lpe-powerstroke-interpolators.h

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// SPDX-License-Identifier: GPL-2.0-or-later
/* Authors:
 *   Johan Engelen <j.b.c.engelen@alumnus.utwente.nl>
 *
 * Copyright (C) 2010-2011 Authors
 *
 * Released under GNU GPL v2+, read the file 'COPYING' for more information.
 */
 
#ifndef INKSCAPE_LPE_POWERSTROKE_INTERPOLATORS_H
#define INKSCAPE_LPE_POWERSTROKE_INTERPOLATORS_H
 
#include <2geom/path.h>
#include <2geom/bezier-utils.h>
#include <2geom/sbasis-to-bezier.h>
 
#include "live_effects/spiro.h"
 
 
namespace Geom {
namespace Interpolate {
 
enum InterpolatorType {
  INTERP_LINEAR,
  INTERP_CUBICBEZIER,
  INTERP_CUBICBEZIER_JOHAN,
  INTERP_SPIRO,
  INTERP_CUBICBEZIER_SMOOTH,
  INTERP_CENTRIPETAL_CATMULLROM
};
 
class Interpolator {
public:
    Interpolator() = default;;
    virtual ~Interpolator() = default;;
 
    static Interpolator* create(InterpolatorType type);
 
    virtual Geom::Path interpolateToPath(std::vector<Point> const &points) const = 0;
 
private:
    Interpolator(const Interpolator&) = delete;
    Interpolator& operator=(const Interpolator&) = delete;
};
 
class Linear : public Interpolator {
public:
    Linear() = default;;
    ~Linear() override = default;;
 
    Path interpolateToPath(std::vector<Point> const &points) const override {
        Path path;
        path.start( points.at(0) );
        for (unsigned int i = 1 ; i < points.size(); ++i) {
            path.appendNew<Geom::LineSegment>(points.at(i));
        }
        return path;
    };
 
private:
    Linear(const Linear&) = delete;
    Linear& operator=(const Linear&) = delete;
};
 
// this class is terrible
class CubicBezierFit : public Interpolator {
public:
    CubicBezierFit() = default;;
    ~CubicBezierFit() override = default;;
 
    Path interpolateToPath(std::vector<Point> const &points) const override {
        unsigned int n_points = points.size();
        // worst case gives us 2 segment per point
        int max_segs = 8*n_points;
        Geom::Point * b = g_new(Geom::Point, max_segs);
        Geom::Point * points_array = g_new(Geom::Point, 4*n_points);
        for (unsigned i = 0; i < n_points; ++i) {
            points_array[i] = points.at(i);
        }
 
        double tolerance_sq = 0; // this value is just a random guess
 
        int const n_segs = Geom::bezier_fit_cubic_r(b, points_array, n_points,
                                                 tolerance_sq, max_segs);
 
        Geom::Path fit;
        if ( n_segs > 0)
        {
            fit.start(b[0]);
            for (int c = 0; c < n_segs; c++) {
                fit.appendNew<Geom::CubicBezier>(b[4*c+1], b[4*c+2], b[4*c+3]);
            }
        }
        g_free(b);
        g_free(points_array);
        return fit;
    };
 
private:
    CubicBezierFit(const CubicBezierFit&) = delete;
    CubicBezierFit& operator=(const CubicBezierFit&) = delete;
};
 
class CubicBezierJohan : public Interpolator {
public:
    CubicBezierJohan(double beta = 0.2) {
        _beta = beta;
    };
    ~CubicBezierJohan() override = default;;
 
    Path interpolateToPath(std::vector<Point> const &points) const override {
        Path fit;
        fit.start(points.at(0));
        for (unsigned int i = 1; i < points.size(); ++i) {
            Point p0 = points.at(i-1);
            Point p1 = points.at(i);
            Point dx = Point(p1[X] - p0[X], 0);
            fit.appendNew<CubicBezier>(p0+_beta*dx, p1-_beta*dx, p1);
        }
        return fit;
    };
 
    void setBeta(double beta) {
        _beta = beta;
    }
 
    double _beta;
 
private:
    CubicBezierJohan(const CubicBezierJohan&) = delete;
    CubicBezierJohan& operator=(const CubicBezierJohan&) = delete;
};
 
class CubicBezierSmooth : public Interpolator {
public:
    CubicBezierSmooth(double beta = 0.2) {
        _beta = beta;
    };
    ~CubicBezierSmooth() override = default;;
 
    Path interpolateToPath(std::vector<Point> const &points) const override {
        Path fit;
        fit.start(points.at(0));
        unsigned int num_points = points.size();
        for (unsigned int i = 1; i < num_points; ++i) {
            Point p0 = points.at(i-1);
            Point p1 = points.at(i);
            Point dx = Point(p1[X] - p0[X], 0);
            if (i == 1) {
                fit.appendNew<CubicBezier>(p0, p1-0.75*dx, p1);
            } else if (i == points.size() - 1) {
                fit.appendNew<CubicBezier>(p0+0.75*dx, p1, p1);
            } else {
                fit.appendNew<CubicBezier>(p0+_beta*dx, p1-_beta*dx, p1);
            }
        }
        return fit;
    };
 
    void setBeta(double beta) {
        _beta = beta;
    }
 
    double _beta;
 
private:
    CubicBezierSmooth(const CubicBezierSmooth&) = delete;
    CubicBezierSmooth& operator=(const CubicBezierSmooth&) = delete;
};
 
class SpiroInterpolator : public Interpolator {
public:
    SpiroInterpolator() = default;;
    ~SpiroInterpolator() override = default;;
 
