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Diffstat (limited to 'src/gallium/state_trackers/vega/arc.c')
| -rw-r--r-- | src/gallium/state_trackers/vega/arc.c | 708 |
1 files changed, 708 insertions, 0 deletions
diff --git a/src/gallium/state_trackers/vega/arc.c b/src/gallium/state_trackers/vega/arc.c new file mode 100644 index 0000000000..e74c7f0334 --- /dev/null +++ b/src/gallium/state_trackers/vega/arc.c @@ -0,0 +1,708 @@ +/************************************************************************** + * + * 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); +} |