#include "live_effects/lpe-powerstroke.h"

#include "live_effects/lpe-powerstroke-interpolators.h"

#include "sp-shape.h"

#include "display/curve.h"

#include <2geom/path.h>

#include <2geom/piecewise.h>

#include <2geom/sbasis-geometric.h>

#include <2geom/transforms.h>

#include <2geom/bezier-utils.h>

#include <2geom/svg-elliptical-arc.h>

#include <2geom/sbasis-to-bezier.h>

#include <2geom/svg-path.h>

#include <2geom/path-intersection.h>

#include <2geom/crossing.h>

#include <2geom/ellipse.h>

namespace Geom {

Point unitTangentAt( D2<SBasis> const & a, Coord t, unsigned n = 3) {

std::vector<Point> derivs = a.valueAndDerivatives(t, n);

for (unsigned deriv_n = 1; deriv_n < derivs.size(); deriv_n++) {

Coord length = derivs[deriv_n].length();

if ( ! are_near(length, 0) ) {

// length of derivative is non-zero, so return unit vector

return derivs[deriv_n] / length;

}

}

return Point (0,0);

}

boost::optional<Point> intersection_point( Point const & origin_a, Point const & vector_a,

Point const & origin_b, Point const & 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 + t * vector_a;

}

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 );

}

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 {

static const Util::EnumData<unsigned> InterpolatorTypeData[] = {

{Geom::Interpolate::INTERP_LINEAR , N_("Linear"), "Linear"},

{Geom::Interpolate::INTERP_CUBICBEZIER , N_("CubicBezierFit"), "CubicBezierFit"},

{Geom::Interpolate::INTERP_CUBICBEZIER_JOHAN , N_("CubicBezierJohan"), "CubicBezierJohan"},

{Geom::Interpolate::INTERP_SPIRO , N_("SpiroInterpolator"), "SpiroInterpolator"}

};

static const Util::EnumDataConverter<unsigned> InterpolatorTypeConverter(InterpolatorTypeData, sizeof(InterpolatorTypeData)/sizeof(*InterpolatorTypeData));

enum LineCapType {

LINECAP_BUTT,

LINECAP_SQUARE,

LINECAP_ROUND,

LINECAP_PEAK,

LINECAP_ZERO_WIDTH

};

static const Util::EnumData<unsigned> LineCapTypeData[] = {

{LINECAP_BUTT, N_("Butt"), "butt"},

{LINECAP_SQUARE, N_("Square"), "square"},

{LINECAP_ROUND, N_("Round"), "round"},

{LINECAP_PEAK, N_("Peak"), "peak"},

{LINECAP_ZERO_WIDTH, N_("Zero width"), "zerowidth"}

};

static const Util::EnumDataConverter<unsigned> LineCapTypeConverter(LineCapTypeData, sizeof(LineCapTypeData)/sizeof(*LineCapTypeData));

enum LineJoinType {

LINEJOIN_BEVEL,

LINEJOIN_ROUND,

LINEJOIN_EXTRP_MITER,

LINEJOIN_MITER

};

static const Util::EnumData<unsigned> LineJoinTypeData[] = {

{LINEJOIN_BEVEL, N_("Beveled"), "bevel"},

{LINEJOIN_ROUND, N_("Rounded"), "round"},

{LINEJOIN_EXTRP_MITER, N_("Extrapolated"), "extrapolated"},

{LINEJOIN_MITER, N_("Miter"), "miter"},

};

static const Util::EnumDataConverter<unsigned> LineJoinTypeConverter(LineJoinTypeData, sizeof(LineJoinTypeData)/sizeof(*LineJoinTypeData));

LPEPowerStroke::LPEPowerStroke(LivePathEffectObject *lpeobject) :

Effect(lpeobject),

offset_points(_("Offset points"), _("Offset points"), "offset_points", &wr, this),

sort_points(_("Sort points"), _("Sort offset points according to their time value along the curve."), "sort_points", &wr, this, true),

interpolator_type(_("Interpolator type"), _("Determines which kind of interpolator will be used to interpolate between stroke width along the path."), "interpolator_type", InterpolatorTypeConverter, &wr, this, Geom::Interpolate::INTERP_CUBICBEZIER_JOHAN),

interpolator_beta(_("Smoothness"), _("Sets the smoothness for the CubicBezierJohan interpolator. 0 = linear interpolation, 1 = smooth"), "interpolator_beta", &wr, this, 0.2),

start_linecap_type(_("Start cap"), _("Determines the shape of the path's start."), "start_linecap_type", LineCapTypeConverter, &wr, this, LINECAP_ROUND),

linejoin_type(_("Join"), _("Specifies the shape of the path's corners."), "linejoin_type", LineJoinTypeConverter, &wr, this, LINEJOIN_ROUND),

miter_limit(_("Miter limit"), _("Maximum length of the miter (in units of stroke width)"), "miter_limit", &wr, this, 4.),

end_linecap_type(_("End cap"), _("Determines the shape of the path's end."), "end_linecap_type", LineCapTypeConverter, &wr, this, LINECAP_ROUND)

