geom-pathstroke.cpp revision a9f579cc260027d89b33d51735963a98cc77d5e9
/* Author:
* Liam P. White
*
* Copyright (C) 2014-2015 Author
*
* Released under GNU GPL, read the file 'COPYING' for more information
*/
#include <iomanip>
#include <2geom/path-sink.h>
#include <2geom/point.h>
#include <2geom/bezier-curve.h>
#include <2geom/svg-elliptical-arc.h>
#include <2geom/sbasis-to-bezier.h> // cubicbezierpath_from_sbasis
#include <2geom/path-intersection.h>
#include "helper/geom-pathstroke.h"
namespace Geom {
// 2geom/circle-circle.cpp, no header
int circle_circle_intersection(Point X0, double r0, Point X1, double r1, Point &p0, Point &p1);
/**
* Determine the intersection points between a circle C0 and a line defined
* by two points, X0 and X1.
*
* Which intersection point is assigned to p0 or p1 is unspecified, and callers
* should not depend on any particular intersection always being assigned to p0.
*
* Returns:
* If the line and circle do not cross, 0 is returned.
* If solution(s) exist, 2 is returned, and the results are written to p0 and p1.
*/
static int circle_line_intersection(Circle C0, Point X0, Point X1, Point &p0, Point &p1)
{
/* equation of a circle: (x - h)^2 + (y - k)^2 = r^2 */
Coord r = C0.ray();
Coord h = C0.center()[X];
Coord k = C0.center()[Y];
Coord x0, y0;
Coord x1, y1;
if (are_near(X1[X], X0[X])) {
/* slope is undefined (vertical line) */
Coord c = X0[X];
Coord det = r*r - (c-h)*(c-h);
/* no intersection */
if (det < 0)
return 0;
/* solve for y */
y0 = k + std::sqrt(det);
y1 = k - std::sqrt(det);
// x == c (always)
x0 = c;
x1 = c;
} else {
/* equation of a line: y = mx + b */
Coord m = (X1[Y] - X0[Y]) / (X1[X] - X0[X]);
Coord b = X0[Y] - m*X0[X];
/* obtain quadratic for x: */
Coord A = m*m + 1;
Coord B = 2*h - 2*b*m + 2*k*m;
Coord C = b*b + h*h + k*k - r*r - 2*b*k;
Coord det = B*B - 4*A*C;
/* no intersection, circle and line do not cross */
if (det < 0)
return 0;
/* solve quadratic */
x0 = (B + std::sqrt(det)) / (2*A);
x1 = (B - std::sqrt(det)) / (2*A);
/* substitute the calculated x times to determine the y values */
y0 = m*x0 + b;
y1 = m*x1 + b;
}
p0 = Point(x0, y0);
p1 = Point(x1, y1);
return 2;
}
static Point intersection_point(Point origin_a, Point vector_a, Point origin_b, Point vector_b)
{
Coord denom = cross(vector_b, vector_a);
if (!are_near(denom,0.)) {
Coord t = (cross(origin_a,vector_b) + cross(vector_b,origin_b)) / denom;
return origin_a + vector_a*t;
}
return Point(infinity(), infinity());
}
/**
* Find circle that touches inside of the curve, with radius matching the curvature, at time value \c t.
* Because this method internally uses unitTangentAt, t should be smaller than 1.0 (see unitTangentAt).
