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path: root/src/gallium/state_trackers/vega/arc.c
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+/**************************************************************************
+ *
+ * Copyright 2009 VMware, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sub license, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice (including the
+ * next paragraph) shall be included in all copies or substantial portions
+ * of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
+ * IN NO EVENT SHALL VMWARE AND/OR ITS SUPPLIERS BE LIABLE FOR
+ * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+ * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+ * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+ *
+ **************************************************************************/
+
+#include "arc.h"
+
+#include "matrix.h"
+#include "bezier.h"
+#include "polygon.h"
+#include "stroker.h"
+#include "path.h"
+
+#include "util/u_debug.h"
+
+#include <math.h>
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+#define DEBUG_ARCS 0
+
+static const VGfloat two_pi = M_PI * 2;
+
+
+static const double coeffs3Low[2][4][4] = {
+ {
+ { 3.85268, -21.229, -0.330434, 0.0127842 },
+ { -1.61486, 0.706564, 0.225945, 0.263682 },
+ { -0.910164, 0.388383, 0.00551445, 0.00671814 },
+ { -0.630184, 0.192402, 0.0098871, 0.0102527 }
+ },
+ {
+ { -0.162211, 9.94329, 0.13723, 0.0124084 },
+ { -0.253135, 0.00187735, 0.0230286, 0.01264 },
+ { -0.0695069, -0.0437594, 0.0120636, 0.0163087 },
+ { -0.0328856, -0.00926032, -0.00173573, 0.00527385 }
+ }
+};
+
+/* coefficients for error estimation
+ while using cubic Bézier curves for approximation
+ 1/4 <= b/a <= 1 */
+static const double coeffs3High[2][4][4] = {
+ {
+ { 0.0899116, -19.2349, -4.11711, 0.183362 },
+ { 0.138148, -1.45804, 1.32044, 1.38474 },
+ { 0.230903, -0.450262, 0.219963, 0.414038 },
+ { 0.0590565, -0.101062, 0.0430592, 0.0204699 }
+ },
+ {
+ { 0.0164649, 9.89394, 0.0919496, 0.00760802 },
+ { 0.0191603, -0.0322058, 0.0134667, -0.0825018 },
+ { 0.0156192, -0.017535, 0.00326508, -0.228157 },
+ { -0.0236752, 0.0405821, -0.0173086, 0.176187 }
+ }
+};
+
+/* safety factor to convert the "best" error approximation
+ into a "max bound" error */
+static const double safety3[] = {
+ 0.001, 4.98, 0.207, 0.0067
+};
+
+/* The code below is from the OpenVG 1.1 Spec
+ * Section 18.4 */
+
+/* Given: Points (x0, y0) and (x1, y1)
+ * Return: TRUE if a solution exists, FALSE otherwise
+ * Circle centers are written to (cx0, cy0) and (cx1, cy1)
+ */
+static VGboolean
+find_unit_circles(double x0, double y0, double x1, double y1,
+ double *cx0, double *cy0,
+ double *cx1, double *cy1)
+{
+ /* Compute differences and averages */
+ double dx = x0 - x1;
+ double dy = y0 - y1;
+ double xm = (x0 + x1)/2;
+ double ym = (y0 + y1)/2;
+ double dsq, disc, s, sdx, sdy;
+
+ /* Solve for intersecting unit circles */
+ dsq = dx*dx + dy*dy;
+ if (dsq == 0.0) return VG_FALSE; /* Points are coincident */
+ disc = 1.0/dsq - 1.0/4.0;