    Path interpolateToPath(std::vector<Point> const &points) const override {
        Coord scale_y = 100.;
 
        guint len = points.size();
        Spiro::spiro_cp *controlpoints = g_new (Spiro::spiro_cp, len);
        for (unsigned int i = 0; i < len; ++i) {
            controlpoints[i].x = points[i][X];
            controlpoints[i].y = points[i][Y] / scale_y;
            controlpoints[i].ty = 'c';
        }
        controlpoints[0].ty = '{';
        controlpoints[1].ty = 'v';
        controlpoints[len-2].ty = 'v';
        controlpoints[len-1].ty = '}';
 
        auto fit = Spiro::spiro_run(controlpoints, len);
 
        fit *= Scale(1,scale_y);
        g_free(controlpoints);
        return fit;
    };
 
private:
    SpiroInterpolator(const SpiroInterpolator&) = delete;
    SpiroInterpolator& operator=(const SpiroInterpolator&) = delete;
};
 
// Quick mockup for testing the behavior for powerstroke controlpoint interpolation
class CentripetalCatmullRomInterpolator : public Interpolator {
public:
    CentripetalCatmullRomInterpolator() = default;;
    ~CentripetalCatmullRomInterpolator() override = default;;
 
    Path interpolateToPath(std::vector<Point> const &points) const override {
        unsigned int n_points = points.size();
 
        Geom::Path fit(points.front());
 
        if (n_points < 3) return fit; // TODO special cases for 0,1 and 2 input points
 
        // return n_points-1 cubic segments
 
        // duplicate first point
        fit.append(calc_bezier(points[0],points[0],points[1],points[2]));
 
        for (std::size_t i = 0; i < n_points-2; ++i) {
            Point p0 = points[i];
            Point p1 = points[i+1];
            Point p2 = points[i+2];
            Point p3 = (i < n_points-3) ? points[i+3] : points[i+2];
 
            fit.append(calc_bezier(p0, p1, p2, p3));
        }
 
        return fit;
    };
 
private:
    CubicBezier calc_bezier(Point p0, Point p1, Point p2, Point p3) const {
        // create interpolating bezier between p1 and p2
 
        // Part of the code comes from StackOverflow user eriatarka84
        // http://stackoverflow.com/a/23980479/2929337
 
        // calculate time coords (deltas) of points
        // the factor 0.25 can be generalized for other Catmull-Rom interpolation types 
        // see alpha in Yuksel et al. "On the Parameterization of Catmull-Rom Curves", 
        // --> http://www.cemyuksel.com/research/catmullrom_param/catmullrom.pdf
        double dt0 = powf(distanceSq(p0, p1), 0.25);
        double dt1 = powf(distanceSq(p1, p2), 0.25);
        double dt2 = powf(distanceSq(p2, p3), 0.25);
 
 
        // safety check for repeated points
        double eps = Geom::EPSILON;
        if (dt1 < eps)
            dt1 = 1.0;
        if (dt0 < eps)
            dt0 = dt1;
        if (dt2 < eps)
            dt2 = dt1;
 
        // compute tangents when parameterized in [t1,t2]
        Point tan1 = (p1 - p0) / dt0 - (p2 - p0) / (dt0 + dt1) + (p2 - p1) / dt1;
        Point tan2 = (p2 - p1) / dt1 - (p3 - p1) / (dt1 + dt2) + (p3 - p2) / dt2;
        // rescale tangents for parametrization in [0,1]
        tan1 *= dt1;
        tan2 *= dt1;
 
        // create bezier from tangents (this is already in 2geom somewhere, or should be moved to it)
        // 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)
        // So we have to make sure that B'(0) = tan1  and  B'(1) = tan2, and we already know that b0=p1 and b3=p2
        // tan1 = B'(0) = 3 (b1 - p1)  --> p1 + (tan1)/3 = b1
        // tan2 = B'(1) = 3 (p2 - b2)  --> p2 - (tan2)/3 = b2
 
        Point b0 = p1;
        Point b1 = p1 + tan1 / 3;
        Point b2 = p2 - tan2 / 3;
        Point b3 = p2;
 
        return CubicBezier(b0, b1, b2, b3);
    }
 
    CentripetalCatmullRomInterpolator(const CentripetalCatmullRomInterpolator&) = delete;
    CentripetalCatmullRomInterpolator& operator=(const CentripetalCatmullRomInterpolator&) = delete;
};
 
 
inline Interpolator*
Interpolator::create(InterpolatorType type) {
    switch (type) {
      case INTERP_LINEAR:
        return new Geom::Interpolate::Linear();
      case INTERP_CUBICBEZIER:
        return new Geom::Interpolate::CubicBezierFit();
      case INTERP_CUBICBEZIER_JOHAN:
        return new Geom::Interpolate::CubicBezierJohan();
      case INTERP_SPIRO:
        return new Geom::Interpolate::SpiroInterpolator();
      case INTERP_CUBICBEZIER_SMOOTH:
        return new Geom::Interpolate::CubicBezierSmooth();
      case INTERP_CENTRIPETAL_CATMULLROM:
        return new Geom::Interpolate::CentripetalCatmullRomInterpolator();
      default:
        return new Geom::Interpolate::Linear();
    }
}
 
} //namespace Interpolate
} //namespace Geom
 
#endif
 
/*
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  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
  indent-tabs-mode:nil
  fill-column:99
  End:
*/
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