*/
static Circle touching_circle( D2<SBasis> const &curve, double t, double tol=0.01 )
{
D2<SBasis> dM=derivative(curve);
if ( are_near(L2sq(dM(t)),0.) ) {
dM=derivative(dM);
}
if ( are_near(L2sq(dM(t)),0.) ) { // try second time
dM=derivative(dM);
}
Piecewise<D2<SBasis> > unitv = unitVector(dM,tol);
Piecewise<SBasis> dMlength = dot(Piecewise<D2<SBasis> >(dM),unitv);
Piecewise<SBasis> k = cross(derivative(unitv),unitv);
k = divide(k,dMlength,tol,3);
double curv = k(t); // note that this value is signed
Geom::Point normal = unitTangentAt(curve, t).cw();
double radius = 1/curv;
Geom::Point center = curve(t) + radius*normal;
return Geom::Circle(center, fabs(radius));
}
}
namespace {
// Join functions may:
// - inspect any curve of the current path
// - append any type of curve to the current path
// - inspect the outgoing path
//
// Join functions must:
// - append the outgoing curve
// OR
// - end at outgoing.finalPoint
typedef void join_func(Geom::Path& res, Geom::Curve const& outgoing, double miter, double width);
void bevel_join(Geom::Path& res, Geom::Curve const& outgoing, double /*miter*/, double /*width*/)
{
res.appendNew<Geom::LineSegment>(outgoing.initialPoint());
res.append(outgoing);
}
void round_join(Geom::Path& res, Geom::Curve const& outgoing, double /*miter*/, double width)
{
res.appendNew<Geom::SVGEllipticalArc>(width, width, 0, false, width <= 0, outgoing.initialPoint());
res.append(outgoing);
}
void miter_join_internal(Geom::Path& res, Geom::Curve const& outgoing, double miter, double width, bool clip)
{
Geom::Curve const& incoming = res.back();
Geom::Point tang1 = Geom::unitTangentAt(reverse(incoming.toSBasis()), 0.);
Geom::Point tang2 = outgoing.unitTangentAt(0);
Geom::Point p = Geom::intersection_point(incoming.finalPoint(), tang1, outgoing.initialPoint(), tang2);
bool satisfied = false;
bool inc_ls = res.back_open().degreesOfFreedom() <= 4;
if (p.isFinite()) {
// check size of miter
Geom::Point point_on_path = incoming.finalPoint() + Geom::rot90(tang1)*width;
satisfied = Geom::distance(p, point_on_path) <= miter * 2.0 * width;
if (satisfied) {
// miter OK, check to see if we can do a relocation
if (inc_ls) {
res.setFinal(p);
} else {
res.appendNew<Geom::LineSegment>(p);
}
} else if (clip) {
// miter needs clipping, find two points
Geom::Point bisector_versor = Geom::Line(point_on_path, p).versor();
Geom::Point point_limit = point_on_path + miter * 2.0 * width * bisector_versor;
Geom::Point p1 = Geom::intersection_point(incoming.finalPoint(), tang1, point_limit, bisector_versor.cw());
Geom::Point p2 = Geom::intersection_point(outgoing.initialPoint(), tang2, point_limit, bisector_versor.cw());
if (inc_ls) {
res.setFinal(p1);
} else {
res.appendNew<Geom::LineSegment>(p1);
}
res.appendNew<Geom::LineSegment>(p2);
}
}
res.appendNew<Geom::LineSegment>(outgoing.initialPoint());
// check if we can do another relocation
bool out_ls = outgoing.degreesOfFreedom() <= 4;
if ( (satisfied || clip) && out_ls) {
res.setFinal(outgoing.finalPoint());
} else {
res.append(outgoing);
}
}
void miter_join(Geom::Path& res, Geom::Curve const& outgoing, double miter, double width) {
miter_join_internal( res, outgoing, miter, width, false );
}
void miter_clip_join(Geom::Path& res, Geom::Curve const& outgoing, double miter, double width) {
miter_join_internal( res, outgoing, miter, width, true );
}
Geom::Point pick_solution(Geom::Point points[2], Geom::Point tang2, Geom::Point endPt)
{
Geom::Point sol;
if ( dot(tang2,points[0]-endPt) > 0 ) {
// points[0] is bad, choose points[1]
sol = points[1];
} else if ( dot(tang2,points[1]-endPt) > 0 ) { // points[0] could be good, now check points[1]
// points[1] is bad, choose points[0]
sol = points[0];
} else {
// both points are good, choose nearest
sol = ( distanceSq(endPt, points[0]) < distanceSq(endPt, points[1]) ) ? points[0] : points[1];
}
