pathoutlineprovider.cpp revision 49ab42a72a35618fae86c8f4ffbe98c85c743247
#include <glib.h> //g_critical
#include "pathoutlineprovider.h"
#include "livarot/path-description.h"
#include <2geom/angle.h>
#include <2geom/path.h>
#include <2geom/circle.h>
#include <2geom/sbasis-to-bezier.h>
#include <2geom/shape.h>
#include <2geom/transforms.h>
#include <2geom/path-sink.h>
#include "helper/geom-nodetype.h"
#include <svg/svg.h>
namespace Geom {
/**
* 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;
}
/**
* 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));
}
std::vector<Geom::Path> split_at_cusps(const Geom::Path& in)
{
PathVector out = PathVector();
Path temp = Path();
for (unsigned i = 0; i < in.size(); i++) {
temp.append(in[i]);
if ( get_nodetype(in[i], in[i + 1]) != Geom::NODE_SMOOTH ) {
out.push_back(temp);
temp = Path();
}
}
if (temp.size() > 0) {
out.push_back(temp);
}
return out;
}
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 );
}
static boost::optional<Geom::Point> intersection_point( Geom::Point const & origin_a, Geom::Point const & vector_a,
Geom::Point const & origin_b, Geom::Point const & vector_b)
{
Geom::Coord denom = cross(vector_b, vector_a);
if (!Geom::are_near(denom,0.)) {
Geom::Coord t = (cross(origin_a,vector_b) + cross(vector_b,origin_b)) / denom;
return origin_a + t * vector_a;
}
return boost::none;
}
}
namespace Outline {
typedef Geom::D2<Geom::SBasis> D2SB;
typedef Geom::Piecewise<D2SB> PWD2;
unsigned bezierOrder (const Geom::Curve* curve_in)
{
using namespace Geom;
if ( const BezierCurve* bz = dynamic_cast<const BezierCurve*>(curve_in) ) {
return bz->order();
}
return 0;
}
//returns true if the angle formed by the curves and their handles
//is >180 clockwise, otherwise false.
bool outside_angle (const Geom::Curve& cbc1, const Geom::Curve& cbc2)
{
Geom::Point start_point;
Geom::Point cross_point = cbc1.finalPoint();
Geom::Point end_point;
//assert(cbc1.finalPoint() == cbc2.initialPoint());
//short circuiting?
if (cbc1.finalPoint() != cbc2.initialPoint()) {
printf("There was an issue when asserting that one curve's end is the start of the other. Line %d, File %s\n"
"By default we are going to say that this is an inside join, so we cannot make a line join for it.\n", __LINE__, __FILE__);
return false;
}
//let's try:
Geom::CubicBezier cubicBezier = Geom::sbasis_to_cubicbezier(cbc1.toSBasis());
start_point = cubicBezier [2];
//stupid thing Inkscape does:
if (are_near(start_point, cross_point, 0.0000001)) {
start_point = cubicBezier [1];
}
cubicBezier = Geom::sbasis_to_cubicbezier(cbc2.toSBasis());
end_point = cubicBezier [1];
if (are_near(end_point, cross_point, 0.0000001)) {
end_point = cubicBezier [2];
}
//got our three points, now let's see what their clockwise angle is
//Much credit to Wikipedia for the following ( http://en.wikipedia.org/wiki/Graham_scan )