{

show_orig_path = true;

/// @todo offset_points are initialized with empty path, is that bug-save?

interpolator_beta.addSlider(true);

interpolator_beta.param_set_range(0.,1.);

registerParameter( dynamic_cast<Parameter *>(&offset_points) );

registerParameter( dynamic_cast<Parameter *>(&sort_points) );

registerParameter( dynamic_cast<Parameter *>(&interpolator_type) );

registerParameter( dynamic_cast<Parameter *>(&interpolator_beta) );

registerParameter( dynamic_cast<Parameter *>(&start_linecap_type) );

registerParameter( dynamic_cast<Parameter *>(&linejoin_type) );

registerParameter( dynamic_cast<Parameter *>(&miter_limit) );

registerParameter( dynamic_cast<Parameter *>(&end_linecap_type) );

}

LPEPowerStroke::~LPEPowerStroke()

{

}

LPEPowerStroke::doOnApply(SPLPEItem *lpeitem)

{

if (SP_IS_SHAPE(lpeitem)) {

std::vector<Geom::Point> points;

Geom::PathVector pathv = SP_SHAPE(lpeitem)->_curve->get_pathvector();

Geom::Path::size_type size = pathv.empty() ? 1 : pathv.front().size_open();

points.push_back( Geom::Point(0,0) );

points.push_back( Geom::Point(0.5*size,0) );

points.push_back( Geom::Point(size,0) );

offset_points.param_set_and_write_new_value(points);

} else {

g_warning("LPE Powerstroke can only be applied to shapes (not groups).");

}

}

LPEPowerStroke::adjustForNewPath(std::vector<Geom::Path> const & path_in)

{

if (!path_in.empty()) {

offset_points.recalculate_controlpoints_for_new_pwd2(path_in[0].toPwSb());

}

}

static bool compare_offsets (Geom::Point first, Geom::Point second)

{

return first[Geom::X] < second[Geom::X];

}

struct discontinuity_data {

Geom::Point der0; // unit derivative of 'left' side of join

Geom::Point der1; // unit derivative of 'right' side of join

double width; // intended stroke width at join

};

std::vector<discontinuity_data> find_discontinuities( Geom::Piecewise<Geom::D2<Geom::SBasis> > const & der,

Geom::Piecewise<Geom::SBasis> const & x,

Geom::Piecewise<Geom::SBasis> const & y,

double eps=Geom::EPSILON )

{

std::vector<discontinuity_data> vect;

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()) {

data.width = y(rts.front());

} else {

data.width = 1;

}

vect.push_back(data);

}

}

return vect;

}

Geom::Path path_from_piecewise_fix_cusps( Geom::Piecewise<Geom::D2<Geom::SBasis> > const & B,

std::vector<discontinuity_data> const & cusps,

LineJoinType jointype,

double miter_limit,

bool forward_direction,

double tol=Geom::EPSILON)

{

Geom::PathBuilder pb;

if (B.size() == 0) {

return pb.peek().front();

}

double sign = forward_direction ? 1. : -1.;

unsigned int cusp_i = forward_direction ? 0 : cusps.size()-1;

Geom::Point start = B[0].at0();

pb.moveTo(start);

build_from_sbasis(pb, B[0], tol, false);

unsigned prev_i = 0;

for (unsigned i=1; i < B.size(); i++) {

// if segment is degenerate, skip it

// the degeneracy/constancy test had to be loosened (eps > 1e-5)

if (B[i].isConstant(1e-4)) {

continue;

}

if (!are_near(B[prev_i].at1(), B[i].at0(), tol) )

{ // discontinuity found, so fix it :-)

discontinuity_data cusp = cusps[cusp_i];

switch (jointype) {

case LINEJOIN_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),

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 LINEJOIN_EXTRP_MITER: {

// first figure out whether we are on the outside or inside of the corner in the path

if ( sign*cusp.width*angle_between(cusp.der0, cusp.der1) < 0.) {

// we are on the outside, do something complicated to make it look good ;)

Geom::Point der1 = unitTangentAt(B[prev_i],1);

Geom::Point der2 = unitTangentAt(B[i],0);

Geom::D2<Geom::SBasis> newcurve1 = B[prev_i] * Geom::reflection(rot90(der1), B[prev_i].at1());

Geom::CubicBezier bzr1 = sbasis_to_cubicbezier( reverse(newcurve1) );

Geom::D2<Geom::SBasis> newcurve2 = B[i] * Geom::reflection(rot90(der2), B[i].at0());