+
+ /* the precision we care about here is around float so if we're
+ * around the float defined zero then make it official to avoid
+ * precision problems later on */
+ if (floatIsZero(disc))
+ disc = 0.0;
+
+ if (disc < 0.0) return VG_FALSE; /* Points are too far apart */
+ s = sqrt(disc);
+ sdx = s*dx;
+ sdy = s*dy;
+ *cx0 = xm + sdy;
+ *cy0 = ym - sdx;
+ *cx1 = xm - sdy;
+ *cy1 = ym + sdx;
+ return VG_TRUE;
+}
+
+
+/* Given: Ellipse parameters rh, rv, rot (in degrees),
+ * endpoints (x0, y0) and (x1, y1)
+ * Return: TRUE if a solution exists, FALSE otherwise
+ * Ellipse centers are written to (cx0, cy0) and (cx1, cy1)
+ */
+static VGboolean
+find_ellipses(double rh, double rv, double rot,
+ double x0, double y0, double x1, double y1,
+ double *cx0, double *cy0, double *cx1, double *cy1)
+{
+ double COS, SIN, x0p, y0p, x1p, y1p, pcx0, pcy0, pcx1, pcy1;
+ /* Convert rotation angle from degrees to radians */
+ rot *= M_PI/180.0;
+ /* Pre-compute rotation matrix entries */
+ COS = cos(rot); SIN = sin(rot);
+ /* Transform (x0, y0) and (x1, y1) into unit space */
+ /* using (inverse) rotate, followed by (inverse) scale */
+ x0p = (x0*COS + y0*SIN)/rh;
+ y0p = (-x0*SIN + y0*COS)/rv;
+ x1p = (x1*COS + y1*SIN)/rh;
+ y1p = (-x1*SIN + y1*COS)/rv;
+ if (!find_unit_circles(x0p, y0p, x1p, y1p,
+ &pcx0, &pcy0, &pcx1, &pcy1)) {
+ return VG_FALSE;
+ }
+ /* Transform back to original coordinate space */
+ /* using (forward) scale followed by (forward) rotate */
+ pcx0 *= rh; pcy0 *= rv;
+ pcx1 *= rh; pcy1 *= rv;
+ *cx0 = pcx0*COS - pcy0*SIN;
+ *cy0 = pcx0*SIN + pcy0*COS;
+ *cx1 = pcx1*COS - pcy1*SIN;
+ *cy1 = pcx1*SIN + pcy1*COS;
+ return VG_TRUE;
+}
+
+static INLINE VGboolean
+try_to_fix_radii(struct arc *arc)
+{
+ double COS, SIN, rot, x0p, y0p, x1p, y1p;
+ double dx, dy, dsq, scale;
+
+ /* Convert rotation angle from degrees to radians */
+ rot = DEGREES_TO_RADIANS(arc->theta);
+
+ /* Pre-compute rotation matrix entries */
+ COS = cos(rot); SIN = sin(rot);
+
+ /* Transform (x0, y0) and (x1, y1) into unit space */
+ /* using (inverse) rotate, followed by (inverse) scale */
+ x0p = (arc->x1*COS + arc->y1*SIN)/arc->a;
+ y0p = (-arc->x1*SIN + arc->y1*COS)/arc->b;
+ x1p = (arc->x2*COS + arc->y2*SIN)/arc->a;
+ y1p = (-arc->x2*SIN + arc->y2*COS)/arc->b;
+ /* Compute differences and averages */
+ dx = x0p - x1p;
+ dy = y0p - y1p;
+
+ dsq = dx*dx + dy*dy;
+#if 0
+ if (dsq <= 0.001) {
+ debug_printf("AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAaaaaa\n");
+ }
+#endif
+ scale = 1/(2/sqrt(dsq));
+ arc->a *= scale;
+ arc->b *= scale;
+ return VG_TRUE;
+}
+
+static INLINE double vector_normalize(double *v)
+{
+ double sq = v[0] * v[0] + v[1] * v[1];
+ return sqrt(sq);
+}
+static INLINE double vector_orientation(double *v)
+{
+ double norm = vector_normalize(v);
+ double cosa = v[0] / norm;
+ double sina = v[1] / norm;
+ return (sina>=0 ? acos(cosa) : 2*M_PI - acos(cosa));
+}
+static INLINE double vector_dot(double *v0,
+ double *v1)
+{
+ return v0[0] * v1[0] + v0[1] * v1[1];
+}
+
