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curve: Add gsk_curve_get_curvature

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This will be used in the stroker.
This commit is contained in:
Matthias Clasen
2020-12-23 14:59:56 -05:00
parent 73a06b6b2a
commit 98f0e57d14
2 changed files with 183 additions and 0 deletions
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179
gsk/gskcurve.c
View File

@@ -70,6 +70,8 @@ struct _GskCurveClass
GskBoundingBox *bounds);
void (* get_tight_bounds) (const GskCurve *curve,
GskBoundingBox *bounds);
float (* get_curvature) (const GskCurve *curve,
float t);
};
static void
@@ -247,6 +249,13 @@ gsk_line_curve_get_bounds (const GskCurve *curve,
gsk_bounding_box_init (bounds, &pts[0], &pts[1]);
}
static float
gsk_line_curve_get_curvature (const GskCurve *curve,
float t)
{
return 0;
}
static const GskCurveClass GSK_LINE_CURVE_CLASS = {
gsk_line_curve_init,
gsk_line_curve_init_foreach,
@@ -264,6 +273,7 @@ static const GskCurveClass GSK_LINE_CURVE_CLASS = {
gsk_line_curve_reverse,
gsk_line_curve_get_bounds,
gsk_line_curve_get_bounds,
gsk_line_curve_get_curvature,
};
/** QUADRATIC **/
@@ -589,6 +599,16 @@ gsk_quad_curve_get_tight_bounds (const GskCurve *curve,
}
}
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 const GskCurveClass GSK_QUAD_CURVE_CLASS = {
gsk_quad_curve_init,
gsk_quad_curve_init_foreach,
@@ -606,6 +626,7 @@ static const GskCurveClass GSK_QUAD_CURVE_CLASS = {
gsk_quad_curve_reverse,
gsk_quad_curve_get_bounds,
gsk_quad_curve_get_tight_bounds,
gsk_quad_curve_get_curvature,
};
/** CUBIC **/
@@ -941,6 +962,105 @@ gsk_cubic_curve_get_tight_bounds (const GskCurve *curve,
}
}
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:
case GSK_PATH_CONIC:
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 const GskCurveClass GSK_CUBIC_CURVE_CLASS = {
gsk_cubic_curve_init,
gsk_cubic_curve_init_foreach,
@@ -958,6 +1078,7 @@ static const GskCurveClass GSK_CUBIC_CURVE_CLASS = {
gsk_cubic_curve_reverse,
gsk_cubic_curve_get_bounds,
gsk_cubic_curve_get_tight_bounds,
gsk_cubic_curve_get_curvature,
};
/** CONIC **/
@@ -1553,6 +1674,38 @@ gsk_conic_curve_get_tight_bounds (const GskCurve *curve,
}
}
/* See M. Floater, Derivatives of rational Bezier curves */
static float
gsk_conic_curve_get_curvature (const GskCurve *curve,
float t)
{
graphene_point_t p[3], p1[2];
float w, w1[2], w2;
graphene_vec2_t t1, t2, t3;
w = curve->conic.points[2].x;
p[0] = curve->conic.points[0];
p[1] = curve->conic.points[1];
p[2] = curve->conic.points[3];
w1[0] = (1 - t) + t*w;
w1[1] = (1 - t)*w + t;
w2 = (1 - t)*w1[0] + t*w1[1];
p1[0].x = ((1 - t)*p[0].x + t*w*p[1].x)/w1[0];
p1[0].y = ((1 - t)*p[0].y + t*w*p[1].y)/w1[0];
p1[1].x = ((1 - t)*w*p[1].x + t*p[2].x)/w1[1];
p1[1].y = ((1 - t)*w*p[1].y + t*p[2].y)/w1[1];
graphene_vec2_init (&t1, p[1].x - p[0].x, p[1].y - p[0].y);
graphene_vec2_init (&t2, p[2].x - p[1].x, p[2].y - p[1].y);
graphene_vec2_init (&t3, p1[1].x - p1[0].x, p1[1].y - p1[0].y);
return 0.5 * ((w*pow3 (w2))/(pow3 (w1[0])*pow3 (w1[1]))) * (cross (&t1, &t2) / pow3 (graphene_vec2_length (&t3)));
}
static const GskCurveClass GSK_CONIC_CURVE_CLASS = {
gsk_conic_curve_init,
gsk_conic_curve_init_foreach,
@@ -1570,6 +1723,7 @@ static const GskCurveClass GSK_CONIC_CURVE_CLASS = {
gsk_conic_curve_reverse,
gsk_conic_curve_get_bounds,
gsk_conic_curve_get_tight_bounds,
gsk_conic_curve_get_curvature,
};
/** API **/
@@ -1734,6 +1888,31 @@ gsk_curve_get_tight_bounds (const GskCurve *curve,
get_class (curve->op)->get_tight_bounds (curve, bounds);
}
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 n;
float r;
r = 1/k;
gsk_curve_get_point (curve, t, &p);
gsk_curve_get_normal (curve, t, &n);
center->x = p.x + r * graphene_vec2_get_x (&n);
center->y = p.y + r * graphene_vec2_get_y (&n);
}
return k;
}
static inline void
_sincosf (float angle,
float *out_s,

4
gsk/gskcurveprivate.h
View File

@@ -167,6 +167,10 @@ int gsk_curve_get_curvature_points (const GskCurve
int gsk_curve_get_cusps (const GskCurve *curve,
float t[2]);
float gsk_curve_get_curvature (const GskCurve *curve,
float t,
graphene_point_t *center);
G_END_DECLS
#endif /* __GSK_CURVE_PRIVATE_H__ */