Geom::CubicBezier bzr2 = sbasis_to_cubicbezier( reverse(newcurve2) );

Geom::Crossings cross = crossings(bzr1, bzr2);

if (cross.empty()) {

// empty crossing: default to bevel

pb.lineTo(B[i].at0());

} else {

// check size of miter

Geom::Point point_on_path = B[prev_i].at1() - rot90(der1) * cusp.width;

Geom::Coord len = distance(bzr1.pointAt(cross[0].ta), point_on_path);

if (len > cusp.width * miter_limit) {

// miter too big: default to bevel

pb.lineTo(B[i].at0());

} else {

std::pair<Geom::CubicBezier, Geom::CubicBezier> sub1 = bzr1.subdivide(cross[0].ta);

std::pair<Geom::CubicBezier, Geom::CubicBezier> sub2 = bzr2.subdivide(cross[0].tb);

pb.curveTo(sub1.first[1], sub1.first[2], sub1.first[3]);

pb.curveTo(sub2.second[1], sub2.second[2], sub2.second[3]);

}

}

} 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 LINEJOIN_MITER: {

// first figure out whether we are on the outside or inside of the corner in the path

if ( sign*cusp.width*angle_between(cusp.der0, cusp.der1) < 0.) {

// we are on the outside, do something complicated to make it look good ;)

Geom::Point der1 = unitTangentAt(B[prev_i],1);

Geom::Point der2 = unitTangentAt(B[i],0);

boost::optional<Geom::Point> p = intersection_point( B[prev_i].at1(), der1,

B[i].at0(), der2 );

if (p) {

// check size of miter

Geom::Point point_on_path = B[prev_i].at1() - rot90(der1) * cusp.width;

Geom::Coord len = distance(*p, point_on_path);

if (len <= cusp.width * miter_limit) {

// miter OK

pb.lineTo(*p);

}

}

pb.lineTo(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 LINEJOIN_BEVEL:

default:

pb.lineTo(B[i].at0());

break;

}

cusp_i += forward_direction ? 1 : -1;

}

build_from_sbasis(pb, B[i], tol, false);

prev_i = i;

}

pb.finish();

return pb.peek().front();

}

std::vector<Geom::Path>

LPEPowerStroke::doEffect_path (std::vector<Geom::Path> const & path_in)

{

using namespace Geom;

std::vector<Geom::Path> path_out;

if (path_in.empty()) {

return path_out;

}

// for now, only regard first subpath and ignore the rest

Geom::Piecewise<Geom::D2<Geom::SBasis> > pwd2_in = path_in[0].toPwSb();

Piecewise<D2<SBasis> > der = derivative(pwd2_in);

Piecewise<D2<SBasis> > n = rot90(unitVector(der));

offset_points.set_pwd2(pwd2_in, n);

LineCapType end_linecap = static_cast<LineCapType>(end_linecap_type.get_value());

LineCapType start_linecap = static_cast<LineCapType>(start_linecap_type.get_value());

std::vector<Geom::Point> ts = offset_points.data();

if (ts.empty()) {

return path_out;

}

if (sort_points) {

sort(ts.begin(), ts.end(), compare_offsets);

}

if (path_in[0].closed()) {

// add extra points for interpolation between first and last point

Point first_point = ts.front();

Point last_point = ts.back();

ts.insert(ts.begin(), last_point - Point(pwd2_in.domain().extent() ,0));

ts.push_back( first_point + Point(pwd2_in.domain().extent() ,0) );

} else {

// add width data for first and last point on the path

// depending on cap type, these first and last points have width zero or take the width from the closest width point.

ts.insert(ts.begin(), Point( pwd2_in.domain().min(),

(start_linecap==LINECAP_ZERO_WIDTH) ? 0. : ts.front()[Geom::Y]) );

ts.push_back( Point( pwd2_in.domain().max(),

(end_linecap==LINECAP_ZERO_WIDTH) ? 0. : ts.back()[Geom::Y]) );

}

// create stroke path where points (x,y) := (t, offset)

Geom::Interpolate::Interpolator *interpolator = Geom::Interpolate::Interpolator::create(static_cast<Geom::Interpolate::InterpolatorType>(interpolator_type.get_value()));

if (Geom::Interpolate::CubicBezierJohan *johan = dynamic_cast<Geom::Interpolate::CubicBezierJohan*>(interpolator)) {

johan->setBeta(interpolator_beta);

}

Geom::Path strokepath = interpolator->interpolateToPath(ts);

delete interpolator;

D2<Piecewise<SBasis> > patternd2 = make_cuts_independent(strokepath.toPwSb());

Piecewise<SBasis> x = Piecewise<SBasis>(patternd2[0]);

Piecewise<SBasis> y = Piecewise<SBasis>(patternd2[1]);

