From: Vincent Sanders Date: Sat, 3 Oct 2020 14:12:30 +0000 (+0100) Subject: implement svg path arc correctly X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=f66051cab457438eefd23e1e2c6e2197894b2d52;p=libsvgtiny.git implement svg path arc correctly --- diff --git a/src/svgtiny.c b/src/svgtiny.c index 8831b92..ee0c59c 100644 --- a/src/svgtiny.c +++ b/src/svgtiny.c @@ -23,12 +23,21 @@ /* Source file generated by `gperf`. */ #include "autogenerated_colors.c" +#define TAU 6.28318530717958647692 + #ifndef M_PI #define M_PI 3.14159265358979323846 #endif +#ifndef M_PI_2 +#define M_PI_2 1.57079632679489661923 +#endif + #define KAPPA 0.5522847498 +#define degToRad(angleInDegrees) ((angleInDegrees) * M_PI / 180.0) +#define radToDeg(angleInRadians) ((angleInRadians) * 180.0 / M_PI) + static svgtiny_code svgtiny_parse_svg(dom_element *svg, struct svgtiny_parse_state state); static svgtiny_code svgtiny_parse_path(dom_element *path, @@ -60,6 +69,449 @@ static void _svgtiny_parse_color(const char *s, svgtiny_colour *c, struct svgtiny_parse_state_gradient *grad, struct svgtiny_parse_state *state); +/** + * rotate midpoint vector + */ +static void +rotate_midpoint_vector(float ax, float ay, + float bx, float by, + double radangle, + double *x_out, double *y_out) +{ + double dx2; /* midpoint x coordinate */ + double dy2; /* midpoint y coordinate */ + double cosangle; /* cosine of rotation angle */ + double sinangle; /* sine of rotation angle */ + + /* compute the sin and cos of the angle */ + cosangle = cos(radangle); + sinangle = sin(radangle); + + /* compute the midpoint between start and end points */ + dx2 = (ax - bx) / 2.0; + dy2 = (ay - by) / 2.0; + + /* rotate vector to remove angle */ + *x_out = ((cosangle * dx2) + (sinangle * dy2)); + *y_out = ((-sinangle * dx2) + (cosangle * dy2)); +} + + +/** + * ensure the arc radii are large enough and scale as appropriate + * + * the radii need to be large enough if they are not they must be + * adjusted. This allows for elimination of differences between + * implementations especialy with rounding. + */ +static void +ensure_radii_scale(double x1_sq, double y1_sq, + float *rx, float *ry, + double *rx_sq, double *ry_sq) +{ + double radiisum; + double radiiscale; + + /* set radii square values */ + (*rx_sq) = (*rx) * (*rx); + (*ry_sq) = (*ry) * (*ry); + + radiisum = (x1_sq / (*rx_sq)) + (y1_sq / (*ry_sq)); + if (radiisum > 0.99999) { + /* need to scale radii */ + radiiscale = sqrt(radiisum) * 1.00001; + *rx = (float)(radiiscale * (*rx)); + *ry = (float)(radiiscale * (*ry)); + /* update squares too */ + (*rx_sq) = (*rx) * (*rx); + (*ry_sq) = (*ry) * (*ry); + } +} + + +/** + * compute the transformed centre point + */ +static void +compute_transformed_centre_point(double sign, float rx, float ry, + double rx_sq, double ry_sq, + double x1, double y1, + double x1_sq, double y1_sq, + double *cx1, double *cy1) +{ + double sq; + double coef; + sq = ((rx_sq * ry_sq) - (rx_sq * y1_sq) - (ry_sq * x1_sq)) / + ((rx_sq * y1_sq) + (ry_sq * x1_sq)); + sq = (sq < 0) ? 