (&tan2), graphene_vec2_get_x (&tan2));
|
|
|
|
line_intersection (&p, &tan, &p2, &tan2, &q);
|
|
|
|
return 1.f / graphene_point_distance (&p, &q, NULL, NULL);
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_reverse (const GskCurve *curve,
|
|
GskCurve *reverse)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
|
|
reverse->op = GSK_PATH_ARC;
|
|
reverse->arc.points[0] = self->points[2];
|
|
reverse->arc.points[1] = self->points[1];
|
|
reverse->arc.points[2] = self->points[0];
|
|
reverse->arc.has_matrix = FALSE;
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_split (const GskCurve *curve,
|
|
float progress,
|
|
GskCurve *start,
|
|
GskCurve *end)
|
|
{
|
|
const graphene_point_t *p0, *p1;
|
|
graphene_point_t p, q;
|
|
graphene_vec2_t t0, t1, t;
|
|
|
|
p0 = gsk_curve_get_start_point (curve);
|
|
gsk_curve_get_start_tangent (curve, &t0);
|
|
|
|
p1 = gsk_curve_get_end_point (curve);
|
|
gsk_curve_get_end_tangent (curve, &t1);
|
|
|
|
gsk_arc_curve_get_point (curve, progress, &p);
|
|
gsk_arc_curve_get_tangent (curve, progress, &t);
|
|
|
|
if (start)
|
|
{
|
|
if (line_intersection (p0, &t0, &p, &t, &q))
|
|
gsk_arc_curve_init_from_points ((GskArcCurve *)start,
|
|
(const graphene_point_t[3]) { *p0, q, p });
|
|
else
|
|
gsk_line_curve_init_from_points ((GskLineCurve *)start, GSK_PATH_LINE, p0, &p);
|
|
}
|
|
|
|
if (end)
|
|
{
|
|
if (line_intersection (&p, &t, p1, &t1, &q))
|
|
gsk_arc_curve_init_from_points ((GskArcCurve *)end,
|
|
(const graphene_point_t[3]) { p, q, *p1 });
|
|
else
|
|
gsk_line_curve_init_from_points ((GskLineCurve *)end, GSK_PATH_LINE, &p, p1);
|
|
}
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_segment (const GskCurve *curve,
|
|
float start,
|
|
float end,
|
|
GskCurve *segment)
|
|
{
|
|
graphene_point_t p0, p1, q;
|
|
graphene_vec2_t t0, t1;
|
|
|
|
if (start <= 0.0f)
|
|
return gsk_arc_curve_split (curve, end, segment, NULL);
|
|
else if (end >= 1.0f)
|
|
return gsk_arc_curve_split (curve, start, NULL, segment);
|
|
|
|
gsk_curve_get_point (curve, start, &p0);
|
|
gsk_curve_get_tangent (curve, start, &t0);
|
|
gsk_curve_get_point (curve, end, &p1);
|
|
gsk_curve_get_tangent (curve, end, &t1);
|
|
|
|
if (line_intersection (&p0, &t0, &p1, &t1, &q))
|
|
gsk_arc_curve_init_from_points ((GskArcCurve *)segment,
|
|
(const graphene_point_t[3]) { p0, q, p1 });
|
|
else
|
|
gsk_line_curve_init_from_points ((GskLineCurve *)segment, GSK_PATH_LINE, &p0, &p1);
|
|
}
|
|
|
|
/* taken from Skia, including the very descriptive name */
|
|
static gboolean
|
|
gsk_arc_curve_too_curvy (const graphene_point_t *start,
|
|
const graphene_point_t *mid,
|
|
const graphene_point_t *end,
|
|
float tolerance)
|
|
{
|
|
return fabs ((start->x + end->x) * 0.5 - mid->x) > tolerance
|
|
|| fabs ((start->y + end->y) * 0.5 - mid->y) > tolerance;
|
|
}
|
|
|
|
static gboolean
|
|
gsk_arc_curve_decompose_subdivide (const GskArcCurve *self,
|
|
float tolerance,
|
|
const graphene_point_t *start,
|
|
float start_progress,
|
|
const graphene_point_t *end,
|
|
float end_progress,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
graphene_point_t mid;
|
|
float mid_progress;
