4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen#ifndef INKSCAPE_LPE_POWERSTROKE_INTERPOLATORS_H

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen#define INKSCAPE_LPE_POWERSTROKE_INTERPOLATORS_H

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen#include <2geom/path.h>

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen#include <2geom/bezier-utils.h>

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen#include <2geom/sbasis-to-bezier.h>

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen#include "live_effects/spiro.h"

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelennamespace Geom {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelennamespace Interpolate {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenenum InterpolatorType {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen INTERP_LINEAR,

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen INTERP_CUBICBEZIER,

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen INTERP_CUBICBEZIER_JOHAN,

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White INTERP_SPIRO,

0ed512dfeb94b481858723f9ba692fd4682f9012Liam P. White INTERP_CUBICBEZIER_SMOOTH,

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen INTERP_CENTRIPETAL_CATMULLROM

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenclass Interpolator {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenpublic:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Interpolator() {};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen virtual ~Interpolator() {};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen static Interpolator* create(InterpolatorType type);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen virtual Geom::Path interpolateToPath(std::vector<Point> const &points) const = 0;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenprivate:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Interpolator(const Interpolator&);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Interpolator& operator=(const Interpolator&);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenclass Linear : public Interpolator {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenpublic:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Linear() {};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen virtual ~Linear() {};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen virtual Path interpolateToPath(std::vector<Point> const &points) const {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Path path;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen path.start( points.at(0) );

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen for (unsigned int i = 1 ; i < points.size(); ++i) {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen path.appendNew<Geom::LineSegment>(points.at(i));

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen }

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen return path;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen };

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenprivate:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Linear(const Linear&);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Linear& operator=(const Linear&);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenclass CubicBezierFit : public Interpolator {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenpublic:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen CubicBezierFit() {};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen virtual ~CubicBezierFit() {};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen virtual Path interpolateToPath(std::vector<Point> const &points) const {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen unsigned int n_points = points.size();

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen // worst case gives us 2 segment per point

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen int max_segs = 8*n_points;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Geom::Point * b = g_new(Geom::Point, max_segs);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Geom::Point * points_array = g_new(Geom::Point, 4*n_points);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen for (unsigned i = 0; i < n_points; ++i) {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen points_array[i] = points.at(i);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen }

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen double tolerance_sq = 0; // this value is just a random guess

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen int const n_segs = Geom::bezier_fit_cubic_r(b, points_array, n_points,

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen tolerance_sq, max_segs);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Geom::Path fit;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen if ( n_segs > 0)

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen fit.start(b[0]);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen for (int c = 0; c < n_segs; c++) {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen fit.appendNew<Geom::CubicBezier>(b[4*c+1], b[4*c+2], b[4*c+3]);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen }

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen }

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen g_free(b);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen g_free(points_array);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen return fit;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen };

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenprivate:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen CubicBezierFit(const CubicBezierFit&);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen CubicBezierFit& operator=(const CubicBezierFit&);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenclass CubicBezierJohan : public Interpolator {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenpublic:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen CubicBezierJohan(double beta = 0.2) {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen _beta = beta;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen };

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen virtual ~CubicBezierJohan() {};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen virtual Path interpolateToPath(std::vector<Point> const &points) const {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Path fit;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen fit.start(points.at(0));

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen for (unsigned int i = 1; i < points.size(); ++i) {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Point p0 = points.at(i-1);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Point p1 = points.at(i);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Point dx = Point(p1[X] - p0[X], 0);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen fit.appendNew<CubicBezier>(p0+_beta*dx, p1-_beta*dx, p1);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen }

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen return fit;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen };

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

ea7d8c8f5752fe8fe4f814fc01baf6f250825817Johan Engelen void setBeta(double beta) {

ea7d8c8f5752fe8fe4f814fc01baf6f250825817Johan Engelen _beta = beta;

ea7d8c8f5752fe8fe4f814fc01baf6f250825817Johan Engelen }

ea7d8c8f5752fe8fe4f814fc01baf6f250825817Johan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen double _beta;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenprivate:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen CubicBezierJohan(const CubicBezierJohan&);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen CubicBezierJohan& operator=(const CubicBezierJohan&);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. Whiteclass CubicBezierSmooth : public Interpolator {