/********************************************************************
# Three points are a counter-clockwise turn if ccw > 0, clockwise if
# ccw < 0, and collinear if ccw = 0 because ccw is a determinant that
# gives the signed area of the triangle formed by p1, p2 and p3.
function ccw(p1, p2, p3):
return (p2.x - p1.x)*(p3.y - p1.y) - (p2.y - p1.y)*(p3.x - p1.x)
*********************************************************************/
double ccw = ( (cross_point.x() - start_point.x()) * (end_point.y() - start_point.y()) ) -
( (cross_point.y() - start_point.y()) * (end_point.x() - start_point.x()) );
if (ccw > 0) return true;
return false;
}
void extrapolate_curves(Geom::Path& path_builder, Geom::Curve* cbc1, Geom::Curve* cbc2, Geom::Point endPt,
double miter_limit, double line_width, bool outside = false)
{
bool lineProblem = (dynamic_cast<Geom::BezierCurveN<1u> *>(cbc1)) || (dynamic_cast<Geom::BezierCurveN<1u> *>(cbc2));
if ( outside && !lineProblem ) {
Geom::Path pth;
pth.append(*cbc1);
Geom::Point tang1 = Geom::unitTangentAt(Geom::reverse(pth.toPwSb()[0]), 0.);
pth = Geom::Path();
pth.append( *cbc2 );
Geom::Point tang2 = Geom::unitTangentAt(pth.toPwSb()[0], 0);
Geom::Circle circle1 = Geom::touching_circle(Geom::reverse(cbc1->toSBasis()), 0.);
Geom::Circle circle2 = Geom::touching_circle(cbc2->toSBasis(), 0);
Geom::Point points[2];
int solutions = Geom::circle_circle_intersection(circle1, circle2, points[0], points[1]);
if (solutions == 2) {
Geom::Point sol(0,0);
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];
}
Geom::EllipticalArc *arc0 = circle1.arc(cbc1->finalPoint(), 0.5*(cbc1->finalPoint()+sol), sol, true);
Geom::EllipticalArc *arc1 = circle2.arc(sol, 0.5*(sol+endPt), endPt, true);
try {
if (arc0) {
path_builder.append (arc0->toSBasis());
delete arc0;
arc0 = NULL;
}
if (arc1) {
path_builder.append (arc1->toSBasis());
delete arc1;
arc1 = NULL;
}
} catch (std::exception & ex) {
printf("Exception occured, probably NaN or infinite valued points: %s\n", ex.what());
path_builder.appendNew<Geom::LineSegment>(endPt);
}
} else {
boost::optional <Geom::Point> p = intersection_point (cbc1->finalPoint(), tang1,
cbc2->initialPoint(), tang2);
if (p) {
//check size of miter
Geom::Point point_on_path = cbc1->finalPoint() - rot90(tang1) * line_width;
Geom::Coord len = distance(*p, point_on_path);
if (len <= miter_limit) {
// miter OK
path_builder.appendNew<Geom::LineSegment> (*p);
}
}
path_builder.appendNew<Geom::LineSegment> (endPt);
}
}
if ( outside && lineProblem ) {
Geom::Path pth;
pth.append(*cbc1);
Geom::Point tang1 = Geom::unitTangentAt(Geom::reverse(pth.toPwSb()[0]), 0.);
pth = Geom::Path();
pth.append( *cbc2 );
Geom::Point tang2 = Geom::unitTangentAt(pth.toPwSb()[0], 0);
boost::optional <Geom::Point> p = intersection_point (cbc1->finalPoint(), tang1,
cbc2->initialPoint(), tang2);
if (p) {
//check size of miter
Geom::Point point_on_path = cbc1->finalPoint() - rot90(tang1) * line_width;
Geom::Coord len = distance(*p, point_on_path);
if (len <= miter_limit) {
// miter OK
path_builder.appendNew<Geom::LineSegment> (*p);
}
}
path_builder.appendNew<Geom::LineSegment> (endPt);
}
if ( !outside ) {
path_builder.appendNew<Geom::LineSegment> (endPt);
}
}
void reflect_curves(Geom::Path& path_builder, Geom::Curve* cbc1, Geom::Curve* cbc2, Geom::Point endPt,
double miter_limit, double line_width, bool outside = false)
{
//the most important work for the reflected join is done here
//determine where we are in the path. If we're on the inside, ignore
