diff options
Diffstat (limited to 'src/live_effects')
| -rw-r--r-- | src/live_effects/lpe-powerstroke.cpp | 164 |
1 files changed, 163 insertions, 1 deletions
diff --git a/src/live_effects/lpe-powerstroke.cpp b/src/live_effects/lpe-powerstroke.cpp index 69d0808e4..df94a761e 100644 --- a/src/live_effects/lpe-powerstroke.cpp +++ b/src/live_effects/lpe-powerstroke.cpp @@ -28,6 +28,8 @@ #include <2geom/path-intersection.h> #include <2geom/crossing.h> #include <2geom/ellipse.h> +#include <2geom/math-utils.h> +#include <math.h> #include "spiro.h" @@ -86,6 +88,70 @@ static Ellipse find_ellipse(Point P, Point Q, Point O) return Ellipse(A, B, C, D, E, F); } +/** + * Refer to: Weisstein, Eric W. "Circle-Circle Intersection." + From MathWorld--A Wolfram Web Resource. + http://mathworld.wolfram.com/Circle-CircleIntersection.html + * + * @return 0 if no intersection + * @return 1 if one circle is contained in the other + * @return 2 if intersections are found (they are written to p0 and p1) + */ +static int circle_circle_intersection(Circle const &circle0, Circle const &circle1, + Point & p0, Point & p1) +{ + Point X0 = circle0.center(); + double r0 = circle0.ray(); + Point X1 = circle1.center(); + double r1 = circle1.ray(); + + /* dx and dy are the vertical and horizontal distances between + * the circle centers. + */ + Point D = X1 - X0; + + /* Determine the straight-line distance between the centers. */ + double d = L2(D); + + /* Check for solvability. */ + if (d > (r0 + r1)) + { + /* no solution. circles do not intersect. */ + return 0; + } + if (d <= fabs(r0 - r1)) + { + /* no solution. one circle is contained in the other */ + return 1; + } + + /* 'point 2' is the point where the line through the circle + * intersection points crosses the line between the circle + * centers. + */ + + /* Determine the distance from point 0 to point 2. */ + double a = ((r0*r0) - (r1*r1) + (d*d)) / (2.0 * d) ; + + /* Determine the coordinates of point 2. */ + Point p2 = X0 + D * (a/d); + + /* Determine the distance from point 2 to either of the + * intersection points. + */ + double h = std::sqrt((r0*r0) - (a*a)); + + /* Now determine the offsets of the intersection points from + * point 2. + */ + Point r = (h/d)*rot90(D); + + /* Determine the absolute intersection points. */ + p0 = p2 + r; + p1 = p2 - r; + + return 2; +} } // namespace Geom @@ -121,7 +187,8 @@ enum LineJoinType { LINEJOIN_ROUND, LINEJOIN_EXTRP_MITER, LINEJOIN_MITER, - LINEJOIN_SPIRO + LINEJOIN_SPIRO, + LINEJOIN_EXTRP_MITER_ARC }; static const Util::EnumData<unsigned> LineJoinTypeData[] = { {LINEJOIN_BEVEL, N_("Beveled"), "bevel"}, @@ -129,6 +196,9 @@ static const Util::EnumData<unsigned> LineJoinTypeData[] = { {LINEJOIN_EXTRP_MITER, N_("Extrapolated"), "extrapolated"}, {LINEJOIN_MITER, N_("Miter"), "miter"}, {LINEJOIN_SPIRO, N_("Spiro"), "spiro"}, +#ifdef LPE_ENABLE_TEST_EFFECTS + {LINEJOIN_EXTRP_MITER_ARC, N_("Extrapolated arc"), "extrp_arc"}, +#endif }; static const Util::EnumDataConverter<unsigned> LineJoinTypeConverter(LineJoinTypeData, sizeof(LineJoinTypeData)/sizeof(*LineJoinTypeData)); @@ -310,6 +380,98 @@ static Geom::Path path_from_piecewise_fix_cusps( Geom::Piecewise<Geom::D2<Geom:: } break; } + case LINEJOIN_EXTRP_MITER_ARC: { + Geom::Circle circle0; + Geom::Circle circle1; + Geom::Point tang0(0.,0.); + { + Geom::Point norm0(0.,0.); + Geom::Coord curv0 = 0; + std::vector<Geom::Point> derivs = reverse(B[prev_i]).valueAndDerivatives(0.,5); + for (unsigned deriv_n = 1, count = 0; deriv_n < derivs.size(); deriv_n++) { + Geom::Coord length = derivs[deriv_n].length(); + if ( ! Geom::are_near(length, 0) ) { + if (count == 0) { + tang0 = derivs[deriv_n] / length; + curv0 = length; // save the length of the tangent + count++; + } else { + // curv0 = need good way to calculate curvature + // calculate direction of normal + double angle = angle_between(tang0, derivs[deriv_n]); + if (angle >= 0 ) { + norm0 = tang0.ccw(); + } else { + norm0 = tang0.cw(); + } + break; // break out of for-loop + } + } + } + double r0 = curv0; + Geom::Point center0 = B[prev_i].at1() - r0*norm0; + circle0 = Geom::Circle(center0, r0); + } + Geom::Point tang1(0.,0.); + { + Geom::Point norm1(0.,0.); + Geom::Coord curv1 = 0; + std::vector<Geom::Point> derivs = B[i].valueAndDerivatives(0.,5); + for (unsigned deriv_n = 1, count = 0; deriv_n < derivs.size(); deriv_n++) { + Geom::Coord length = derivs[deriv_n].length(); + if ( ! Geom::are_near(length, 0) ) { + if (count == 0) { + tang1 = derivs[deriv_n] / length; + curv1 = length; // save the length of the tangent + count++; + } else { + //curv1 = length / curv1; // curvature = tangent' / tangent + // calculate direction of normal + double angle = angle_between(tang1, derivs[deriv_n]); + if (angle >= 0 ) { + norm1 = tang1.ccw(); + } else { + norm1 = tang1.cw(); + } + break; // break out of for-loop + } + } + } + double r1 = curv1; + Geom::Point center1 = B[i].at0() - r1*norm1; + circle1 = Geom::Circle(center1, r1); + } + + Geom::Point points[2]; + int solutions = circle_circle_intersection(circle0, circle1, points[0], points[1]); + if (solutions == 2) { + Geom::Point sol = points[0]; + if ( dot(tang0,sol-B[prev_i].at1()) > 0 ) { + sol = points[1]; + } + Geom::EllipticalArc *arc0 = circle0.arc(B[prev_i].at1(), 0.5*(B[prev_i].at1()+sol), sol, true); + Geom::EllipticalArc *arc1 = circle1.arc(sol, 0.5*(sol+B[i].at0()), B[i].at0(), true); + + if (arc0) { + build_from_sbasis(pb,arc0->toSBasis(), tol, false); + delete arc0; + arc0 = NULL; + } + if (arc1) { + build_from_sbasis(pb,arc1->toSBasis(), tol, false); + delete arc1; + arc1 = NULL; + } + } else if (solutions == 1) { // one circle is inside the other + // don't know what to do: default to bevel + pb.lineTo(B[i].at0()); + } else { // no intersections + // don't know what to do: default to bevel + pb.lineTo(B[i].at0()); + } + + break; + } case LINEJOIN_MITER: { boost::optional<Geom::Point> p = intersection_point( B[prev_i].at1(), tang1, B[i].at0(), tang2 ); |