diff options
Diffstat (limited to 'src/2geom/ellipse.cpp')
| -rw-r--r-- | src/2geom/ellipse.cpp | 52 |
1 files changed, 40 insertions, 12 deletions
diff --git a/src/2geom/ellipse.cpp b/src/2geom/ellipse.cpp index fed3bf86f..4b5ad9762 100644 --- a/src/2geom/ellipse.cpp +++ b/src/2geom/ellipse.cpp @@ -205,22 +205,50 @@ Ellipse::arc(Point const &ip, Point const &inner, Point const &fp) bool sweep_flag = false; // Determination of large arc flag: - // The arc is larger than half of the ellipse if the inner point - // is on the same side of the line going from the initial - // to the final point as the center of the ellipse - Point versor = fp - ip; - double sdist_c = cross(versor, _center - ip); - double sdist_inner = cross(versor, inner - ip); - - // if we have exactly half of an arc, do not set the large flag. - if (sdist_c != 0 && sgn(sdist_c) == sgn(sdist_inner)) { + // large_arc is false when the inner point is on the same side + // of the center---initial point line as the final point, AND + // is on the same side of the center---final point line as the + // initial point. + // Additionally, large_arc is always false when we have exactly + // 1/2 of an arc, i.e. the cross product of the center -> initial point + // and center -> final point vectors is zero. + // Negating the above leads to the condition for large_arc being true. + Point fv = fp - _center; + Point iv = ip - _center; + Point innerv = inner - _center; + double ifcp = cross(fv, iv); + + if (ifcp != 0 && (sgn(cross(fv, innerv)) != sgn(ifcp) || + sgn(cross(iv, innerv)) != sgn(-ifcp))) + { large_arc_flag = true; } + //cross(-iv, fv) && large_arc_flag + + // Determination of sweep flag: - // If the inner point is on the left side of the ip-fp line, - // we go in clockwise direction. - if (sdist_inner < 0) { + // For clarity, let's assume that Y grows up. Then the cross product + // is positive for points on the left side of a vector and negative + // on the right side of a vector. + // + // cross(?, v) > 0 + // o-------------------> + // cross(?, v) < 0 + // + // If the arc is small (large_arc_flag is false) and the final point + // is on the right side of the vector initial point -> center, + // we have to go in the direction of increasing angles + // (counter-clockwise) and the sweep flag is true. + // If the arc is large, the opposite is true, since we have to reach + // the final point going the long way - in the other direction. + // We can express this observation as: + // cross(_center - ip, fp - _center) < 0 xor large_arc flag + // This is equal to: + // cross(-iv, fv) < 0 xor large_arc flag + // But cross(-iv, fv) is equal to cross(fv, iv) due to antisymmetry + // of the cross product, so we end up with the condition below. + if ((ifcp < 0) ^ large_arc_flag) { sweep_flag = true; } |