//and just lineTo. On the outside, we'll do a little reflection magic :)
Geom::Crossings cross;
if (outside) {
Geom::Path pth;
pth.append(*cbc1);
Geom::Point tang1 = Geom::unitTangentAt(Geom::reverse(pth.toPwSb()[0]), 0.);
//reflect curves along the bevel
D2SB newcurve1 = pth.toPwSb()[0] *
Geom::reflection ( -Geom::rot90(tang1) ,
cbc1->finalPoint() );
Geom::CubicBezier bzr1 = sbasis_to_cubicbezier(Geom::reverse(newcurve1));
pth = Geom::Path();
pth.append( *cbc2 );
Geom::Point tang2 = Geom::unitTangentAt(pth.toPwSb()[0], 0);
D2SB newcurve2 = pth.toPwSb()[0] *
Geom::reflection ( -Geom::rot90(tang2) ,
cbc2->initialPoint() );
Geom::CubicBezier bzr2 = sbasis_to_cubicbezier(Geom::reverse(newcurve2));
cross = Geom::crossings(bzr1, bzr2);
if ( cross.empty() ) {
//curves didn't cross; default to miter
boost::optional <Geom::Point> p = intersection_point (cbc1->finalPoint(), tang1,
cbc2->initialPoint(), tang2);
if (p) {
//check size of miter
Geom::Point point_on_path = cbc1->finalPoint() - rot90(tang1) * line_width;
Geom::Coord len = distance(*p, point_on_path);
if (len <= miter_limit) {
// miter OK
path_builder.appendNew<Geom::LineSegment> (*p);
}
}
//bevel
path_builder.appendNew<Geom::LineSegment>( endPt );
} else {
//join
std::pair<Geom::CubicBezier, Geom::CubicBezier> sub1 = bzr1.subdivide(cross[0].ta);
std::pair<Geom::CubicBezier, Geom::CubicBezier> sub2 = bzr2.subdivide(cross[0].tb);
//@TODO joins have a strange tendency to cross themselves twice. Check this.
//sections commented out are for general stability
path_builder.appendNew <Geom::CubicBezier> (sub1.first[1], sub1.first[2], /*sub1.first[3]*/ sub2.second[0] );
path_builder.appendNew <Geom::CubicBezier> (sub2.second[1], sub2.second[2], /*sub2.second[3]*/ endPt );
}
} else { // cross.empty()
//probably on the inside of the corner
path_builder.appendNew<Geom::LineSegment> ( endPt );
}
}
/** @brief Converts a path to one half of an outline.
* path_in: The input path to use. (To create the other side use path_in.reverse() )
* line_width: the line width to use (usually you want to divide this by 2)
* miter_limit: the miter parameter
* extrapolate: whether the join should be extrapolated instead of reflected
*/
Geom::Path doAdvHalfOutline(const Geom::Path& path_in, double line_width, double miter_limit, bool extrapolate = false)
{
// NOTE: it is important to notice the distinction between a Geom::Path and a livarot Path here!
// if you do not see "Geom::" there is a different function set!
Geom::PathVector pv = split_at_cusps(path_in);
Path to_outline;
Path outlined_result;
Geom::Path path_builder = Geom::Path(); //the path to store the result in
Geom::PathVector * path_vec; //needed because livarot returns a goddamn pointer
const unsigned k = pv.size();
for (unsigned u = 0; u < k; u+=2) {
to_outline = Path();
outlined_result = Path();
to_outline.LoadPath(pv[u], Geom::Affine(), false, false);
to_outline.OutsideOutline(&outlined_result, line_width / 2, join_straight, butt_straight, 10);
//now a curve has been outside outlined and loaded into outlined_result
//get the Geom::Path
path_vec = outlined_result.MakePathVector();
//thing to do on the first run through
if (u == 0) {
//I could use the pv->operator[] (0) notation but that looks terrible
path_builder.start( (*path_vec)[0].initialPoint() );
} else {
//get the curves ready for the operation
Geom::Curve * cbc1 = path_builder[path_builder.size() - 1].duplicate();
Geom::Curve * cbc2 = (*path_vec)[0] [0].duplicate();