// find time values for which x lies outside path domain

// and only take portion of x and y that lies within those time values

std::vector< double > rtsmin = roots (x - pwd2_in.domain().min());

std::vector< double > rtsmax = roots (x - pwd2_in.domain().max());

if ( !rtsmin.empty() && !rtsmax.empty() ) {

x = portion(x, rtsmin.at(0), rtsmax.at(0));

y = portion(y, rtsmin.at(0), rtsmax.at(0));

}

std::vector<discontinuity_data> cusps = find_discontinuities(der, x, y);

LineJoinType jointype = static_cast<LineJoinType>(linejoin_type.get_value());

Piecewise<D2<SBasis> > pwd2_out = compose(pwd2_in,x) + y*compose(n,x);

Piecewise<D2<SBasis> > mirrorpath = reverse(compose(pwd2_in,x) - y*compose(n,x));

Geom::Path fixed_path = path_from_piecewise_fix_cusps( pwd2_out, cusps, jointype, miter_limit, true, LPE_CONVERSION_TOLERANCE);

Geom::Path fixed_mirrorpath = path_from_piecewise_fix_cusps( mirrorpath, cusps, jointype, miter_limit, false, LPE_CONVERSION_TOLERANCE);

if (path_in[0].closed()) {

fixed_path.close(true);

path_out.push_back(fixed_path);

fixed_mirrorpath.close(true);

path_out.push_back(fixed_mirrorpath);

} else {

// add linecaps...

switch (end_linecap) {

case LINECAP_ZERO_WIDTH:

// do nothing

break;

case LINECAP_PEAK:

{

Geom::Point end_deriv = unit_vector(der.lastValue());

double radius = 0.5 * distance(pwd2_out.lastValue(), mirrorpath.firstValue());

Geom::Point midpoint = 0.5*(pwd2_out.lastValue() + mirrorpath.firstValue()) + radius*end_deriv;

fixed_path.appendNew<LineSegment>(midpoint);

fixed_path.appendNew<LineSegment>(mirrorpath.firstValue());

break;

}

case LINECAP_SQUARE:

{

Geom::Point end_deriv = unit_vector(der.lastValue());

double radius = 0.5 * distance(pwd2_out.lastValue(), mirrorpath.firstValue());

fixed_path.appendNew<LineSegment>( pwd2_out.lastValue() + radius*end_deriv );

fixed_path.appendNew<LineSegment>( mirrorpath.firstValue() + radius*end_deriv );

fixed_path.appendNew<LineSegment>( mirrorpath.firstValue() );

break;

}

case LINECAP_BUTT:

{

fixed_path.appendNew<LineSegment>( mirrorpath.firstValue() );

break;

}

case LINECAP_ROUND:

default:

{

double radius1 = 0.5 * distance(pwd2_out.lastValue(), mirrorpath.firstValue());

fixed_path.appendNew<SVGEllipticalArc>( radius1, radius1, M_PI/2., false, y.lastValue() < 0, mirrorpath.firstValue() );

break;

}

}

fixed_path.append(fixed_mirrorpath, Geom::Path::STITCH_DISCONTINUOUS);

switch (start_linecap) {

case LINECAP_ZERO_WIDTH:

// do nothing

break;

case LINECAP_PEAK:

{

Geom::Point start_deriv = unit_vector(der.firstValue());

double radius = 0.5 * distance(pwd2_out.firstValue(), mirrorpath.lastValue());

Geom::Point midpoint = 0.5*(mirrorpath.lastValue() + pwd2_out.firstValue()) - radius*start_deriv;

fixed_path.appendNew<LineSegment>( midpoint );

fixed_path.appendNew<LineSegment>( pwd2_out.firstValue() );

break;

}

case LINECAP_SQUARE:

{

Geom::Point start_deriv = unit_vector(der.firstValue());

double radius = 0.5 * distance(pwd2_out.firstValue(), mirrorpath.lastValue());

fixed_path.appendNew<LineSegment>( mirrorpath.lastValue() - radius*start_deriv );

fixed_path.appendNew<LineSegment>( pwd2_out.firstValue() - radius*start_deriv );

fixed_path.appendNew<LineSegment>( pwd2_out.firstValue() );

break;

}

case LINECAP_BUTT:

{

fixed_path.appendNew<LineSegment>( pwd2_out.firstValue() );

break;

}

case LINECAP_ROUND:

default:

{

double radius2 = 0.5 * distance(pwd2_out.firstValue(), mirrorpath.lastValue());

fixed_path.appendNew<SVGEllipticalArc>( radius2, radius2, M_PI/2., false, y.firstValue() < 0, pwd2_out.firstValue() );

break;

}

}

fixed_path.close(true);

path_out.push_back(fixed_path);

}

return path_out;

}

} //namespace LivePathEffect

} /* namespace Inkscape */