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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 3a4c3c3d8c
commit e293f10fa1
2 changed files with 227 additions and 16 deletions
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239
gsk/gskcurve.c
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@@ -72,6 +72,8 @@ struct _GskCurveClass
GskCurve *offset_curve);
void (* reverse) (const GskCurve *curve,
GskCurve *reverse);
float (* get_curvature) (const GskCurve *curve,
float t);
};
static void
@@ -326,6 +328,13 @@ gsk_line_curve_reverse (const GskCurve *curve,
reverse->line.points[1] = self->points[0];
}
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,
@@ -343,7 +352,8 @@ static const GskCurveClass GSK_LINE_CURVE_CLASS = {
gsk_line_curve_get_bounds,
gsk_line_curve_get_bounds,
gsk_line_curve_offset,
gsk_line_curve_reverse
gsk_line_curve_reverse,
gsk_line_curve_get_curvature
};
/** CURVE **/
@@ -430,19 +440,6 @@ gsk_curve_curve_get_tangent (const GskCurve *curve,
graphene_vec2_normalize (tangent, tangent);
}
void
gsk_curve_get_normal (const GskCurve *curve,
float t,
graphene_vec2_t *normal)
{
graphene_vec2_t tangent;
gsk_curve_get_tangent (curve, t, &tangent);
graphene_vec2_init (normal,
- graphene_vec2_get_y (&tangent),
graphene_vec2_get_x (&tangent));
}
static void
gsk_curve_curve_split (const GskCurve *curve,
float progress,
@@ -800,6 +797,80 @@ gsk_curve_curve_reverse (const GskCurve *curve,
reverse->curve.has_coefficients = FALSE;
}
static void
get_derivatives (const GskCurve *curve,
float t,
graphene_vec2_t *d,
graphene_vec2_t *dd)
{
const graphene_point_t *p = curve->curve.points;
graphene_point_t dp[3];
graphene_point_t ddp[2];
float t1, t2, t3;
dp[0].x = 3 * (p[1].x - p[0].x);
dp[0].y = 3 * (p[1].y - p[0].y);
dp[1].x = 3 * (p[2].x - p[1].x);
dp[1].y = 3 * (p[2].y - p[1].y);
dp[2].x = 3 * (p[3].x - p[2].x);
dp[2].y = 3 * (p[3].y - p[2].y);
if (d)
{
t1 = (1 - t) * (1 - t);
t2 = t * (1 - t);
t3 = t * t;
graphene_vec2_init (d,
dp[0].x * t1 + 2 * dp[1].x * t2 + dp[2].x * t3,
dp[0].y * t1 + 2 * dp[1].y * t2 + dp[2].y * t3);
}
if (dd)
{
ddp[0].x = 2 * (dp[1].x - dp[0].x);
ddp[0].y = 2 * (dp[1].y - dp[0].y);
ddp[1].x = 2 * (dp[2].x - dp[1].x);
ddp[1].y = 2 * (dp[2].y - dp[1].y);
graphene_vec2_init (dd,
ddp[0].x * (1 - t) + ddp[1].x * t,
ddp[0].y * (1 - t) + ddp[1].y * t);
}
}
static float
cross (const graphene_vec2_t *t1,
const graphene_vec2_t *t2)
{
return graphene_vec2_get_x (t1)*graphene_vec2_get_y (t2)
- graphene_vec2_get_y (t1)*graphene_vec2_get_x (t2);
}
static float
pow3 (float w)
{
return w*w*w;
}
static float
gsk_curve_curve_get_curvature (const GskCurve *curve,
float t)
{
graphene_vec2_t d, dd;
float num, denom;
get_derivatives (curve, t, &d, &dd);
num = cross (&d, &dd);
denom = pow3 (graphene_vec2_length (&d));
if (denom == 0)
return 0;
return num / denom;
}
static const GskCurveClass GSK_CURVE_CURVE_CLASS = {
gsk_curve_curve_init,
