/**
* \file
* \brief Bezier curve
*//*
* Authors:
* MenTaLguY <mental@rydia.net>
* Marco Cecchetti <mrcekets at gmail.com>
* Krzysztof Kosiński <tweenk.pl@gmail.com>
*
* Copyright 2007-2011 Authors
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*/
#ifndef LIB2GEOM_SEEN_BEZIER_CURVE_H
#define LIB2GEOM_SEEN_BEZIER_CURVE_H
#include <2geom/curve.h>
#include <2geom/sbasis-curve.h> // for non-native winding method
#include <2geom/bezier.h>
#include <2geom/transforms.h>
namespace Geom
{
class BezierCurve : public Curve {
protected:
D2<Bezier> inner;
BezierCurve() {}
BezierCurve(Bezier const &x, Bezier const &y) : inner(x, y) {}
BezierCurve(std::vector<Point> const &pts);
public:
explicit BezierCurve(D2<Bezier> const &b) : inner(b) {}
/// @name Access and modify control points
/// @{
/** @brief Get the order of the Bezier curve.
* A Bezier curve has order() + 1 control points. */
unsigned order() const { return inner[X].order(); }
/** @brief Get the number of control points. */
unsigned size() const { return inner[X].order() + 1; }
/** @brief Access control points of the curve.
* @param ix The (zero-based) index of the control point. Note that the caller is responsible for checking that this value is <= order().
* @return The control point. No-reference return, use setPoint() to modify control points. */
Point controlPoint(unsigned ix) const { return Point(inner[X][ix], inner[Y][ix]); }
Point operator[](unsigned ix) const { return Point(inner[X][ix], inner[Y][ix]); }
/** @brief Get the control points.
* @return Vector with order() + 1 control points. */
std::vector<Point> controlPoints() const { return bezier_points(inner); }
D2<Bezier> const &fragment() const { return inner; }
/** @brief Modify a control point.
* @param ix The zero-based index of the point to modify. Note that the caller is responsible for checking that this value is <= order().
* @param v The new value of the point */
void setPoint(unsigned ix, Point const &v) {
inner[X][ix] = v[X];
inner[Y][ix] = v[Y];
}
/** @brief Set new control points.
* @param ps Vector which must contain order() + 1 points.
* Note that the caller is responsible for checking the size of this vector.
* @throws LogicalError Thrown when the size of the vector does not match the order. */
virtual void setPoints(std::vector<Point> const &ps) {
// must be virtual, because HLineSegment will need to redefine it
if (ps.size() != order() + 1)
THROW_LOGICALERROR("BezierCurve::setPoints: incorrect number of points in vector");
for(unsigned i = 0; i <= order(); i++) {
setPoint(i, ps[i]);
}
}
/// @}
/// @name Construct a Bezier curve with runtime-determined order.
/// @{
/** @brief Construct a curve from a vector of control points.
* This will construct the appropriate specialization of BezierCurve (i.e. LineSegment,
* QuadraticBezier or Cubic Bezier) if the number of control points in the passed vector
* does not exceed 4. */
static BezierCurve *create(std::vector<Point> const &pts);
/// @}
// implementation of virtual methods goes here
virtual Point initialPoint() const { return inner.at0(); }
virtual Point finalPoint() const { return inner.at1(); }
virtual bool isDegenerate() const;
virtual bool isLineSegment() const { return size() == 2; }
virtual void setInitial(Point const &v) { setPoint(0, v); }
virtual void setFinal(Point const &v) { setPoint(order(), v); }
virtual Rect boundsFast() const { return *bounds_fast(inner); }
virtual Rect boundsExact() const { return *bounds_exact(inner); }
virtual OptRect boundsLocal(OptInterval const &i, unsigned deg) const {
if (!i) return OptRect();
if(i->min() == 0 && i->max() == 1) return boundsFast();
if(deg == 0) return bounds_local(inner, i);
// TODO: UUUUUUGGGLLY