+static INLINE double vector_angles(double *v0,
+ double *v1)
+{
+ double dot = vector_dot(v0, v1);
+ double norm0 = vector_normalize(v0);
+ double norm1 = vector_normalize(v1);
+
+ return acos(dot / (norm0 * norm1));
+}
+
+static VGboolean find_angles(struct arc *arc)
+{
+ double vec0[2], vec1[2];
+ double lambda1, lambda2;
+ double angle;
+ struct matrix matrix;
+
+ if (floatIsZero(arc->a) || floatIsZero(arc->b)) {
+ return VG_FALSE;
+ }
+ /* map the points to an identity circle */
+ matrix_load_identity(&matrix);
+ matrix_scale(&matrix, 1.f, arc->a/arc->b);
+ matrix_rotate(&matrix, -arc->theta);
+ matrix_map_point(&matrix,
+ arc->x1, arc->y1,
+ &arc->x1, &arc->y1);
+ matrix_map_point(&matrix,
+ arc->x2, arc->y2,
+ &arc->x2, &arc->y2);
+ matrix_map_point(&matrix,
+ arc->cx, arc->cy,
+ &arc->cx, &arc->cy);
+
+#if DEBUG_ARCS
+ debug_printf("Matrix 3 [%f, %f, %f| %f, %f, %f| %f, %f, %f]\n",
+ matrix.m[0], matrix.m[1], matrix.m[2],
+ matrix.m[3], matrix.m[4], matrix.m[5],
+ matrix.m[6], matrix.m[7], matrix.m[8]);
+ debug_printf("Endpoints [%f, %f], [%f, %f]\n",
+ arc->x1, arc->y1, arc->x2, arc->y2);
+#endif
+
+ vec0[0] = arc->x1 - arc->cx;
+ vec0[1] = arc->y1 - arc->cy;
+ vec1[0] = arc->x2 - arc->cx;
+ vec1[1] = arc->y2 - arc->cy;
+
+#if DEBUG_ARCS
+ debug_printf("Vec is [%f, %f], [%f, %f], [%f, %f]\n",
+ vec0[0], vec0[1], vec1[0], vec1[1], arc->cx, arc->cy);
+#endif
+
+ lambda1 = vector_orientation(vec0);
+
+ if (isnan(lambda1))
+ lambda1 = 0.f;
+
+ if (arc->type == VG_SCWARC_TO ||
+ arc->type == VG_SCCWARC_TO)
+ angle = vector_angles(vec0, vec1);
+ else if (arc->type == VG_LCWARC_TO ||
+ arc->type == VG_LCCWARC_TO) {
+ angle = 2*M_PI - vector_angles(vec0, vec1);
+ } else
+ abort();
+
+ if (isnan(angle))
+ angle = M_PI;
+
+
+ if (arc->type == VG_SCWARC_TO ||
+ arc->type == VG_LCWARC_TO)
+ lambda2 = lambda1 - angle;
+ else
+ lambda2 = lambda1 + angle;
+
+#if DEBUG_ARCS
+ debug_printf("Angle is %f and (%f, %f)\n", angle, lambda1, lambda2);
+#endif
+
+#if 0
+ arc->eta1 = atan2(sin(lambda1) / arc->b,
+ cos(lambda1) / arc->a);
+ arc->eta2 = atan2(sin(lambda2) / arc->b,
+ cos(lambda2) / arc->a);
+
+ /* make sure we have eta1 <= eta2 <= eta1 + 2 PI */
+ arc->eta2 -= two_pi * floor((arc->eta2 - arc->eta1) / two_pi);
+
+ /* the preceding correction fails if we have exactly et2 - eta1 = 2 PI
+ it reduces the interval to zero length */
+ if ((lambda2 - lambda1 > M_PI) && (arc->eta2 - arc->eta1 < M_PI)) {
+ arc->eta2 += 2 * M_PI;
+ }
+#else
+ arc->eta1 = lambda1;
+ arc->eta2 = lambda2;
+#endif
+
+ return VG_TRUE;
+}
+
+#if DEBUG_ARCS
+static void check_endpoints(struct arc *arc)
+{
+ double x1, y1, x2, y2;
+
+ double a_cos_eta1 = arc->a * cos(arc->eta1);
+ double b_sin_eta1 = arc->b * sin(arc->eta1);
+ x1 = arc->cx + a_cos_eta1 * arc->cos_theta -
+ b_sin_eta1 * arc->sin_theta;
+ y1 = arc->cy + a_cos_eta1 * arc->sin_theta +
+ b_sin_eta1 * arc->cos_theta;
+
+ double a_cos_eta2 = arc->a * cos(arc->eta2);
+ double b_sin_eta2 = arc->b * sin(arc->eta2);
+ x2 = arc->cx + a_cos_eta2 * arc->cos_theta -
