/** @file
* Interpolators for lists of points.
*/
/* Authors:
* Johan Engelen <j.b.c.engelen@alumnus.utwente.nl>
*
* Copyright (C) 2010-2011 Authors
*
* Released under GNU GPL, 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"
/// @TODO Move this to 2geom?
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() {};
virtual ~Interpolator() {};
static Interpolator* create(InterpolatorType type);
virtual Geom::Path interpolateToPath(std::vector<Point> const &points) const = 0;
private:
Interpolator(const Interpolator&);
Interpolator& operator=(const Interpolator&);
};
class Linear : public Interpolator {
public:
Linear() {};
virtual ~Linear() {};
virtual Path interpolateToPath(std::vector<Point> const &points) const {
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&);
Linear& operator=(const Linear&);
};
// this class is terrible
class CubicBezierFit : public Interpolator {
public:
CubicBezierFit() {};
virtual ~CubicBezierFit() {};
virtual Path interpolateToPath(std::vector<Point> const &points) const {
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&);
CubicBezierFit& operator=(const CubicBezierFit&);
};
/// @todo invent name for this class
class CubicBezierJohan : public Interpolator {
public:
CubicBezierJohan(double beta = 0.2) {
_beta = beta;
};
virtual ~CubicBezierJohan() {};
virtual Path interpolateToPath(std::vector<Point> const &points) const {
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&);
CubicBezierJohan& operator=(const CubicBezierJohan&);
};
/// @todo invent name for this class
class CubicBezierSmooth : public Interpolator {
public:
CubicBezierSmooth(double beta = 0.2) {
_beta = beta;
};
virtual ~CubicBezierSmooth() {};
virtual Path interpolateToPath(std::vector<Point> const &points) const {
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&);
CubicBezierSmooth& operator=(const CubicBezierSmooth&);
};
class SpiroInterpolator : public Interpolator {
public:
SpiroInterpolator() {};
virtual ~SpiroInterpolator() {};
virtual Path interpolateToPath(std::vector<Point> const &points) const {
Path fit;
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 = '}';
Spiro::spiro_run(controlpoints, len, fit);
fit *= Scale(1,scale_y);
return fit;
};
private:
SpiroInterpolator(const SpiroInterpolator&);
SpiroInterpolator& operator=(const SpiroInterpolator&);
};
// Quick mockup for testing the behavior for powerstroke controlpoint interpolation
class CentripetalCatmullRomInterpolator : public Interpolator {
public:
CentripetalCatmullRomInterpolator() {};
virtual ~CentripetalCatmullRomInterpolator() {};
virtual Path interpolateToPath(std::vector<Point> const &points) const {
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&);
CentripetalCatmullRomInterpolator& operator=(const CentripetalCatmullRomInterpolator&);
};
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
/*
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:fileencoding=utf-8:textwidth=99 :