/**
* Calculate the transform required to get a marker's path object in the
* right place for particular path segment on a shape.
*
* \see sp_shape_marker_update_marker_view.
*
* From SVG spec:
* The axes of the temporary new user coordinate system are aligned according to the orient attribute on the 'marker'
* element and the slope of the curve at the given vertex. (Note: if there is a discontinuity at a vertex, the slope
* is the average of the slopes of the two segments of the curve that join at the given vertex. If a slope cannot be
* determined, the slope is assumed to be zero.)
*
* Reference: http://www.w3.org/TR/SVG11/painting.html#MarkerElement, the `orient' attribute.
* Reference for behaviour of zero-length segments:
* http://www.w3.org/TR/SVG11/implnote.html#PathElementImplementationNotes
*/
Geom::Affine sp_shape_marker_get_transform(Geom::Curve const & c1, Geom::Curve const & c2)
{
Geom::Point p = c1.pointAt(1);
Geom::Curve * c1_reverse = c1.reverse();
Geom::Point tang1 = - c1_reverse->unitTangentAt(0);
delete c1_reverse;
Geom::Point tang2 = c2.unitTangentAt(0);
double const angle1 = Geom::atan2(tang1);
double const angle2 = Geom::atan2(tang2);
double ret_angle = .5 * (angle1 + angle2);
if ( fabs( angle2 - angle1 ) > M_PI ) {
/* ret_angle is in the middle of the larger of the two sectors between angle1 and
* angle2, so flip it by 180degrees to force it to the middle of the smaller sector.
*
* (Imagine a circle with rays drawn at angle1 and angle2 from the centre of the
* circle. Those two rays divide the circle into two sectors.)
*/
ret_angle += M_PI;
}
return Geom::Rotate(ret_angle) * Geom::Translate(p);
}
Geom::Affine sp_shape_marker_get_transform_at_end(Geom::Curve const & c)
{
Geom::Point p = c.pointAt(1);
Geom::Affine ret = Geom::Translate(p);
if ( !c.isDegenerate() ) {
Geom::Curve * c_reverse = c.reverse();
Geom::Point tang = - c_reverse->unitTangentAt(0);
delete c_reverse;
double const angle = Geom::atan2(tang);
ret = Geom::Rotate(angle) * Geom::Translate(p);
} else {
/* FIXME: the svg spec says to search for a better alternative than zero angle directionality:
* http://www.w3.org/TR/SVG11/implnote.html#PathElementImplementationNotes */
}
return ret;
}