+ b_sin_eta2 * arc->sin_theta;
+ y2 = arc->cy + a_cos_eta2 * arc->sin_theta +
+ b_sin_eta2 * arc->cos_theta;
+
+ debug_printf("Computed (%f, %f), (%f, %f)\n",
+ x1, y1, x2, y2);
+ debug_printf("Real (%f, %f), (%f, %f)\n",
+ arc->x1, arc->y1,
+ arc->x2, arc->y2);
+}
+#endif
+
+void arc_init(struct arc *arc,
+ VGPathSegment type,
+ VGfloat x1, VGfloat y1,
+ VGfloat x2, VGfloat y2,
+ VGfloat rh, VGfloat rv,
+ VGfloat rot)
+{
+ assert(type == VG_SCCWARC_TO ||
+ type == VG_SCWARC_TO ||
+ type == VG_LCCWARC_TO ||
+ type == VG_LCWARC_TO);
+ arc->type = type;
+ arc->x1 = x1;
+ arc->y1 = y1;
+ arc->x2 = x2;
+ arc->y2 = y2;
+ arc->a = rh;
+ arc->b = rv;
+ arc->theta = rot;
+ arc->cos_theta = cos(arc->theta);
+ arc->sin_theta = sin(arc->theta);
+ {
+ double cx0, cy0, cx1, cy1;
+ double cx, cy;
+ arc->is_valid = find_ellipses(rh, rv, rot, x1, y1, x2, y2,
+ &cx0, &cy0, &cx1, &cy1);
+
+ if (!arc->is_valid && try_to_fix_radii(arc)) {
+ rh = arc->a;
+ rv = arc->b;
+ arc->is_valid =
+ find_ellipses(rh, rv, rot, x1, y1, x2, y2,
+ &cx0, &cy0, &cx1, &cy1);
+ }
+
+ if (type == VG_SCWARC_TO ||
+ type == VG_LCCWARC_TO) {
+ cx = cx1;
+ cy = cy1;
+ } else {
+ cx = cx0;
+ cy = cy0;
+ }
+#if DEBUG_ARCS
+ debug_printf("Centers are : (%f, %f) , (%f, %f). Real (%f, %f)\n",
+ cx0, cy0, cx1, cy1, cx, cy);
+#endif
+ arc->cx = cx;
+ arc->cy = cy;
+ if (arc->is_valid) {
+ arc->is_valid = find_angles(arc);
+#if DEBUG_ARCS
+ check_endpoints(arc);
+#endif
+ /* remap a few points. find_angles requires
+ * rot in angles, the rest of the code
+ * will need them in radians. and find_angles
+ * modifies the center to match an identity
+ * circle so lets reset it */
+ arc->theta = DEGREES_TO_RADIANS(rot);
+ arc->cos_theta = cos(arc->theta);
+ arc->sin_theta = sin(arc->theta);
+ arc->cx = cx;
+ arc->cy = cy;
+ }
+ }
+}
+
+static INLINE double rational_function(double x, const double *c)
+{
+ return (x * (x * c[0] + c[1]) + c[2]) / (x + c[3]);
+}
+
+static double estimate_error(struct arc *arc,
+ double etaA, double etaB)
+{
+ double eta = 0.5 * (etaA + etaB);
+
+ double x = arc->b / arc->a;
+ double dEta = etaB - etaA;
+ double cos2 = cos(2 * eta);
+ double cos4 = cos(4 * eta);
+ double cos6 = cos(6 * eta);
+ double c0, c1;
+
+ /* select the right coeficients set according to degree and b/a */
+ const double (*coeffs)[4][4];
+ const double *safety;
+ coeffs = (x < 0.25) ? coeffs3Low : coeffs3High;
+ safety = safety3;
+
+ c0 = rational_function(x, coeffs[0][0])
+ + cos2 * rational_function(x, coeffs[0][1])
+ + cos4 * rational_function(x, coeffs[0][2])
+ + cos6 * rational_function(x, coeffs[0][3]);
+
+ c1 = rational_function(x, coeffs[1][0])
+ + cos2 * rational_function(x, coeffs[1][1])
+ + cos4 * rational_function(x, coeffs[1][2])
+ + cos6 * rational_function(x, coeffs[1][3]);
+
+ return rational_function(x, safety) * arc->a * exp(c0 + c1 * dEta);
+}
+
+struct arc_cb {
+ void (*move)(struct arc_cb *cb, VGfloat x, VGfloat y);
+ void (*point)(struct arc_cb *cb, VGfloat x, VGfloat y);
+ void (*bezier)(struct arc_cb *cb, struct bezier *bezier);
