diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/live_effects/lpe-powerstroke.cpp | 93 |
1 files changed, 81 insertions, 12 deletions
diff --git a/src/live_effects/lpe-powerstroke.cpp b/src/live_effects/lpe-powerstroke.cpp index 257dba8ea..6cc2d2368 100644 --- a/src/live_effects/lpe-powerstroke.cpp +++ b/src/live_effects/lpe-powerstroke.cpp @@ -26,9 +26,10 @@ #include <2geom/svg-path.h> #include <2geom/path-intersection.h> #include <2geom/crossing.h> +#include <2geom/ellipse.h> namespace Geom { - +// should all be moved to 2geom at some point Point unitTangentAt( D2<SBasis> const & a, Coord t, unsigned n = 3) { std::vector<Point> derivs = a.valueAndDerivatives(t, n); @@ -55,8 +56,48 @@ boost::optional<Point> intersection_point( Point const & origin_a, Point const & return boost::none; } +Geom::CubicBezier sbasis_to_cubicbezier(Geom::D2<Geom::SBasis> const & sbasis_in) +{ + std::vector<Geom::Point> temp; + sbasis_to_bezier(temp, sbasis_in, 4); + return Geom::CubicBezier( temp ); } +/** + * document this! + * very quick: this finds the ellipse with minimum eccentricity + passing through point P and Q, with tangent PO at P and QO at Q + http://mathforum.org/kb/message.jspa?messageID=7471596&tstart=0 + */ +static Ellipse find_ellipse(Point P, Point Q, Point O) +{ + Point p = P - O; + Point q = Q - O; + Coord K = 4 * dot(p,q) / (L2sq(p) + L2sq(q)); + + double cross = p[Y]*q[X] - p[X]*q[Y]; + double a = -q[Y]/cross; + double b = q[X]/cross; + double c = (O[X]*q[Y] - O[Y]*q[X])/cross; + + double d = p[Y]/cross; + double e = -p[X]/cross; + double f = (-O[X]*p[Y] + O[Y]*p[X])/cross; + + // Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 + double A = (a*d*K+d*d+a*a); + double B = (a*e*K+b*d*K+2*d*e+2*a*b); + double C = (b*e*K+e*e+b*b); + double D = (a*f*K+c*d*K+2*d*f-2*d+2*a*c-2*a); + double E = (b*f*K+c*e*K+2*e*f-2*e+2*b*c-2*b); + double F = c*f*K+f*f-2*f+c*c-2*c+1; + + return Ellipse(A, B, C, D, E, F); +} + + +} // namespace Geom + namespace Inkscape { namespace LivePathEffect { @@ -176,8 +217,16 @@ std::vector<discontinuity_data> find_discontinuities( Geom::Piecewise<Geom::D2<G for(unsigned i = 1; i < der.size(); i++) { if ( ! are_near(der[i-1].at1(), der[i].at0(), eps) ) { discontinuity_data data; + data.der0 = der[i-1].at1(); data.der1 = der[i].at0(); + if ( Geom::are_near(data.der0.length(), 0) ) { + data.der0 = unitTangentAt(der[i-1], 1, 2); + } + if ( Geom::are_near(data.der1.length(), 0) ) { + data.der1 = unitTangentAt(der[i], 0, 2); + } + double t = der.cuts[i]; std::vector< double > rts = roots (x - t); /// @todo this has multiple solutions for general strokewidth paths (generated by spiro interpolator...), ignore for now if (!rts.empty()) { @@ -224,11 +273,36 @@ Geom::Path path_from_piecewise_fix_cusps( Geom::Piecewise<Geom::D2<Geom::SBasis> discontinuity_data cusp = cusps[cusp_i]; switch (cusp_linecap) { - case LINECUSP_ROUND: // properly bugged ^_^ - pb.arcTo( abs(cusp.width), abs(cusp.width), - angle_between(cusp.der0, cusp.der1), false, cusp.width < 0, - B[i].at0() ); + case LINECUSP_ROUND: { + if ( sign*cusp.width*angle_between(cusp.der0, cusp.der1) < 0.) { + // we are on the outside: round corner + /* for constant width paths, the rounding is a circular arc (rx == ry), + for non-constant width paths, the rounding can be done with an ellipse but is hard and ambiguous. + The elliptical arc should go through the discontinuity's start and end points (of course!) + and also should match the discontinuity tangents at those start and end points. + To resolve the ambiguity, the elliptical arc with minimal eccentricity should be chosen. + A 2Geom method was created to do exactly this :) + */ + + Geom::Point tang1 = unitTangentAt(B[prev_i],1); + Geom::Point tang2 = unitTangentAt(B[i],0); + boost::optional<Geom::Point> O = intersection_point( B[prev_i].at1(), tang1, + B[i].at0(), tang2 ); + if (!O) { + // no center found, i.e. 180 degrees round + pb.lineTo(B[i].at0()); // default to bevel for too shallow cusp angles + break; + } + + Geom::Ellipse ellipse = find_ellipse(B[prev_i].at1(), B[i].at0(), *O); + pb.arcTo( ellipse.ray(Geom::X), ellipse.ray(Geom::Y), ellipse.rot_angle(), + false, cusp.width < 0, B[i].at0() ); + } else { + // we are on the inside, do a simple bevel to connect the paths + pb.lineTo(B[i].at0()); // default to bevel for too shallow cusp angles + } break; + } /* case LINECUSP_NONE: { if ( sign*cusp.width*angle_between(cusp.der0, cusp.der1) < 0.) { // we are on the outside @@ -250,15 +324,10 @@ Geom::Path path_from_piecewise_fix_cusps( Geom::Piecewise<Geom::D2<Geom::SBasis> Geom::Point der2 = unitTangentAt(B[i],0); Geom::D2<Geom::SBasis> newcurve1 = B[prev_i] * Geom::reflection(rot90(der1), B[prev_i].at1()); - newcurve1 = reverse(newcurve1); - std::vector<Geom::Point> temp; - sbasis_to_bezier(temp, newcurve1, 4); - Geom::CubicBezier bzr1( temp ); + Geom::CubicBezier bzr1 = sbasis_to_cubicbezier( reverse(newcurve1) ); Geom::D2<Geom::SBasis> newcurve2 = B[i] * Geom::reflection(rot90(der2), B[i].at0()); - newcurve2 = reverse(newcurve2); - sbasis_to_bezier(temp, newcurve2, 4); - Geom::CubicBezier bzr2( temp ); + Geom::CubicBezier bzr2 = sbasis_to_cubicbezier( reverse(newcurve2) ); Geom::Crossings cross = crossings(bzr1, bzr2); if (cross.empty()) { |