return sol;
}
void extrapolate_join(Geom::Path& res, Geom::Curve const& outgoing, double miter, double width)
{
using namespace Geom;
Geom::Curve const& incoming = res.back();
Geom::Point startPt = incoming.finalPoint();
Geom::Point endPt = outgoing.initialPoint();
Geom::Point tang1 = Geom::unitTangentAt(reverse(incoming.toSBasis()), 0.);
Geom::Point tang2 = outgoing.unitTangentAt(0);
Geom::Circle circle1 = Geom::touching_circle(Geom::reverse(incoming.toSBasis()), 0.);
Geom::Circle circle2 = Geom::touching_circle(outgoing.toSBasis(), 0);
bool inc_ls = !circle1.center().isFinite();
bool out_ls = !circle2.center().isFinite();
Geom::Point points[2];
int solutions = 0;
Geom::EllipticalArc *arc1 = NULL;
Geom::EllipticalArc *arc2 = NULL;
Geom::Point sol;
Geom::Point p1;
Geom::Point p2;
if (!inc_ls && !out_ls) {
// Two circles
solutions = Geom::circle_circle_intersection(circle1.center(), circle1.ray(),
circle2.center(), circle2.ray(),
points[0], points[1]);
if (solutions == 2) {
sol = pick_solution(points, tang2, endPt);
arc1 = circle1.arc(startPt, 0.5*(startPt+sol), sol, true);
arc2 = circle2.arc(sol, 0.5*(sol+endPt), endPt, true);
}
} else if (inc_ls && !out_ls) {
// Line and circle
solutions = Geom::circle_line_intersection(circle2, incoming.initialPoint(), incoming.finalPoint(), points[0], points[1]);
if (solutions == 2) {
sol = pick_solution(points, tang2, endPt);
arc2 = circle2.arc(sol, 0.5*(sol+endPt), endPt, true);
}
} else if (!inc_ls && out_ls) {
// Circle and line
solutions = Geom::circle_line_intersection(circle1, outgoing.initialPoint(), outgoing.finalPoint(), points[0], points[1]);
if (solutions == 2) {
sol = pick_solution(points, tang2, endPt);
arc1 = circle1.arc(startPt, 0.5*(sol+startPt), sol, true);
}
}
if (solutions != 2)
// no solutions available, fall back to miter
return miter_clip_join(res, outgoing, miter, width);
// We have a solution, thus sol is defined.
p1 = sol;
// See if we need to clip. Miter length is measured along a circular arc that is tangent to the
// bisector of the incoming and out going angles and passes through the end point (sol) of the
// line join.
// Center of circle is intersection of a line orthogonal to bisector and a line bisecting
// a chord connecting the path end point (point_on_path) and the join end point (sol).
Geom::Point point_on_path = startPt + Geom::rot90(tang1)*width;
Geom::Line bisector = make_angle_bisector_line(startPt, point_on_path, endPt);
Geom::Line ortho = make_orthogonal_line(point_on_path, bisector);
Geom::LineSegment chord(point_on_path, sol);
Geom::Line bisector_chord = make_bisector_line(chord);
Geom::Line limit_line;
double miter_limit = 2.0 * width * miter;
bool clipped = false;
if (are_parallel(bisector_chord, ortho)) {
// No intersection (can happen if curvatures are equal but opposite)
if (Geom::distance(point_on_path, sol) > miter_limit) {
clipped = true;
Geom::Point limit_point = point_on_path + miter_limit * bisector.versor();
limit_line = make_parallel_line( limit_point, ortho );
}
} else {
Geom::Point center =
Geom::intersection_point( bisector_chord.pointAt(0), bisector_chord.versor(),
ortho.pointAt(0), ortho.versor() );
Geom::Coord radius = distance(center, point_on_path);
Geom::Circle circle_center(center, radius);
double limit_angle = miter_limit / radius;
Geom::Ray start_ray(center, point_on_path);
Geom::Ray end_ray(center, sol);
Geom::Line limit_line(center, 0); // Angle set below
if (Geom::cross(start_ray.versor(), end_ray.versor()) > 0) {
limit_line.setAngle(start_ray.angle() - limit_angle);
} else {
limit_line.setAngle(start_ray.angle() + limit_angle);
}
Geom::EllipticalArc *arc_center = circle_center.arc(point_on_path, 0.5*(point_on_path + sol), sol, true);
if (arc_center && arc_center->sweepAngle() > limit_angle) {
// We need to clip
clipped = true;
if (!inc_ls) {
// Incoming circular