+
+ void *user_data;
+};
+
+static void cb_null_move(struct arc_cb *cb, VGfloat x, VGfloat y)
+{
+}
+
+static void polygon_point(struct arc_cb *cb, VGfloat x, VGfloat y)
+{
+ struct polygon *poly = (struct polygon*)cb->user_data;
+ polygon_vertex_append(poly, x, y);
+}
+
+static void polygon_bezier(struct arc_cb *cb, struct bezier *bezier)
+{
+ struct polygon *poly = (struct polygon*)cb->user_data;
+ bezier_add_to_polygon(bezier, poly);
+}
+
+static void stroke_point(struct arc_cb *cb, VGfloat x, VGfloat y)
+{
+ struct stroker *stroker = (struct stroker*)cb->user_data;
+ stroker_line_to(stroker, x, y);
+}
+
+static void stroke_curve(struct arc_cb *cb, struct bezier *bezier)
+{
+ struct stroker *stroker = (struct stroker*)cb->user_data;
+ stroker_curve_to(stroker,
+ bezier->x2, bezier->y2,
+ bezier->x3, bezier->y3,
+ bezier->x4, bezier->y4);
+}
+
+static void stroke_emit_point(struct arc_cb *cb, VGfloat x, VGfloat y)
+{
+ struct stroker *stroker = (struct stroker*)cb->user_data;
+ stroker_emit_line_to(stroker, x, y);
+}
+
+static void stroke_emit_curve(struct arc_cb *cb, struct bezier *bezier)
+{
+ struct stroker *stroker = (struct stroker*)cb->user_data;
+ stroker_emit_curve_to(stroker,
+ bezier->x2, bezier->y2,
+ bezier->x3, bezier->y3,
+ bezier->x4, bezier->y4);
+}
+
+static void arc_path_move(struct arc_cb *cb, VGfloat x, VGfloat y)
+{
+ struct path *path = (struct path*)cb->user_data;
+ path_move_to(path, x, y);
+}
+
+static void arc_path_point(struct arc_cb *cb, VGfloat x, VGfloat y)
+{
+ struct path *path = (struct path*)cb->user_data;
+ path_line_to(path, x, y);
+}
+
+static void arc_path_bezier(struct arc_cb *cb, struct bezier *bezier)
+{
+ struct path *path = (struct path*)cb->user_data;
+ path_cubic_to(path,
+ bezier->x2, bezier->y2,
+ bezier->x3, bezier->y3,
+ bezier->x4, bezier->y4);
+}
+
+static INLINE int num_beziers_needed(struct arc *arc)
+{
+ double threshold = 0.05;
+ VGboolean found = VG_FALSE;
+ int n = 1;
+ double min_eta, max_eta;
+
+ min_eta = MIN2(arc->eta1, arc->eta2);
+ max_eta = MAX2(arc->eta1, arc->eta2);
+
+ while ((! found) && (n < 1024)) {
+ double d_eta = (max_eta - min_eta) / n;
+ if (d_eta <= 0.5 * M_PI) {
+ double eta_b = min_eta;
+ found = VG_TRUE;
+ for (int i = 0; found && (i < n); ++i) {
+ double etaA = eta_b;
+ eta_b += d_eta;
+ found = (estimate_error(arc, etaA, eta_b) <= threshold);
+ }
+ }
+ n = n << 1;
+ }
+
+ return n;
+}
+
+static void arc_to_beziers(struct arc *arc,
+ struct arc_cb cb,
+ struct matrix *matrix)
+{
+ int n = 1;
+ double d_eta, eta_b, cos_eta_b,
+ sin_eta_b, a_cos_eta_b, b_sin_eta_b, a_sin_eta_b,
+ b_cos_eta_b, x_b, y_b, x_b_dot, y_b_dot, lx, ly;
+ double t, alpha;
+
+ { /* always move to the start of the arc */
+ VGfloat x = arc->x1;
+ VGfloat y = arc->y1;
+ matrix_map_point(matrix, x, y, &x, &y);
+ cb.move(&cb, x, y);
+ }
+
+ if (!arc->is_valid) {
+ VGfloat x = arc->x2;
+ VGfloat y = arc->y2;
+ matrix_map_point(matrix, x, y, &x, &y);
+ cb.point(&cb, x, y);
+ return;
+ }
+
+ /* find the number of Bézier curves needed */