gsk_curve_curve_init_foreach,
@@ -817,7 +888,8 @@ static const GskCurveClass GSK_CURVE_CURVE_CLASS = {
gsk_curve_curve_get_bounds,
gsk_curve_curve_get_tight_bounds,
gsk_curve_curve_offset,
gsk_curve_curve_reverse
gsk_curve_curve_reverse,
gsk_curve_curve_get_curvature,
};
/** CONIC **/
@@ -1424,6 +1496,102 @@ gsk_conic_curve_reverse (const GskCurve *curve,
reverse->conic.has_coefficients = FALSE;
}
static void
get_conic_derivatives (const GskCurve *curve,
float t,
graphene_vec2_t *d,
graphene_vec2_t *dd)
{
/* See M. Floater, Derivatives of rational Bezier curves */
graphene_point_t p[3], p1[2];
float w, w1[2], w2;
graphene_vec2_t t1, t2;
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];
if (d)
{
get_tangent (&p1[0], &p1[1], &t1);
graphene_vec2_scale (&t1, 2 * (w1[0]*w1[1])/(w2*w2), d);
}
if (dd)
{
get_tangent (&p[1], &p[2], &t1);
graphene_vec2_scale (&t1, 2 * (1/pow3 (w2))*(4*w1[0]*w1[0] - w2 - 2*w1[0]*w2), &t1);
get_tangent (&p[0], &p[1], &t2);
graphene_vec2_scale (&t2, 2 * (1/pow3 (w2))*(4*w1[1]*w1[1] - w2 - 2*w1[1]*w2), &t2);
graphene_vec2_subtract (&t1, &t2, dd);
}
}
#if 0
static float
gsk_conic_curve_get_curvature (const GskCurve *curve,
float t)
{
/* See M. Floater, Derivatives of rational Bezier curves */
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];
get_tangent (&p[0], &p[1], &t1);
get_tangent (&p[1], &p[2], &t2);
get_tangent (&p1[0], &p1[1], &t3);
return 0.5 * ((w*pow3 (w2))/(pow3 (w1[0])*pow3 (w1[1]))) * (cross (&t1, &t2) / pow3 (graphene_vec2_length (&t3)));
}
#endif
static float
gsk_conic_curve_get_curvature (const GskCurve *curve,
float t)
{
graphene_vec2_t d, dd;
float num, denom;
get_conic_derivatives (curve, t, &d, &dd);
num = cross (&d, &dd);
denom = pow3 (graphene_vec2_length (&d));
if (denom == 0)
return 0;
return num / denom;
}
static const GskCurveClass GSK_CONIC_CURVE_CLASS = {
gsk_conic_curve_init,
gsk_conic_curve_init_foreach,
@@ -1441,7 +1609,8 @@ static const GskCurveClass GSK_CONIC_CURVE_CLASS = {
gsk_conic_curve_get_bounds,
gsk_conic_curve_get_tight_bounds,
gsk_conic_curve_offset,
gsk_conic_curve_reverse
gsk_conic_curve_reverse,
gsk_conic_curve_get_curvature
};
/** API **/
@@ -1596,3 +1765,41 @@ gsk_curve_reverse (const GskCurve *curve,
{
get_class (curve->op)->reverse (curve, reverse);
}
void
gsk_curve_get_normal (const GskCurve *curve,
float t,
graphene_vec2_t *normal)
{
graphene_vec2_t tangent;
gsk_curve_get_tangent (curve, t, &tangent);
graphene_vec2_init (normal,
- graphene_vec2_get_y (&tangent),
graphene_vec2_get_x (&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 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;
}

4
gsk/gskcurveprivate.h
View File

@@ -141,6 +141,10 @@ void gsk_curve_offset (const GskCurve
void gsk_curve_reverse (const GskCurve *curve,
GskCurve *reverse);
float gsk_curve_get_curvature (const GskCurve *curve,
float t,
graphene_point_t *center);
G_END_DECLS
#endif /* __GSK_CURVE_PRIVATE_H__ */