solutions = Geom::circle_line_intersection(circle1, limit_line.pointAt(0), limit_line.pointAt(1), points[0], points[1]);
if (solutions == 2) {
p1 = pick_solution(points, tang2, endPt);
delete arc1;
arc1 = circle1.arc(startPt, 0.5*(p1+startPt), p1, true);
}
} else {
p1 = Geom::intersection_point(startPt, tang1, limit_line.pointAt(0), limit_line.versor());
}
if (!out_ls) {
// Outgoing circular
solutions = Geom::circle_line_intersection(circle2, limit_line.pointAt(0), limit_line.pointAt(1), points[0], points[1]);
if (solutions == 2) {
p2 = pick_solution(points, tang1, endPt);
delete arc2;
arc2 = circle2.arc(p2, 0.5*(p2+endPt), endPt, true);
}
} else {
p2 = Geom::intersection_point(endPt, tang2, limit_line.pointAt(0), limit_line.versor());
}
}
}
// Add initial
if (arc1) {
res.append(*arc1);
} else {
// Straight line segment: move last point
res.setFinal(p1);
}
if (clipped) {
res.appendNew<Geom::LineSegment>(p2);
}
// Add outgoing
if (arc2) {
res.append(*arc2);
res.append(outgoing);
} else {
// Straight line segment:
res.appendNew<Geom::LineSegment>(outgoing.finalPoint());
}
delete arc1;
delete arc2;
}
void join_inside(Geom::Path& res, Geom::Curve const& outgoing)
{
Geom::Curve const& incoming = res.back_open();
Geom::Crossings cross = Geom::crossings(incoming, outgoing);
if (!cross.empty()) {
// yeah if we could avoid allocing that'd be great
Geom::Curve *d1 = incoming.portion(0., cross[0].ta);
res.erase_last();
res.append(*d1);
delete d1;
Geom::Curve *d2 = outgoing.portion(cross[0].tb, 1.);
res.setFinal(d2->initialPoint());
res.append(*d2);
delete d2;
} else {
res.appendNew<Geom::LineSegment>(outgoing.initialPoint());
res.append(outgoing);
}
}
bool decide(Geom::Curve const& incoming, Geom::Curve const& outgoing)
{
Geom::Point tang1 = Geom::unitTangentAt(reverse(incoming.toSBasis()), 0.);
Geom::Point tang2 = outgoing.unitTangentAt(0.);
return (Geom::cross(tang1, tang2) < 0);
}
void outline_helper(Geom::Path& res, Geom::Path const& to_add, double width, bool on_outside, double miter, Inkscape::LineJoinType join)
{
if (res.size() == 0 || to_add.size() == 0)
return;
Geom::Curve const& outgoing = to_add[0];
if (Geom::are_near(res.finalPoint(), outgoing.initialPoint())) {
// if the points are /that/ close, just ignore this one
res.setFinal(outgoing.initialPoint());
res.append(outgoing);
return;
}
if (on_outside) {
join_func *jf;
switch (join) {
case Inkscape::JOIN_BEVEL:
jf = &bevel_join;
break;
case Inkscape::JOIN_ROUND:
jf = &round_join;
break;
case Inkscape::JOIN_EXTRAPOLATE:
jf = &extrapolate_join;
break;
case Inkscape::JOIN_MITER_CLIP:
jf = &miter_clip_join;
break;
default:
jf = &miter_join;
}
jf(res, outgoing, miter, width);
} else {
join_inside(res, outgoing);
}
}
// Offsetting a line segment is mathematically stable and quick to do
Geom::LineSegment offset_line(Geom::LineSegment const& l, double width)
{
Geom::Point tang1 = Geom::rot90(l.unitTangentAt(0));
Geom::Point tang2 = Geom::rot90(unitTangentAt(reverse(l.toSBasis()), 0.));
Geom::Point start = l.initialPoint() + tang1 * width;
Geom::Point end = l.finalPoint() - tang2 * width;
return Geom::LineSegment(start, end);
}
void get_cubic_data(Geom::CubicBezier const& bez, double time, double& len, double& rad)
{
// get derivatives
std::vector<Geom::Point> derivs = bez.pointAndDerivatives(time, 3);
Geom::Point der1 = derivs[1]; // first deriv (tangent vector)
Geom::Point der2 = derivs[2]; // second deriv (tangent's tangent)
double l = Geom::L2(der1); // length
len = rad = 0;
// TODO: we might want to consider using Geom::touching_circle to determine the
// curvature radius here. Less code duplication, but slower
if (Geom::are_near(l, 0, 1e-4)) {
l = Geom::L2(der2);
Geom::Point der3 = derivs.at(3); // try second time
if (Geom::are_near(l, 0, 1e-4)) {
l = Geom::L2(der3);
if (Geom::are_near(l, 0)) {
return; // this isn't a segment...