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. Whitepublic:

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White CubicBezierSmooth(double beta = 0.2) {

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White _beta = beta;

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White };

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White virtual ~CubicBezierSmooth() {};

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White virtual Path interpolateToPath(std::vector<Point> const &points) const {

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White Path fit;

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White fit.start(points.at(0));

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White unsigned int num_points = points.size();

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White for (unsigned int i = 1; i < num_points; ++i) {

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White Point p0 = points.at(i-1);

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White Point p1 = points.at(i);

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White Point dx = Point(p1[X] - p0[X], 0);

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White if (i == 1) {

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White fit.appendNew<CubicBezier>(p0, p1-0.75*dx, p1);

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White } else if (i == points.size() - 1) {

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White fit.appendNew<CubicBezier>(p0+0.75*dx, p1, p1);

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White } else {

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White fit.appendNew<CubicBezier>(p0+_beta*dx, p1-_beta*dx, p1);

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White }

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White }

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White return fit;

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White };

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White void setBeta(double beta) {

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White _beta = beta;

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White }

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White double _beta;

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. Whiteprivate:

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White CubicBezierSmooth(const CubicBezierSmooth&);

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White CubicBezierSmooth& operator=(const CubicBezierSmooth&);

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenclass SpiroInterpolator : public Interpolator {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenpublic:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen SpiroInterpolator() {};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen virtual ~SpiroInterpolator() {};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen virtual Path interpolateToPath(std::vector<Point> const &points) const {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Path fit;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen Coord scale_y = 100.;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen guint len = points.size();

b49365c42b99e3cc135dcde0077aad31d930f6c1Johan B. C. Engelen Spiro::spiro_cp *controlpoints = g_new (Spiro::spiro_cp, len);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen for (unsigned int i = 0; i < len; ++i) {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen controlpoints[i].x = points[i][X];

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen controlpoints[i].y = points[i][Y] / scale_y;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen controlpoints[i].ty = 'c';

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen }

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen controlpoints[0].ty = '{';

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen controlpoints[1].ty = 'v';

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen controlpoints[len-2].ty = 'v';

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen controlpoints[len-1].ty = '}';

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

b49365c42b99e3cc135dcde0077aad31d930f6c1Johan B. C. Engelen Spiro::spiro_run(controlpoints, len, fit);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen fit *= Scale(1,scale_y);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen return fit;

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen };

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelenprivate:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen SpiroInterpolator(const SpiroInterpolator&);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen SpiroInterpolator& operator=(const SpiroInterpolator&);

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen};

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelenclass CentripetalCatmullRomInterpolator : public Interpolator {

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelenpublic:

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen CentripetalCatmullRomInterpolator() {};

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen virtual ~CentripetalCatmullRomInterpolator() {};

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen virtual Path interpolateToPath(std::vector<Point> const &points) const {

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen unsigned int n_points = points.size();

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Geom::Path fit(points.front());

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen if (n_points < 3) return fit; // TODO special cases for 0,1 and 2 input points

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // return n_points-1 cubic segments

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // duplicate first point

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen fit.append(calc_bezier(points[0],points[0],points[1],points[2]));

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen for (std::size_t i = 0; i < n_points-2; ++i) {

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Point p0 = points[i];

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Point p1 = points[i+1];

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Point p2 = points[i+2];

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Point p3 = (i < n_points-3) ? points[i+3] : points[i+2];

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen fit.append(calc_bezier(p0, p1, p2, p3));

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen }

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen return fit;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen };

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelenprivate:

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen CubicBezier calc_bezier(Point p0, Point p1, Point p2, Point p3) const {

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // create interpolating bezier between p1 and p2

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

26467da82c920aae52b2c00844c12f9ea236b480Johan B. C. Engelen // Part of the code comes from StackOverflow user eriatarka84

