/**
* rsvg_path_arc: Add an RSVG arc to the path context.
* @ctx: Path context.
* @rx: Radius in x direction (before rotation).
* @ry: Radius in y direction (before rotation).
* @x_axis_rotation: Rotation angle for axes.
* @large_arc_flag: 0 for arc length <= 180, 1 for arc >= 180.
* @sweep: 0 for "negative angle", 1 for "positive angle".
* @x: New x coordinate.
* @y: New y coordinate.
*
**/
static void
rsvg_path_arc (RSVGParsePathCtx *ctx,
double rx, double ry, double x_axis_rotation,
int large_arc_flag, int sweep_flag,
double x, double y)
{
double sin_th, cos_th;
double a00, a01, a10, a11;
double x0, y0, x1, y1, xc, yc;
double d, sfactor, sfactor_sq;
double th0, th1, th_arc;
int i, n_segs;
sin_th = sin (x_axis_rotation * (M_PI / 180.0));
cos_th = cos (x_axis_rotation * (M_PI / 180.0));
a00 = cos_th / rx;
a01 = sin_th / rx;
a10 = -sin_th / ry;
a11 = cos_th / ry;
x0 = a00 * ctx->cpx + a01 * ctx->cpy;
y0 = a10 * ctx->cpx + a11 * ctx->cpy;
x1 = a00 * x + a01 * y;
y1 = a10 * x + a11 * y;
/* (x0, y0) is current point in transformed coordinate space.
(x1, y1) is new point in transformed coordinate space.
The arc fits a unit-radius circle in this space.
*/
d = (x1 - x0) * (x1 - x0) + (y1 - y0) * (y1 - y0);
sfactor_sq = 1.0 / d - 0.25;
if (sfactor_sq < 0) sfactor_sq = 0;
sfactor = sqrt (sfactor_sq);
if (sweep_flag == large_arc_flag) sfactor = -sfactor;
xc = 0.5 * (x0 + x1) - sfactor * (y1 - y0);
yc = 0.5 * (y0 + y1) + sfactor * (x1 - x0);
/* (xc, yc) is center of the circle. */
th0 = atan2 (y0 - yc, x0 - xc);
th1 = atan2 (y1 - yc, x1 - xc);
th_arc = th1 - th0;
if (th_arc < 0 && sweep_flag)
th_arc += 2 * M_PI;
else if (th_arc > 0 && !sweep_flag)
th_arc -= 2 * M_PI;
n_segs = (int) ceil (fabs (th_arc / (M_PI * 0.5 + 0.001)));
for (i = 0; i < n_segs; i++)
rsvg_path_arc_segment (ctx, xc, yc,
th0 + i * th_arc / n_segs,
th0 + (i + 1) * th_arc / n_segs,
rx, ry, x_axis_rotation);
ctx->cpx = x;
ctx->cpy = y;
}
/**
* rsvg_path_arc: Add an RSVG arc to the path context.
* @ctx: Path context.
* @rx: Radius in x direction (before rotation).
* @ry: Radius in y direction (before rotation).
* @x_axis_rotation: Rotation angle for axes.
* @large_arc_flag: 0 for arc length <= 180, 1 for arc >= 180.
* @sweep: 0 for "negative angle", 1 for "positive angle".
* @x: New x coordinate.
* @y: New y coordinate.
*
**/
static void
rsvg_path_arc (RSVGParsePathCtx * ctx,
double rx, double ry, double x_axis_rotation,
int large_arc_flag, int sweep_flag, double x, double y)
{
/* See Appendix F.6 Elliptical arc implementation notes
http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes */
double f, sinf, cosf;
double x1, y1, x2, y2;
double x1_, y1_;
double cx_, cy_, cx, cy;
double gamma;
double theta1, delta_theta;
double k1, k2, k3, k4, k5;
int i, n_segs;
/* Start and end of path segment */
x1 = ctx->cpx;
y1 = ctx->cpy;
x2 = x;
y2 = y;
if(x1 == x2 && y1 == y2)
return;
/* X-axis */
f = x_axis_rotation * M_PI / 180.0;
sinf = sin(f);
cosf = cos(f);
/* Check the radius */
if ((rx == 0.0) || (ry == 0.0))
{
rsvg_bpath_def_lineto (ctx->bpath, x, y);
return;
}
if(rx < 0)rx = -rx;
if(ry < 0)ry = -ry;
k1 = (x1 - x2)/2;
k2 = (y1 - y2)/2;
x1_ = cosf * k1 + sinf * k2;
y1_ = -sinf * k1 + cosf * k2;
gamma = (x1_*x1_)/(rx*rx) + (y1_*y1_)/(ry*ry);
if(gamma > 1)
{
rx *= sqrt(gamma);
ry *= sqrt(gamma);
}
/* Compute the center */
k1 = rx*rx*y1_*y1_ + ry*ry*x1_*x1_;
if(k1 == 0)
return;
k1 = sqrt(fabs((rx*rx*ry*ry)/k1 - 1));
if(sweep_flag == large_arc_flag)
k1 = -k1;
cx_ = k1*rx*y1_/ry;
cy_ = -k1*ry*x1_/rx;
cx = cosf*cx_ - sinf*cy_ + (x1+x2)/2;
cy = sinf*cx_ + cosf*cy_ + (y1+y2)/2;
/* Compute start angle */
k1 = (x1_ - cx_)/rx;
k2 = (y1_ - cy_)/ry;
k3 = (-x1_ - cx_)/rx;
k4 = (-y1_ - cy_)/ry;
k5 = sqrt(fabs(k1*k1 + k2*k2));
if(k5 == 0)return;
k5 = k1/k5;
if(k5 < -1)k5 = -1;
else if(k5 > 1)k5 = 1;
theta1 = acos(k5);
if(k2 < 0)theta1 = -theta1;
/* Compute delta_theta */
k5 = sqrt(fabs((k1*k1 + k2*k2)*(k3*k3 + k4*k4)));
if(k5 == 0)return;
k5 = (k1*k3 + k2*k4)/k5;
if(k5 < -1)k5 = -1;
else if(k5 > 1)k5 = 1;
delta_theta = acos(k5);
if(k1*k4 - k3*k2 < 0)delta_theta = -delta_theta;
if(sweep_flag && delta_theta < 0)
delta_theta += M_PI*2;
else if(!sweep_flag && delta_theta > 0)
delta_theta -= M_PI*2;
/* Now draw the arc */
n_segs = ceil (fabs (delta_theta / (M_PI * 0.5 + 0.001)));
for (i = 0; i < n_segs; i++)
rsvg_path_arc_segment (ctx, cx, cy,
theta1 + i * delta_theta / n_segs,
theta1 + (i + 1) * delta_theta / n_segs,
rx, ry, x_axis_rotation);
ctx->cpx = x;
ctx->cpy = y;
}