0 : sq; + + coef = (sign * sqrt(sq)); + + *cx1 = coef * ((rx * y1) / ry); + *cy1 = coef * -((ry * x1) / rx); +} + + +/** + * compute untransformed centre point + * + * \param ax The first point x coordinate + * \param ay The first point y coordinate + * \param bx The second point x coordinate + * \param ay The second point y coordinate + */ +static void +compute_centre_point(float ax, float ay, + float bx, float by, + double cx1, double cy1, + double radangle, + double *x_out, double *y_out) +{ + double sx2; + double sy2; + double cosangle; /* cosine of rotation angle */ + double sinangle; /* sine of rotation angle */ + + /* compute the sin and cos of the angle */ + cosangle = cos(radangle); + sinangle = sin(radangle); + + sx2 = (ax + bx) / 2.0; + sy2 = (ay + by) / 2.0; + + *x_out = sx2 + (cosangle * cx1 - sinangle * cy1); + *y_out = sy2 + (sinangle * cx1 + cosangle * cy1); +} + + +/** + * compute the angle start and extent + */ +static void +compute_angle_start_extent(float rx, float ry, + double x1, double y1, + double cx1, double cy1, + double *start, double *extent) +{ + double sign; + double ux; + double uy; + double vx; + double vy; + double p, n; + double actmp; + + /* + * Angle betwen two vectors is +/- acos( u.v / len(u) * len(v)) + * Where: + * '.' is the dot product. + * +/- is calculated from the sign of the cross product (u x v) + */ + + ux = (x1 - cx1) / rx; + uy = (y1 - cy1) / ry; + vx = (-x1 - cx1) / rx; + vy = (-y1 - cy1) / ry; + + /* compute the start angle */ + /* The angle between (ux, uy) and the 0 angle */ + + /* len(u) * len(1,0) == len(u) */ + n = sqrt((ux * ux) + (uy * uy)); + /* u.v == (ux,uy).(1,0) == (1 * ux) + (0 * uy) == ux */ + p = ux; + /* u x v == (1 * uy - ux * 0) == uy */ + sign = (uy < 0) ? -1.0 : 1.0; + /* (p >= n) so safe */ + *start = sign * acos(p / n); + + /* compute the extent angle */ + n = sqrt(((ux * ux) + (uy * uy)) * ((vx * vx) + (vy * vy))); + p = (ux * vx) + (uy * vy); + sign = ((ux * vy) - (uy * vx) < 0) ? -1.0f : 1.0f; + + /* arc cos must operate between -1 and 1 */ + actmp = p / n; + if (actmp < -1.0) { + *extent = sign * M_PI; + } else if (actmp > 1.0) { + *extent = 0; + } else { + *extent = sign * acos(actmp); + } +} + + +/** + * converts a circle centered unit circle arc to a series of bezier curves + * + * Each bezier is stored as six values of three pairs of coordinates + * + * The beziers are stored without their start point as that is assumed + * to be the preceding elements end point. + * + * \param start The start angle of the arc (in radians) + * \param extent The size of the arc (in radians) + * \param bzpt The array to store the bezier values in + * \return The number of bezier segments output (max 4) + */ +static int +circle_arc_to_bezier(double start, double extent, double *bzpt) +{ + int bzsegments; + double increment; + double controllen; + int pos = 0; + int segment; + double angle; + double dx, dy; + + bzsegments = (int) ceil(fabs(extent) / M_PI_2); + increment = extent / bzsegments; + controllen = 4.0 / 3.0 * sin(increment / 2.0) / (1.0 + cos(increment / 2.0)); + + for (segment = 0; segment < bzsegments; segment++) { + /* first control point */ + angle = start + (segment * increment); + dx = cos(angle); + dy = sin(angle); + bzpt[pos++] = dx - controllen * dy; + bzpt[pos++] = dy + controllen * dx; + /* second control point */ + angle+=increment; + dx = cos(angle); + dy = sin(angle); + bzpt[pos++] = dx + controllen * dy; + bzpt[pos++] = dy - controllen * dx; + /* endpoint */ + bzpt[pos++] = dx; + bzpt[pos++] = dy; + + } + return bzsegments; +} + + +/** + * transform coordinate list + * + * perform a scale, rotate and translate on list of coordinates + * + * scale(rx,ry) + * rotate(an) + * translate (cx, cy) + * + * homogeneous transforms + * + * scaling + * | rx 0 0 | + * S = | 0 ry 0 | + * | 0 0 1 | + * + * rotate + * | cos(an) -sin(an) 0 | + * R = | sin(an) cos(an) 0 | + * | 0 0 1 | + * + * {{cos(a), -sin(a) 0}, {sin(a), cos(a),0}, {0,0,1}} + * + * translate + * | 1 0 cx | + * T = | 0 1 cy | + * | 0 0 1 | + * + * note order is significat here and the combined matrix is + * M = T.R.S + * + * | cos(an) -sin(an) cx | + * T.R = | sin(an) cos(an) cy | + * | 0 0 1 | + * + * | rx * cos(an) ry * -sin(an) cx | + * T.R.S = | rx * sin(an) ry * cos(an) cy | + * | 0 0 1 | + * + * {{Cos[a], -Sin[a], c}, {Sin[a], Cos[a], d}, {0, 0, 1}} . {{r, 0, 0}, {0, s, 0}, {0, 0, 1}} + * + * Each point + * | x1 | + * P = | y1 | + * | 1 | + * + * output + * | x2 | + * | y2 | = M . P + * | 1 | + * + * x2 = cx + (rx * x1 * cos(a)) + (ry * y1 * -1 * sin(a)) + * y2 = cy + (ry * y1 * cos(a)) + (rx * x1 * sin(a)) + * + * + * \param rx X scaling to apply + * \param ry Y scaling to apply + * \param radangle rotation to apply (in radians) + * \param cx X translation to apply + * \param cy Y translation to apply + * \param points The size of the bzpoints array + * \param bzpoints an array of x,y values to apply the transform to + */ +static void +scale_rotate_translate_points(double rx, double ry, + double radangle, + double cx, double cy, + int pntsize, + double *points) +{ + int pnt; + double cosangle; /* cosine of rotation angle */ + double sinangle; /* sine of rotation angle */ + double rxcosangle, rxsinangle, rycosangle, rynsinangle; + double x2,y2; + + /* compute the sin and cos of the angle */ + cosangle = cos(radangle); + sinangle = sin(radangle); + + rxcosangle = rx * cosangle; + rxsinangle = rx * sinangle; + rycosangle = ry * cosangle; + rynsinangle = ry * -1 * sinangle; + + for (pnt = 0; pnt < pntsize; pnt+=2) { + x2 = cx + (points[pnt] * rxcosangle) + (points[pnt + 1] * rynsinangle); + y2 = cy + (points[pnt + 1] * rycosangle) + (points[pnt] * rxsinangle); + points[pnt] = x2; + points[pnt + 1] = y2; + } +} + + +/** + * convert an svg path arc to a bezier curve + * + * This function perfoms a transform on the nine arc parameters + * (coordinate pairs for start and end together with the radii of the + * elipse, the rotation angle and which of the four arcs to draw) + * which generates the parameters (coordinate pairs for start, + * end and their control points) for a set of up to four bezier curves. + * + * Obviously the start and end coordinates are not altered between + * representations so the aim is to calculate the coordinate pairs for + * the bezier control points. + * + * \param bzpoints the array to fill with bezier curves + * \return the number of bezier segments generated