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http://git.netsurf-browser.org/libsvgtiny.git/commit/?id=f66051cab457438eefd23e1e2c6e2197894b2d52
commit f66051cab457438eefd23e1e2c6e2197894b2d52
Author: Vincent Sanders <[email protected]>
Commit: Vincent Sanders <[email protected]>
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,
@@ -61,6 +70,449 @@ static void _svgtiny_parse_color(const char *s,
svgtiny_colour *c,
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.
*/
static void svgtiny_grad_string_ref(struct svgtiny_parse_state_gradient *grad)
@@ -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 @@
+<svg width="325" height="325" xmlns="http://www.w3.org/2000/svg";>
+ <path d="M 80 80
+ A 45 45, 0, 0, 0, 125 125
+ L 125 80 Z" fill="green"/>
+ <path d="M 230 80
+ A 45 45, 0, 1, 0, 275 125
+ L 275 80 Z" fill="red"/>
+ <path d="M 80 230
+ A 45 45, 0, 0, 1, 125 275
+ L 125 230 Z" fill="purple"/>
+ <path d="M 230 230
+ A 45 45, 0, 1, 1, 275 275
+ L 275 230 Z" fill="blue"/>
+</svg>
-----------------------------------------------------------------------
Summary of changes:
src/svgtiny.c | 516 ++++++++++++++++++++++++++++++++++++++++++++++--
test/data/arc-path.svg | 14 ++
2 files changed, 512 insertions(+), 18 deletions(-)
create mode 100644 test/data/arc-path.svg
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,
@@ -61,6 +70,449 @@ static void _svgtiny_parse_color(const char *s,
svgtiny_colour *c,
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.
*/
static void svgtiny_grad_string_ref(struct svgtiny_parse_state_gradient *grad)
@@ -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 @@
+<svg width="325" height="325" xmlns="http://www.w3.org/2000/svg";>
+ <path d="M 80 80
+ A 45 45, 0, 0, 0, 125 125
+ L 125 80 Z" fill="green"/>
+ <path d="M 230 80
+ A 45 45, 0, 1, 0, 275 125
+ L 275 80 Z" fill="red"/>
+ <path d="M 80 230
+ A 45 45, 0, 0, 1, 125 275
+ L 125 230 Z" fill="purple"/>
+ <path d="M 230 230
+ A 45 45, 0, 1, 1, 275 275
+ L 275 230 Z" fill="blue"/>
+</svg>
--
NetSurf SVG decoder
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