|
|
|
|
mid_progress = (start_progress + end_progress) / 2;
|
|
gsk_arc_curve_get_point ((const GskCurve *)self, mid_progress, &mid);
|
|
|
|
if (!gsk_arc_curve_too_curvy (start, &mid, end, tolerance))
|
|
return add_line_func (start, end, start_progress, end_progress, GSK_CURVE_LINE_REASON_STRAIGHT, user_data);
|
|
if (end_progress - start_progress <= MIN_PROGRESS)
|
|
return add_line_func (start, end, start_progress, end_progress, GSK_CURVE_LINE_REASON_SHORT, user_data);
|
|
|
|
return gsk_arc_curve_decompose_subdivide (self, tolerance,
|
|
start, start_progress, &mid, mid_progress,
|
|
add_line_func, user_data)
|
|
&& gsk_arc_curve_decompose_subdivide (self, tolerance,
|
|
&mid, mid_progress, end, end_progress,
|
|
add_line_func, user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_arc_curve_decompose (const GskCurve *curve,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
graphene_point_t mid;
|
|
|
|
gsk_arc_curve_get_point (curve, 0.5, &mid);
|
|
|
|
return gsk_arc_curve_decompose_subdivide (self,
|
|
tolerance,
|
|
&self->points[0],
|
|
0.0f,
|
|
&mid,
|
|
0.5f,
|
|
add_line_func,
|
|
user_data) &&
|
|
gsk_arc_curve_decompose_subdivide (self,
|
|
tolerance,
|
|
&mid,
|
|
0.5f,
|
|
&self->points[2],
|
|
1.0f,
|
|
add_line_func,
|
|
user_data);
|
|
}
|
|
|
|
static gboolean
|
|
gsk_arc_curve_decompose_curve (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
|
|
gsk_arc_curve_ensure_matrix (self);
|
|
|
|
if (flags & GSK_PATH_FOREACH_ALLOW_ARC)
|
|
return add_curve_func (GSK_PATH_ARC, self->points, 3, user_data);
|
|
|
|
if (flags & GSK_PATH_FOREACH_ALLOW_CUBIC)
|
|
{
|
|
graphene_point_t p[4];
|
|
float k = 0.55228474983;
|
|
|
|
p[0] = GRAPHENE_POINT_INIT (1, 0);
|
|
p[1] = GRAPHENE_POINT_INIT (1, k);
|
|
p[2] = GRAPHENE_POINT_INIT (k, 1);
|
|
p[3] = GRAPHENE_POINT_INIT (0, 1);
|
|
for (int i = 0; i < 4; i++)
|
|
graphene_matrix_transform_point (&self->m, &p[i], &p[i]);
|
|
|
|
return add_curve_func (GSK_PATH_CUBIC, p, 4, user_data);
|
|
}
|
|
|
|
if (flags & GSK_PATH_FOREACH_ALLOW_QUAD)
|
|
{
|
|
graphene_point_t p[5];
|
|
float s, c, a;
|
|
|
|
_sincosf ((float) DEG_TO_RAD (45), &s, &c);
|
|
a = (1 - c) / s;
|
|
|
|
p[0] = GRAPHENE_POINT_INIT (1, 0);
|
|
p[1] = GRAPHENE_POINT_INIT (1, a);
|
|
p[2] = GRAPHENE_POINT_INIT (c, s);
|
|
p[3] = GRAPHENE_POINT_INIT (a, 1);
|
|
p[4] = GRAPHENE_POINT_INIT (0, 1);
|
|
|
|
for (int i = 0; i < 5; i++)
|
|
graphene_matrix_transform_point (&self->m, &p[i], &p[i]);
|
|
|
|
return add_curve_func (GSK_PATH_QUAD, p, 3, user_data) &&
|
|
add_curve_func (GSK_PATH_QUAD, &p[2], 3, user_data);
|
|
}
|
|
|
|
return gsk_arc_curve_decompose (curve,
|
|
tolerance,
|
|
gsk_curve_add_line_cb,
|
|
&(AddLineData) { add_curve_func, user_data });
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_get_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
const graphene_point_t *pts = self->points;
|
|
|
|
gsk_bounding_box_init (bounds, &pts[0], &pts[2]);
|
|
gsk_bounding_box_expand (bounds, &pts[1]);
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_get_tight_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
// FIXME
|
|