or -1 for a line + */ +static int +svgarc_to_bezier(float start_x, + float start_y, + float end_x, + float end_y, + float rx, + float ry, + float angle, + bool largearc, + bool sweep, + double *bzpoints) +{ + double radangle; /* normalised elipsis rotation angle in radians */ + double rx_sq; /* x radius squared */ + double ry_sq; /* y radius squared */ + double x1, y1; /* rotated midpoint vector */ + double x1_sq, y1_sq; /* x1 vector squared */ + double cx1,cy1; /* transformed circle center */ + double cx,cy; /* circle center */ + double start, extent; + int bzsegments; + + if ((start_x == end_x) && (start_y == end_y)) { + /* + * if the start and end coordinates are the same the + * svg spec says this is equivalent to having no segment + * at all + */ + return 0; + } + + if ((rx == 0) || (ry == 0)) { + /* + * if either radii is zero the specified behaviour is a line + */ + return -1; + } + + /* obtain the absolute values of the radii */ + rx = fabsf(rx); + ry = fabsf(ry); + + /* convert normalised angle to radians */ + radangle = degToRad(fmod(angle, 360.0)); + + /* step 1 */ + /* x1,x2 is the midpoint vector rotated to remove the arc angle */ + rotate_midpoint_vector(start_x, start_y, end_x, end_y, radangle, &x1, &y1); + + /* step 2 */ + /* get squared x1 values */ + x1_sq = x1 * x1; + y1_sq = y1 * y1; + + /* ensure radii are correctly scaled */ + ensure_radii_scale(x1_sq, y1_sq, &rx, &ry, &rx_sq, &ry_sq); + + /* compute the transformed centre point */ + compute_transformed_centre_point(largearc == sweep?-1:1, + rx, ry, + rx_sq, ry_sq, + x1, y1, + x1_sq, y1_sq, + &cx1, &cy1); + + /* step 3 */ + /* get the untransformed centre point */ + compute_centre_point(start_x, start_y, + end_x, end_y, + cx1, cy1, + radangle, + &cx, &cy); + + /* step 4 */ + /* compute anglestart and extent */ + compute_angle_start_extent(rx,ry, + x1,y1, + cx1, cy1, + &start, &extent); + + /* extent of 0 is a straight line */ + if (extent == 0) { + return -1; + } + + /* take account of sweep */ + if (!sweep && extent > 0) { + extent -= TAU; + } else if (sweep && extent < 0) { + extent += TAU; + } + + /* normalise start and extent */ + extent = fmod(extent, TAU); + start = fmod(start, TAU); + + /* convert the arc to unit circle bezier curves */ + bzsegments = circle_arc_to_bezier(start, extent, bzpoints); + + /* transform the bezier curves */ + scale_rotate_translate_points(rx, ry, + radangle, + cx, cy, + bzsegments * 6, + bzpoints); + + return bzsegments; +} + + /** * Call this to ref the strings in a gradient state. */ @@ -692,17 +1144,46 @@ svgtiny_code svgtiny_parse_path(dom_element *path, &rx, &ry, &rotation, &large_arc, &sweep, &x, &y, &n) == 8) { do { - ALLOC_PATH_ELEMENTS(3); + int bzsegments; + double bzpoints[6*4]; /* allow for up to four bezier segments per arc */ - p[i++] = svgtiny_PATH_LINE; if (*command == 'a') { x += last_x; y += last_y; } - p[i++] = last_cubic_x = last_quad_x = last_x - = x; - p[i++] = last_cubic_y = last_quad_y = last_y - = y; + + bzsegments = svgarc_to_bezier(last_x, last_y, + x, y, + rx, ry, + rotation, + large_arc, + sweep, + bzpoints); + if (bzsegments == -1) { + /* draw a line */ + ALLOC_PATH_ELEMENTS(3); + p[i++] = svgtiny_PATH_LINE; + p[i++] = x; + p[i++] = y; + } else if (bzsegments > 0) { + int bzpnt; + ALLOC_PATH_ELEMENTS((unsigned int)bzsegments * 7); + for (bzpnt = 0;bzpnt < (bzsegments * 6); bzpnt+=6) { + p[i++] = svgtiny_PATH_BEZIER; + p[i++] = bzpoints[bzpnt]; + p[i++] = bzpoints[bzpnt+1]; + p[i++] = bzpoints[bzpnt+2]; + p[i++] = bzpoints[bzpnt+3]; + p[i++] = bzpoints[bzpnt+4]; + p[i++] = bzpoints[bzpnt+5]; + } + } + if (bzsegments != 0) { + last_cubic_x = last_quad_x = last_x = p[i-2]; + last_cubic_y = last_quad_y = last_y = p[i-1]; + } + + s += n; } while (sscanf(s, "%f %f %f %f %f %f %f %n", &rx, &ry, &rotation, &large_arc, &sweep, @@ -893,7 +1374,7 @@ svgtiny_code svgtiny_parse_circle(dom_element *circle, err = svgtiny_add_path(p, 32, &state); svgtiny_cleanup_state_local(&state); - + return err; } @@ -1006,7 +1487,7 @@ svgtiny_code svgtiny_parse_ellipse(dom_element *ellipse, p[29] = x + rx; p[30] = y; p[31] = svgtiny_PATH_CLOSE; - + err = svgtiny_add_path(p, 32, &state); svgtiny_cleanup_state_local(&state); @@ -1116,14 +1597,14 @@ svgtiny_code svgtiny_parse_poly(dom_element *poly, svgtiny_parse_paint_attributes(poly, &state); svgtiny_parse_transform_attributes(poly, &state); - + exc = dom_element_get_attribute(poly, state.interned_points, &points_str); if (exc != DOM_NO_ERR) { svgtiny_cleanup_state_local(&state); return svgtiny_LIBDOM_ERROR; } - + if (points_str == NULL) { state.diagram->error_line = -1; /* poly->line; */ state.diagram->error_message = @@ -1166,7 +1647,7 @@ svgtiny_code svgtiny_parse_poly(dom_element *poly, p[i++] = y; s += n; } else { - break; + break; } } if (polygon) @@ -1203,12 +1684,12 @@ svgtiny_code svgtiny_parse_text(dom_element *text, px = state.ctm.a * x + state.ctm.c * y + state.ctm.e; py = state.ctm.b * x + state.ctm.d * y + state.ctm.f; -/* state.ctm.e = px - state.origin_x; */ -/* state.ctm.f = py - state.origin_y; */ +/* state.ctm.e = px - state.origin_x; */ +/* state.ctm.f = py - state.origin_y; */ /*struct css_style style = state.style; style.font_size.value.length.value *= state.ctm.a;*/ - + exc = dom_node_get_first_child(text, &child); if (exc != DOM_NO_ERR) { return svgtiny_LIBDOM_ERROR; @@ -1385,7 +1866,7 @@ void svgtiny_parse_paint_attributes(dom_element *node, { dom_string *attr; dom_exception exc; - + exc = dom_element_get_attribute(node, state->interned_fill, &attr); if (exc == DOM_NO_ERR && attr != NULL) { svgtiny_parse_color(attr, &state->fill, &state->fill_grad, state); @@ -1557,7 +2038,7 @@ void svgtiny_parse_transform_attributes(dom_element *node, char *transform; dom_string *attr; dom_exception exc; - + exc = dom_element_get_attribute(node, state->interned_transform, &attr); if (exc == DOM_NO_ERR && attr != NULL) { @@ -1761,7 +2242,7 @@ void svgtiny_free(struct svgtiny_diagram *svg) free(svg->shape[i].path); free(svg->shape[i].text); } - + free(svg->shape); free(svg); @@ -1786,4 +2267,3 @@ char *svgtiny_strndup(const char *s, size_t n) return s2; } #endif - diff --git a/test/data/arc-path.svg b/test/data/arc-path.svg new file mode 100644 index 0000000..6f0fd0b --- /dev/null +++ b/test/data/arc-path.svg @@ -0,0 +1,14 @@ + + + + + +