}
rad = 1e8;
} else {
rad = -l * (Geom::dot(der2, der2) / Geom::cross(der3, der2));
}
} else {
rad = -l * (Geom::dot(der1, der1) / Geom::cross(der2, der1));
}
len = l;
}
void offset_cubic(Geom::Path& p, Geom::CubicBezier const& bez, double width, double tol, size_t levels)
{
using Geom::X;
using Geom::Y;
Geom::Point start_pos = bez.initialPoint();
Geom::Point end_pos = bez.finalPoint();
Geom::Point start_normal = Geom::rot90(bez.unitTangentAt(0));
Geom::Point end_normal = -Geom::rot90(Geom::unitTangentAt(Geom::reverse(bez.toSBasis()), 0.));
// offset the start and end control points out by the width
Geom::Point start_new = start_pos + start_normal*width;
Geom::Point end_new = end_pos + end_normal*width;
// --------
double start_rad, end_rad;
double start_len, end_len; // tangent lengths
get_cubic_data(bez, 0, start_len, start_rad);
get_cubic_data(bez, 1, end_len, end_rad);
double start_off = 1, end_off = 1;
// correction of the lengths of the tangent to the offset
if (!Geom::are_near(start_rad, 0))
start_off += width / start_rad;
if (!Geom::are_near(end_rad, 0))
end_off += width / end_rad;
start_off *= start_len;
end_off *= end_len;
// --------
Geom::Point mid1_new = start_normal.ccw()*start_off;
mid1_new = Geom::Point(start_new[X] + mid1_new[X]/3., start_new[Y] + mid1_new[Y]/3.);
Geom::Point mid2_new = end_normal.ccw()*end_off;
mid2_new = Geom::Point(end_new[X] - mid2_new[X]/3., end_new[Y] - mid2_new[Y]/3.);
// create the estimate curve
Geom::CubicBezier c = Geom::CubicBezier(start_new, mid1_new, mid2_new, end_new);
// reached maximum recursive depth
// don't bother with any more correction
if (levels == 0) {
p.append(c, Geom::Path::STITCH_DISCONTINUOUS);
return;
}
// check the tolerance for our estimate to be a parallel curve
Geom::Point chk = c.pointAt(.5);
Geom::Point req = bez.pointAt(.5) + Geom::rot90(bez.unitTangentAt(.5))*width; // required accuracy
Geom::Point const diff = req - chk;
double const err = Geom::dot(diff, diff);
if (err < tol) {
if (Geom::are_near(start_new, p.finalPoint())) {
p.setFinal(start_new); // if it isn't near, we throw
}
// we're good, curve is accurate enough
p.append(c);
return;
} else {
// split the curve in two
std::pair<Geom::CubicBezier, Geom::CubicBezier> s = bez.subdivide(.5);
offset_cubic(p, s.first, width, tol, levels - 1);
offset_cubic(p, s.second, width, tol, levels - 1);
}
}
void offset_quadratic(Geom::Path& p, Geom::QuadraticBezier const& bez, double width, double tol, size_t levels)
{
// cheat
// it's faster
// seriously
std::vector<Geom::Point> points = bez.points();
Geom::Point b1 = points[0] + (2./3) * (points[1] - points[0]);
Geom::Point b2 = b1 + (1./3) * (points[2] - points[0]);
Geom::CubicBezier cub = Geom::CubicBezier(points[0], b1, b2, points[2]);
offset_cubic(p, cub, width, tol, levels);
}
void offset_curve(Geom::Path& res, Geom::Curve const* current, double width)
{
double const tolerance = 0.005;
size_t levels = 8;
if (current->isDegenerate()) return; // don't do anything
// TODO: we can handle SVGEllipticalArc here as well, do that!