//do the reflection/extrapolation:
if (extrapolate) {
extrapolate_curves(path_builder, cbc1, cbc2, (*path_vec)[0].initialPoint(), miter_limit, line_width,
outside_angle ( pv[u - 1] [pv[u - 1].size() - 1], pv[u] [0] ));
} else {
reflect_curves (path_builder, cbc1, cbc2, (*path_vec)[0].initialPoint(), miter_limit, line_width,
outside_angle ( pv[u - 1] [pv[u - 1].size() - 1], pv[u] [0] ));
}
}
path_builder.append( (*path_vec)[0] );
//outline the next segment, but don't store it yet
if (path_vec) delete path_vec;
if (u < k - 1) {
outlined_result = Path();
to_outline = Path();
to_outline.LoadPath(pv[u+1], Geom::Affine(), false, false);
to_outline.OutsideOutline(&outlined_result, line_width / 2, join_straight, butt_straight, 10);
path_vec = outlined_result.MakePathVector();
//get the curves ready for the operation
Geom::Curve * cbc1 = path_builder[path_builder.size() - 1].duplicate();
Geom::Curve * cbc2 = (*path_vec)[0] [0].duplicate();
//do the reflection/extrapolation:
if (extrapolate) {
extrapolate_curves(path_builder, cbc1, cbc2, (*path_vec)[0].initialPoint(), miter_limit, line_width,
outside_angle ( pv[u] [pv[u].size()-1], pv[u+1] [0] ));
} else {
reflect_curves (path_builder, cbc1, cbc2, (*path_vec)[0].initialPoint(), miter_limit, line_width,
outside_angle ( pv[u] [pv[u].size()-1], pv[u+1] [0] ));
}
//Now we can store it.
path_builder.append( (*path_vec)[0] );
if (cbc1) delete cbc1;
if (cbc2) delete cbc2;
if (path_vec) delete path_vec;
}
}
return path_builder;
}
Geom::PathVector outlinePath(const Geom::PathVector& path_in, double line_width, LineJoinType join,
ButtType butt, double miter_lim, bool extrapolate)
{
Geom::PathVector path_out;
unsigned pv_size = path_in.size();
for (unsigned i = 0; i < pv_size; i++) {
if (path_in[i].size() > 1) {
//since you've made it this far, hopefully all this is obvious :P
Geom::Path with_direction;
Geom::Path against_direction;
if ( !path_in[i].closed() ) {
with_direction = Outline::doAdvHalfOutline( path_in[i], -line_width, miter_lim, extrapolate );
against_direction = Outline::doAdvHalfOutline( path_in[i].reverse(), -line_width, miter_lim, extrapolate );
} else {
//Geom::Path absolutely refuses to do what I want with these
Geom::Path newPath = path_in[i];
newPath.close(false);
Geom::Piecewise<Geom::D2<Geom::SBasis> > pwd2 = newPath.toPwSb();
newPath = Geom::path_from_piecewise(pwd2, 0.01)[0];
//fuk this
with_direction = Outline::doAdvHalfOutline( newPath, -line_width, miter_lim, extrapolate );
against_direction = Outline::doAdvHalfOutline( newPath.reverse(), -line_width, miter_lim, extrapolate );
/*if (dynamic_cast<const Geom::BezierCurveN<1u> *>(&newPath[newPath.size()])) {
//delete the 'Z'
newPath.erase_last();
newPath.append(path_in[i][path_in[i].size() - 1]);
newPath.appendNew<Geom::LineSegment>(newPath.initialPoint());
newPath.erase_last();
} else {
//delete the 'Z'
newPath.erase_last();
newPath.append(path_in[i][path_in[i].size() - 1]);
newPath.appendNew<Geom::LineSegment>(newPath.initialPoint());
newPath.erase_last();
}*/
}
Geom::PathBuilder pb;
//add in the...do I really need to say this?
pb.moveTo(with_direction.initialPoint());
pb.append(with_direction);
//add in our line caps
if (!path_in[i].closed()) {
switch (butt) {
case butt_straight:
pb.lineTo(against_direction.initialPoint());
break;
case butt_round:
pb.arcTo((-line_width) / 2, (-line_width) / 2, 0., true, true, against_direction.initialPoint() );
break;
case butt_pointy:
//I have ZERO idea what to do here.