26467da82c920aae52b2c00844c12f9ea236b480Johan B. C. Engelen // http://stackoverflow.com/a/23980479/2929337

26467da82c920aae52b2c00844c12f9ea236b480Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // calculate time coords (deltas) of points

26467da82c920aae52b2c00844c12f9ea236b480Johan B. C. Engelen // the factor 0.25 can be generalized for other Catmull-Rom interpolation types

26467da82c920aae52b2c00844c12f9ea236b480Johan B. C. Engelen // see alpha in Yuksel et al. "On the Parameterization of Catmull-Rom Curves",

26467da82c920aae52b2c00844c12f9ea236b480Johan B. C. Engelen // --> http://www.cemyuksel.com/research/catmullrom_param/catmullrom.pdf

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen double dt0 = powf(distanceSq(p0, p1), 0.25);

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen double dt1 = powf(distanceSq(p1, p2), 0.25);

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen double dt2 = powf(distanceSq(p2, p3), 0.25);

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

26467da82c920aae52b2c00844c12f9ea236b480Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // safety check for repeated points

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen double eps = Geom::EPSILON;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen if (dt1 < eps)

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen dt1 = 1.0;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen if (dt0 < eps)

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen dt0 = dt1;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen if (dt2 < eps)

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen dt2 = dt1;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // compute tangents when parameterized in [t1,t2]

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Point tan1 = (p1 - p0) / dt0 - (p2 - p0) / (dt0 + dt1) + (p2 - p1) / dt1;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Point tan2 = (p2 - p1) / dt1 - (p3 - p1) / (dt1 + dt2) + (p3 - p2) / dt2;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // rescale tangents for parametrization in [0,1]

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen tan1 *= dt1;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen tan2 *= dt1;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // create bezier from tangents (this is already in 2geom somewhere, or should be moved to it)

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // the tangent of a bezier curve is: B'(t) = 3(1-t)^2 (b1 - b0) + 6(1-t)t(b2-b1) + 3t^2(b3-b2)

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // So we have to make sure that B'(0) = tan1 and B'(1) = tan2, and we already know that b0=p1 and b3=p2

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // tan1 = B'(0) = 3 (b1 - p1) --> p1 + (tan1)/3 = b1

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen // tan2 = B'(1) = 3 (p2 - b2) --> p2 - (tan2)/3 = b2

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Point b0 = p1;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Point b1 = p1 + tan1 / 3;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Point b2 = p2 - tan2 / 3;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen Point b3 = p2;

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen return CubicBezier(b0, b1, b2, b3);

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen }

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen CentripetalCatmullRomInterpolator(const CentripetalCatmullRomInterpolator&);

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen CentripetalCatmullRomInterpolator& operator=(const CentripetalCatmullRomInterpolator&);

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen};

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engeleninline Interpolator*

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan EngelenInterpolator::create(InterpolatorType type) {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen switch (type) {

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen case INTERP_LINEAR:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen return new Geom::Interpolate::Linear();

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen case INTERP_CUBICBEZIER:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen return new Geom::Interpolate::CubicBezierFit();

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen case INTERP_CUBICBEZIER_JOHAN:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen return new Geom::Interpolate::CubicBezierJohan();

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen case INTERP_SPIRO:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen return new Geom::Interpolate::SpiroInterpolator();

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White case INTERP_CUBICBEZIER_SMOOTH:

8ba84881e79b6175868d04179ca86f4823a69ec0Liam P. White return new Geom::Interpolate::CubicBezierSmooth();

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen case INTERP_CENTRIPETAL_CATMULLROM:

742a1b08138aef8fc3c19730ae48e5477ee43fc5Johan B. C. Engelen return new Geom::Interpolate::CentripetalCatmullRomInterpolator();

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen default:

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen return new Geom::Interpolate::Linear();

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen }

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen}

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen} //namespace Interpolate

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen} //namespace Geom

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen#endif

4fd537e3c7f3fb1b0013f94688e95b0c3ef6649cJohan Engelen