+ n = num_beziers_needed(arc);
+
+ d_eta = (arc->eta2 - arc->eta1) / n;
+ eta_b = arc->eta1;
+
+ cos_eta_b = cos(eta_b);
+ sin_eta_b = sin(eta_b);
+ a_cos_eta_b = arc->a * cos_eta_b;
+ b_sin_eta_b = arc->b * sin_eta_b;
+ a_sin_eta_b = arc->a * sin_eta_b;
+ b_cos_eta_b = arc->b * cos_eta_b;
+ x_b = arc->cx + a_cos_eta_b * arc->cos_theta -
+ b_sin_eta_b * arc->sin_theta;
+ y_b = arc->cy + a_cos_eta_b * arc->sin_theta +
+ b_sin_eta_b * arc->cos_theta;
+ x_b_dot = -a_sin_eta_b * arc->cos_theta -
+ b_cos_eta_b * arc->sin_theta;
+ y_b_dot = -a_sin_eta_b * arc->sin_theta +
+ b_cos_eta_b * arc->cos_theta;
+
+ {
+ VGfloat x = x_b, y = y_b;
+ matrix_map_point(matrix, x, y, &x, &y);
+ cb.point(&cb, x, y);
+ }
+ lx = x_b;
+ ly = y_b;
+
+ t = tan(0.5 * d_eta);
+ alpha = sin(d_eta) * (sqrt(4 + 3 * t * t) - 1) / 3;
+
+ for (int i = 0; i < n; ++i) {
+ struct bezier bezier;
+ double xA = x_b;
+ double yA = y_b;
+ double xADot = x_b_dot;
+ double yADot = y_b_dot;
+
+ eta_b += d_eta;
+ cos_eta_b = cos(eta_b);
+ sin_eta_b = sin(eta_b);
+ a_cos_eta_b = arc->a * cos_eta_b;
+ b_sin_eta_b = arc->b * sin_eta_b;
+ a_sin_eta_b = arc->a * sin_eta_b;
+ b_cos_eta_b = arc->b * cos_eta_b;
+ x_b = arc->cx + a_cos_eta_b * arc->cos_theta -
+ b_sin_eta_b * arc->sin_theta;
+ y_b = arc->cy + a_cos_eta_b * arc->sin_theta +
+ b_sin_eta_b * arc->cos_theta;
+ x_b_dot = -a_sin_eta_b * arc->cos_theta -
+ b_cos_eta_b * arc->sin_theta;
+ y_b_dot = -a_sin_eta_b * arc->sin_theta +
+ b_cos_eta_b * arc->cos_theta;
+
+ bezier_init(&bezier,
+ lx, ly,
+ (float) (xA + alpha * xADot), (float) (yA + alpha * yADot),
+ (float) (x_b - alpha * x_b_dot), (float) (y_b - alpha * y_b_dot),
+ (float) x_b, (float) y_b);
+#if 0
+ debug_printf("%d) Bezier (%f, %f), (%f, %f), (%f, %f), (%f, %f)\n",
+ i,
+ bezier.x1, bezier.y1,
+ bezier.x2, bezier.y2,
+ bezier.x3, bezier.y3,
+ bezier.x4, bezier.y4);
+#endif
+ bezier_transform(&bezier, matrix);
+ cb.bezier(&cb, &bezier);
+ lx = x_b;
+ ly = y_b;
+ }
+}
+
+
+void arc_add_to_polygon(struct arc *arc,
+ struct polygon *poly,
+ struct matrix *matrix)
+{
+ struct arc_cb cb;
+
+ cb.move = cb_null_move;
+ cb.point = polygon_point;
+ cb.bezier = polygon_bezier;
+ cb.user_data = poly;
+
+ arc_to_beziers(arc, cb, matrix);
+}
+
+void arc_stroke_cb(struct arc *arc,
+ struct stroker *stroke,
+ struct matrix *matrix)
+{
+ struct arc_cb cb;
+
+ cb.move = cb_null_move;
+ cb.point = stroke_point;
+ cb.bezier = stroke_curve;
+ cb.user_data = stroke;
+
+ arc_to_beziers(arc, cb, matrix);
+}
+
+void arc_stroker_emit(struct arc *arc,
+ struct stroker *stroker,
+ struct matrix *matrix)
+{
+ struct arc_cb cb;
+
+ cb.move = cb_null_move;
+ cb.point = stroke_emit_point;
+ cb.bezier = stroke_emit_curve;
+ cb.user_data = stroker;
+
+ arc_to_beziers(arc, cb, matrix);
+}
+
+void arc_to_path(struct arc *arc,
+ struct path *path,
+ struct matrix *matrix)
+{
+ struct arc_cb cb;
+
+ cb.move = arc_path_move;
+ cb.point = arc_path_point;
+ cb.bezier = arc_path_bezier;
+ cb.user_data = path;
+
+ arc_to_beziers(arc, cb, matrix);
+}