gsk_arc_curve_get_bounds (curve, bounds);
|
|
}
|
|
|
|
static void
|
|
gsk_arc_curve_get_derivative (const GskCurve *curve,
|
|
GskCurve *derivative)
|
|
{
|
|
const GskArcCurve *self = &curve->arc;
|
|
double xx, yx, xy, yy, x0, y0;
|
|
graphene_matrix_t m;
|
|
graphene_point_t p[3];
|
|
|
|
gsk_arc_curve_ensure_matrix (self);
|
|
|
|
graphene_matrix_to_2d (&self->m, &xx, &yx, &xy, &yy, &x0, &y0);
|
|
graphene_matrix_init_from_2d (&m, M_PI_2 * xy, M_PI_2 * yy, M_PI_2 * -xx, M_PI_2 * -yx, 0, 0);
|
|
|
|
graphene_matrix_transform_point (&m, &GRAPHENE_POINT_INIT (1, 0), &p[0]);
|
|
graphene_matrix_transform_point (&m, &GRAPHENE_POINT_INIT (1, 1), &p[1]);
|
|
graphene_matrix_transform_point (&m, &GRAPHENE_POINT_INIT (0, 1), &p[2]);
|
|
|
|
gsk_arc_curve_init_from_points ((GskArcCurve *)derivative, p);
|
|
}
|
|
|
|
static int
|
|
gsk_arc_curve_get_crossing (const GskCurve *curve,
|
|
const graphene_point_t *point)
|
|
{
|
|
return get_crossing_by_bisection (curve, point);
|
|
}
|
|
|
|
static const GskCurveClass GSK_ARC_CURVE_CLASS = {
|
|
gsk_arc_curve_init,
|
|
gsk_arc_curve_init_foreach,
|
|
gsk_arc_curve_print,
|
|
gsk_arc_curve_pathop,
|
|
gsk_arc_curve_get_start_point,
|
|
gsk_arc_curve_get_end_point,
|
|
gsk_arc_curve_get_start_tangent,
|
|
gsk_arc_curve_get_end_tangent,
|
|
gsk_arc_curve_get_point,
|
|
gsk_arc_curve_get_tangent,
|
|
gsk_arc_curve_reverse,
|
|
gsk_arc_curve_get_curvature,
|
|
gsk_arc_curve_split,
|
|
gsk_arc_curve_segment,
|
|
gsk_arc_curve_decompose,
|
|
gsk_arc_curve_decompose_curve,
|
|
gsk_arc_curve_get_bounds,
|
|
gsk_arc_curve_get_tight_bounds,
|
|
gsk_arc_curve_get_derivative,
|
|
gsk_arc_curve_get_crossing,
|
|
};
|
|
|
|
/* }}} */
|
|
/* {{{ API */
|
|
|
|
static const GskCurveClass *
|
|
get_class (GskPathOperation op)
|
|
{
|
|
const GskCurveClass *klasses[] = {
|
|
[GSK_PATH_CLOSE] = &GSK_LINE_CURVE_CLASS,
|
|
[GSK_PATH_LINE] = &GSK_LINE_CURVE_CLASS,
|
|
[GSK_PATH_QUAD] = &GSK_QUAD_CURVE_CLASS,
|
|
[GSK_PATH_CUBIC] = &GSK_CUBIC_CURVE_CLASS,
|
|
[GSK_PATH_ARC] = &GSK_ARC_CURVE_CLASS,
|
|
};
|
|
|
|
g_assert (op < G_N_ELEMENTS (klasses) && klasses[op] != NULL);
|
|
|
|
return klasses[op];
|
|
}
|
|
|
|
void
|
|
gsk_curve_init (GskCurve *curve,
|
|
gskpathop op)
|
|
{
|
|
memset (curve, 0, sizeof (GskCurve));
|
|
get_class (gsk_pathop_op (op))->init (curve, op);
|
|
}
|
|
|
|
void
|
|
gsk_curve_init_foreach (GskCurve *curve,
|
|
GskPathOperation op,
|
|
const graphene_point_t *pts,
|
|
gsize n_pts)
|
|
{
|
|
memset (curve, 0, sizeof (GskCurve));
|
|
get_class (op)->init_foreach (curve, op, pts, n_pts);
|
|
}
|
|
|
|
void
|
|
gsk_curve_print (const GskCurve *curve,
|
|
GString *string)
|
|
{
|
|
get_class (curve->op)->print (curve, string);
|
|
}
|
|
|
|
char *
|
|
gsk_curve_to_string (const GskCurve *curve)
|
|
{
|
|
GString *s = g_string_new ("");
|
|
gsk_curve_print (curve, s);
|
|
return g_string_free (s, FALSE);
|
|
}
|
|
|
|
gskpathop
|
|
gsk_curve_pathop (const GskCurve *curve)
|
|
{
|
|
return get_class (curve->op)->pathop (curve);
|
|
}
|
|
|
|
const graphene_point_t *
|
|
gsk_curve_get_start_point (const GskCurve *curve)
|
|
{
|
|
return get_class (curve->op)->get_start_point (curve);
