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gtk/gsk/gskcurve.c
Matthias Clasen 1b5dfcba7e gsk: Add GskPath 
This commit adds the basic infrastructure for paths.
The public APIs consists of GskPath, GskPathPoint and
GskPathBuilder.

GskPath is a data structure for paths that consists
of contours, which in turn might contain Bézier curves.
The Bezier data structure is inspired by Skia, with separate
arrays for points and operations. One advantage of this
arrangement is that start and end points are shared
between adjacent curves.

A GskPathPoint represents a point on a path, which can
be queried for various properties.

GskPathBuilder is an auxiliary builder object for paths.
2023-08-06 20:48:09 -04:00

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/*
* 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);
};
/* {{{ Utilities */
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);
}
/* 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 ();
}
/* }}} */
/* {{{ 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 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,
};
/* }}} */
/* {{{ 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 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,
};
/* }}} */
/* {{{ 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 void
gsk_curve_get_derivative (const GskCurve *curve,
GskCurve *deriv)
{
switch (curve->op)
{
case GSK_PATH_LINE:
{
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);
}
break;
case GSK_PATH_QUAD:
{
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]);
}
break;
case GSK_PATH_CUBIC:
{
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);
}
break;
case GSK_PATH_MOVE:
case GSK_PATH_CLOSE:
default:
g_assert_not_reached ();
}
}
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 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_curve_get_derivative (curve, &c1);
gsk_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 conic?) 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 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,
};
/* }}} */
/* {{{ 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,
};
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);
}
static inline 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;
}
int
gsk_curve_get_crossing (const GskCurve *curve,
const graphene_point_t *point)
{
GskBoundingBox bounds;
GskCurve c1, c2;
if (curve->op == GSK_PATH_LINE || curve->op == GSK_PATH_CLOSE)
return line_get_crossing (point, gsk_curve_get_start_point (curve), gsk_curve_get_end_point (curve));
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);
}
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, &center);
if (graphene_point_distance (&center, point, NULL, NULL) > threshold + radius)
return FALSE;
d = INFINITY;
t = (t1 + t2) / 2;
if (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: */
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