pb.lineTo(against_direction.initialPoint());
break;
case butt_square:
pb.lineTo(against_direction.initialPoint());
break;
}
} else {
pb.moveTo(against_direction.initialPoint());
}
pb.append(against_direction);
//cap (if necessary)
if (!path_in[i].closed()) {
switch (butt) {
case butt_straight:
pb.lineTo(with_direction.initialPoint());
break;
case butt_round:
pb.arcTo((-line_width) / 2, (-line_width) / 2, 0., true, true, with_direction.initialPoint() );
break;
case butt_pointy:
//I have ZERO idea what to do here.
pb.lineTo(with_direction.initialPoint());
break;
case butt_square:
pb.lineTo(with_direction.initialPoint());
break;
}
}
pb.flush();
for (unsigned m = 0; i < pb.peek().size(); i++) {
path_out.push_back(pb.peek()[m]);
}
} else {
Path p = Path();
Path outlinepath = Path();
p.LoadPath(path_in[i], Geom::Affine(), false, false);
p.Outline(&outlinepath, line_width / 2, static_cast<join_typ>(join), butt, miter_lim);
Geom::PathVector *pv_p = outlinepath.MakePathVector();
//somewhat hack-ish
path_out.push_back( (*pv_p)[0].reverse() );
if (pv_p) delete pv_p;
}
}
return path_out;
}
Geom::PathVector PathVectorOutline(Geom::PathVector const & path_in, double line_width, ButtType linecap_type,
LineJoinType linejoin_type, double miter_limit)
{
std::vector<Geom::Path> path_out = std::vector<Geom::Path>();
if (path_in.empty()) {
return path_out;
}
Path p = Path();
Path outlinepath = Path();
for (unsigned i = 0; i < path_in.size(); i++) {
p.LoadPath(path_in[i], Geom::Affine(), false, ( (i==0) ? false : true));
}
#define miter_lim fabs(line_width * miter_limit)
//magic!
if (linejoin_type <= 2) {
p.Outline(&outlinepath, line_width / 2, static_cast<join_typ>(linejoin_type),
linecap_type, miter_lim);
//fix memory leak
std::vector<Geom::Path> *pv_p = outlinepath.MakePathVector();
path_out = *pv_p;
delete pv_p;
} else if (linejoin_type == 3) {
//reflected arc join
path_out = outlinePath(path_in, line_width, static_cast<LineJoinType>(linejoin_type),
linecap_type , miter_lim, false);
} else if (linejoin_type == 4) {
//extrapolated arc join
path_out = outlinePath(path_in, line_width, LINEJOIN_STRAIGHT, linecap_type, miter_lim, true);
}
#undef miter_lim
return path_out;
}
Geom::Path PathOutsideOutline(Geom::Path const & path_in, double line_width, LineJoinType linejoin_type, double miter_limit)
{
#define miter_lim fabs(line_width * miter_limit)
Geom::Path path_out;
if (linejoin_type <= LINEJOIN_POINTY || path_in.size() <= 1) {
Geom::PathVector * pathvec;
Path path_tangent = Path();
Path path_outline = Path();
path_outline.LoadPath(path_in, Geom::Affine(), false, false);
path_outline.OutsideOutline(&path_tangent, line_width / 2, static_cast<join_typ>(linejoin_type), butt_straight, miter_lim);
pathvec = path_tangent.MakePathVector();
path_out = pathvec[0]/* deref pointer */[0]/*actual object ref*/;
delete pathvec;
return path_out;
} else if (linejoin_type == LINEJOIN_REFLECTED) {
//reflected half outline
Geom::PathVector pathvec;
pathvec.push_back(path_in);
path_out = doAdvHalfOutline(path_in, line_width, miter_lim, false);
return path_out;
} else if (linejoin_type == LINEJOIN_EXTRAPOLATED) {
//what the hell do you think this is? :P
path_out = doAdvHalfOutline(path_in, line_width, miter_lim, true);
return path_out;
}
#undef miter_lim
return path_out;
}
} // namespace Outline
/*
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:textwidth=99 :