|
|
}
|
|
|
|
const graphene_point_t *
|
|
gsk_curve_get_end_point (const GskCurve *curve)
|
|
{
|
|
return get_class (curve->op)->get_end_point (curve);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_start_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
get_class (curve->op)->get_start_tangent (curve, tangent);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_end_tangent (const GskCurve *curve,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
get_class (curve->op)->get_end_tangent (curve, tangent);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_point (const GskCurve *curve,
|
|
float progress,
|
|
graphene_point_t *pos)
|
|
{
|
|
get_class (curve->op)->get_point (curve, progress, pos);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_tangent (const GskCurve *curve,
|
|
float progress,
|
|
graphene_vec2_t *tangent)
|
|
{
|
|
get_class (curve->op)->get_tangent (curve, progress, tangent);
|
|
}
|
|
|
|
float
|
|
gsk_curve_get_curvature (const GskCurve *curve,
|
|
float t,
|
|
graphene_point_t *center)
|
|
{
|
|
float k;
|
|
|
|
k = get_class (curve->op)->get_curvature (curve, t);
|
|
|
|
if (center != NULL && k != 0)
|
|
{
|
|
graphene_point_t p;
|
|
graphene_vec2_t tangent;
|
|
float r;
|
|
|
|
r = 1/k;
|
|
gsk_curve_get_point (curve, t, &p);
|
|
gsk_curve_get_tangent (curve, t, &tangent);
|
|
center->x = p.x - r * graphene_vec2_get_y (&tangent);
|
|
center->y = p.y + r * graphene_vec2_get_x (&tangent);
|
|
}
|
|
|
|
return k;
|
|
}
|
|
|
|
void
|
|
gsk_curve_reverse (const GskCurve *curve,
|
|
GskCurve *reverse)
|
|
{
|
|
get_class (curve->op)->reverse (curve, reverse);
|
|
}
|
|
|
|
void
|
|
gsk_curve_split (const GskCurve *curve,
|
|
float progress,
|
|
GskCurve *start,
|
|
GskCurve *end)
|
|
{
|
|
get_class (curve->op)->split (curve, progress, start, end);
|
|
}
|
|
|
|
void
|
|
gsk_curve_segment (const GskCurve *curve,
|
|
float start,
|
|
float end,
|
|
GskCurve *segment)
|
|
{
|
|
if (start <= 0 && end >= 1)
|
|
{
|
|
*segment = *curve;
|
|
return;
|
|
}
|
|
|
|
get_class (curve->op)->segment (curve, start, end, segment);
|
|
}
|
|
|
|
gboolean
|
|
gsk_curve_decompose (const GskCurve *curve,
|
|
float tolerance,
|
|
GskCurveAddLineFunc add_line_func,
|
|
gpointer user_data)
|
|
{
|
|
return get_class (curve->op)->decompose (curve, tolerance, add_line_func, user_data);
|
|
}
|
|
|
|
gboolean
|
|
gsk_curve_decompose_curve (const GskCurve *curve,
|
|
GskPathForeachFlags flags,
|
|
float tolerance,
|
|
GskCurveAddCurveFunc add_curve_func,
|
|
gpointer user_data)
|
|
{
|
|
return get_class (curve->op)->decompose_curve (curve, flags, tolerance, add_curve_func, user_data);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
get_class (curve->op)->get_bounds (curve, bounds);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_tight_bounds (const GskCurve *curve,
|
|
GskBoundingBox *bounds)
|
|
{
|
|
get_class (curve->op)->get_tight_bounds (curve, bounds);
|
|
}
|
|
|
|
void
|
|
gsk_curve_get_derivative (const GskCurve *curve,
|
|
GskCurve *deriv)
|
|
{
|
|
get_class (curve->op)->get_derivative (curve, deriv);
|
|
}
|
|
|
|
int
|
|