if (Geom::BezierCurve const *b = dynamic_cast<Geom::BezierCurve const*>(current)) {
size_t order = b->order();
switch (order) {
case 1:
res.append(offset_line(static_cast<Geom::LineSegment const&>(*current), width));
break;
case 2: {
Geom::QuadraticBezier const& q = static_cast<Geom::QuadraticBezier const&>(*current);
offset_quadratic(res, q, width, tolerance, levels);
break;
}
case 3: {
Geom::CubicBezier const& cb = static_cast<Geom::CubicBezier const&>(*current);
offset_cubic(res, cb, width, tolerance, levels);
break;
}
default: {
Geom::Path sbasis_path = Geom::cubicbezierpath_from_sbasis(current->toSBasis(), tolerance);
for (size_t i = 0; i < sbasis_path.size(); ++i)
offset_curve(res, &sbasis_path[i], width);
break;
}
}
} else {
Geom::Path sbasis_path = Geom::cubicbezierpath_from_sbasis(current->toSBasis(), 0.1);
for (size_t i = 0; i < sbasis_path.size(); ++i)
offset_curve(res, &sbasis_path[i], width);
}
}
typedef void cap_func(Geom::PathBuilder& res, Geom::Path const& with_dir, Geom::Path const& against_dir, double width);
void flat_cap(Geom::PathBuilder& res, Geom::Path const&, Geom::Path const& against_dir, double)
{
res.lineTo(against_dir.initialPoint());
}
void round_cap(Geom::PathBuilder& res, Geom::Path const&, Geom::Path const& against_dir, double width)
{
res.arcTo(width / 2., width / 2., 0., true, false, against_dir.initialPoint());
}
void square_cap(Geom::PathBuilder& res, Geom::Path const& with_dir, Geom::Path const& against_dir, double width)
{
width /= 2.;
Geom::Point normal_1 = -Geom::unitTangentAt(Geom::reverse(with_dir.back().toSBasis()), 0.);
Geom::Point normal_2 = -against_dir[0].unitTangentAt(0.);
res.lineTo(with_dir.finalPoint() + normal_1*width);
res.lineTo(against_dir.initialPoint() + normal_2*width);
res.lineTo(against_dir.initialPoint());
}
void peak_cap(Geom::PathBuilder& res, Geom::Path const& with_dir, Geom::Path const& against_dir, double width)
{
width /= 2.;
Geom::Point normal_1 = -Geom::unitTangentAt(Geom::reverse(with_dir.back().toSBasis()), 0.);
Geom::Point normal_2 = -against_dir[0].unitTangentAt(0.);
Geom::Point midpoint = ((with_dir.finalPoint() + normal_1*width) + (against_dir.initialPoint() + normal_2*width)) * 0.5;
res.lineTo(midpoint);
res.lineTo(against_dir.initialPoint());
}
} // namespace
namespace Inkscape {
Geom::PathVector outline(Geom::Path const& input, double width, double miter, LineJoinType join, LineCapType butt)
{
if (input.size() == 0) return Geom::PathVector(); // nope, don't even try
Geom::PathBuilder res;
Geom::Path with_dir = half_outline(input, width/2., miter, join);
Geom::Path against_dir = half_outline(input.reverse(), width/2., miter, join);
res.moveTo(with_dir[0].initialPoint());
res.append(with_dir);
cap_func *cf;
switch (butt) {
case BUTT_ROUND:
cf = &round_cap;
break;
case BUTT_SQUARE:
cf = &square_cap;
break;
case BUTT_PEAK:
cf = &peak_cap;
break;
default:
cf = &flat_cap;
}
// glue caps
if (!input.closed()) {
cf(res, with_dir, against_dir, width);
} else {
res.closePath();
res.moveTo(against_dir.initialPoint());
}
res.append(against_dir);
if (!input.closed()) {
cf(res, against_dir, with_dir, width);
}
res.closePath();
res.flush();
return res.peek();
}
Geom::Path half_outline(Geom::Path const& input, double width, double miter, LineJoinType join)
{
Geom::Path res;
if (input.size() == 0) return res;
Geom::Point tang1 = input[0].unitTangentAt(0);
Geom::Point start = input.initialPoint() + tang1 * width;
Geom::Path temp;
res.start(start);
// Do two curves at a time for efficiency, since the join function needs to know the outgoing curve as well
const size_t k = (input.back_closed().isDegenerate() && input.closed())
?input.size_default()-1:input.size_default();
for (size_t u = 0; u < k; u += 2) {
temp = Geom::Path();
offset_curve(temp, &input[u], width);
// on the first run through, there isn't a join
if (u == 0) {
res.append(temp);
} else {
bool on_outside = decide(input[u-1], input[u]);
outline_helper(res, temp, width, on_outside, miter, join);
if (temp.size() > 0)
res.insert(res.end(), ++temp.begin(), temp.end());
}
// odd number of paths
if (u < k - 1) {
temp = Geom::Path();
offset_curve(temp, &input[u+1], width);
bool on_outside = decide(input[u], input[u+1]);
outline_helper(res, temp, width, on_outside, miter, join);
if (temp.size() > 0)
res.insert(res.end(), ++temp.begin(), temp.end());
}
}
if (input.closed()) {
Geom::Curve const &c1 = res.back();
Geom::Curve const &c2 = res.front();
temp = Geom::Path();
temp.append(c1);
Geom::Path temp2;
temp2.append(c2);
bool on_outside = decide(input.back(), input.front());
outline_helper(temp, temp2, width, on_outside, miter, join);
res.erase(res.begin());
res.erase_last();
//
res.append(temp);
res.close();
}
return res;
}
} // namespace Inkscape
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8 :