gsk_curve_get_crossing (const GskCurve *curve,
|
|
const graphene_point_t *point)
|
|
{
|
|
return get_class (curve->op)->get_crossing (curve, point);
|
|
}
|
|
|
|
static gboolean
|
|
project_point_onto_line (const GskCurve *curve,
|
|
const graphene_point_t *point,
|
|
float threshold,
|
|
float *out_distance,
|
|
float *out_t)
|
|
{
|
|
const graphene_point_t *a = gsk_curve_get_start_point (curve);
|
|
const graphene_point_t *b = gsk_curve_get_end_point (curve);
|
|
graphene_vec2_t n, ap;
|
|
graphene_point_t p;
|
|
|
|
if (graphene_point_equal (a, b))
|
|
{
|
|
*out_t = 0;
|
|
*out_distance = graphene_point_distance (point, a, NULL, NULL);
|
|
}
|
|
else
|
|
{
|
|
graphene_vec2_init (&n, b->x - a->x, b->y - a->y);
|
|
graphene_vec2_init (&ap, point->x - a->x, point->y - a->y);
|
|
|
|
*out_t = graphene_vec2_dot (&n, &ap) / graphene_vec2_dot (&n, &n);
|
|
*out_t = CLAMP (*out_t, 0, 1);
|
|
|
|
graphene_point_interpolate (a, b, *out_t, &p);
|
|
*out_distance = graphene_point_distance (point, &p, NULL, NULL);
|
|
}
|
|
|
|
return *out_distance <= threshold;
|
|
}
|
|
|
|
static float
|
|
get_segment_bounding_sphere (const GskCurve *curve,
|
|
float t1,
|
|
float t2,
|
|
graphene_point_t *center)
|
|
{
|
|
GskCurve c;
|
|
GskBoundingBox bounds;
|
|
|
|
gsk_curve_segment (curve, t1, t2, &c);
|
|
gsk_curve_get_tight_bounds (&c, &bounds);
|
|
graphene_point_interpolate (&bounds.min, &bounds.max, 0.5, center);
|
|
return graphene_point_distance (center, &bounds.min, NULL, NULL);
|
|
}
|
|
|
|
static gboolean
|
|
find_closest_point (const GskCurve *curve,
|
|
const graphene_point_t *point,
|
|
float threshold,
|
|
float t1,
|
|
float t2,
|
|
float *out_distance,
|
|
float *out_t)
|
|
{
|
|
graphene_point_t center;
|
|
float radius;
|
|
float t, d, nt;
|
|
|
|
radius = get_segment_bounding_sphere (curve, t1, t2, ¢er);
|
|
if (graphene_point_distance (¢er, point, NULL, NULL) > threshold + radius)
|
|
return FALSE;
|
|
|
|
d = INFINITY;
|
|
t = (t1 + t2) / 2;
|
|
|
|
if (fabs (t1 - t2) < 0.001 || radius < 1)
|
|
{
|
|
graphene_point_t p;
|
|
gsk_curve_get_point (curve, t, &p);
|
|
d = graphene_point_distance (point, &p, NULL, NULL);
|
|
nt = t;
|
|
}
|
|
else
|
|
{
|
|
float dd, tt;
|
|
|
|
dd = INFINITY;
|
|
nt = 0;
|
|
|
|
if (find_closest_point (curve, point, threshold, t1, t, &dd, &tt))
|
|
{
|
|
d = dd;
|
|
nt = tt;
|
|
}
|
|
|
|
if (find_closest_point (curve, point, MIN (dd, threshold), t, t2, &dd, &tt))
|
|
{
|
|
d = dd;
|
|
nt = tt;
|
|
}
|
|
}
|
|
|
|
if (d < threshold)
|
|
{
|
|
*out_distance = d;
|
|
*out_t = nt;
|
|
return TRUE;
|
|
}
|
|
else
|
|
{
|
|
*out_distance = INFINITY;
|
|
*out_t = 0;
|
|
return FALSE;
|
|
}
|
|
}
|
|
|
|
gboolean
|
|
gsk_curve_get_closest_point (const GskCurve *curve,
|
|
const graphene_point_t *point,
|
|
float threshold,
|
|
float *out_dist,
|
|
float *out_t)
|
|
{
|
|
if (curve->op == GSK_PATH_LINE || curve->op == GSK_PATH_CLOSE)
|
|
return project_point_onto_line (curve, point, threshold, out_dist, out_t);
|
|
else
|
|
return find_closest_point (curve, point, threshold, 0, 1, out_dist, out_t);
|
|
}
|
|
|
|
/* }}} */
|
|
|
|
/* vim:set foldmethod=marker expandtab: */
|