if(deg == 1 && order() > 1) return OptRect(bounds_local(Geom::derivative(inner[X]), i),
bounds_local(Geom::derivative(inner[Y]), i));
return OptRect();
}
virtual Curve *duplicate() const {
return new BezierCurve(*this);
}
virtual Curve *portion(Coord f, Coord t) const {
return new BezierCurve(Geom::portion(inner, f, t));
}
virtual Curve *reverse() const {
return new BezierCurve(Geom::reverse(inner));
}
using Curve::operator*=;
virtual void operator*=(Translate const &tr) {
for (unsigned i = 0; i < size(); ++i) {
inner[X][i] += tr[X];
inner[Y][i] += tr[Y];
}
}
virtual void operator*=(Scale const &s) {
for (unsigned i = 0; i < size(); ++i) {
inner[X][i] *= s[X];
inner[Y][i] *= s[Y];
}
}
virtual void operator*=(Affine const &m) {
for (unsigned i = 0; i < size(); ++i) {
setPoint(i, controlPoint(i) * m);
}
}
virtual Curve *derivative() const {
return new BezierCurve(Geom::derivative(inner[X]), Geom::derivative(inner[Y]));
}
virtual int degreesOfFreedom() const {
return 2 * (order() + 1);
}
virtual std::vector<Coord> roots(Coord v, Dim2 d) const {
return (inner[d] - v).roots();
}
virtual Coord nearestTime(Point const &p, Coord from = 0, Coord to = 1) const;
virtual Coord length(Coord tolerance) const;
virtual std::vector<CurveIntersection> intersect(Curve const &other, Coord eps = EPSILON) const;
virtual Point pointAt(Coord t) const { return inner.pointAt(t); }
virtual std::vector<Point> pointAndDerivatives(Coord t, unsigned n) const {
return inner.valueAndDerivatives(t, n);
}
virtual Coord valueAt(Coord t, Dim2 d) const { return inner[d].valueAt(t); }
virtual D2<SBasis> toSBasis() const {return inner.toSBasis(); }
virtual bool isNear(Curve const &c, Coord precision) const;
virtual bool operator==(Curve const &c) const;
virtual void feed(PathSink &sink, bool) const;
};
template <unsigned degree>
class BezierCurveN
: public BezierCurve
{
template <unsigned required_degree>
static void assert_degree(BezierCurveN<required_degree> const *) {}
public:
/// @name Construct Bezier curves
/// @{
/** @brief Construct a Bezier curve of the specified order with all points zero. */
BezierCurveN() {
inner = D2<Bezier>(Bezier(Bezier::Order(degree)), Bezier(Bezier::Order(degree)));
}
/** @brief Construct from 2D Bezier polynomial. */
explicit BezierCurveN(D2<Bezier > const &x) {
inner = x;
}
/** @brief Construct from two 1D Bezier polynomials of the same order. */
BezierCurveN(Bezier x, Bezier y) {
inner = D2<Bezier > (x,y);
}
/** @brief Construct a Bezier curve from a vector of its control points. */
BezierCurveN(std::vector<Point> const &points) {
unsigned ord = points.size() - 1;
if (ord != degree) THROW_LOGICALERROR("BezierCurve<degree> does not match number of points");
for (unsigned d = 0; d < 2; ++d) {
inner[d] = Bezier(Bezier::Order(ord));
for(unsigned i = 0; i <= ord; i++)
inner[d][i] = points[i][d];
}
}
/** @brief Construct a linear segment from its endpoints. */
BezierCurveN(Point c0, Point c1) {
assert_degree<1>(this);
for(unsigned d = 0; d < 2; d++)
inner[d] = Bezier(c0[d], c1[d]);
}
/** @brief Construct a quadratic Bezier curve from its control points. */
BezierCurveN(Point c0, Point c1, Point c2) {
assert_degree<2>(this);
for(unsigned d = 0; d < 2; d++)
inner[d] = Bezier(c0[d], c1[d], c2[d]);
}
/** @brief Construct a cubic Bezier curve from its control points. */
BezierCurveN(Point c0, Point c1, Point c2, Point c3) {
assert_degree<3>(this);
for(unsigned d = 0; d < 2; d++)
inner[d] = Bezier(c0[d], c1[d], c2[d], c3[d]);
}
// default copy
// default assign
/// @}
/** @brief Divide a Bezier curve into two curves
* @param t Time value
* @return Pair of Bezier curves \f$(\mathbf{D}, \mathbf{E})\f$ such that
* \f$\mathbf{D}[ [0,1] ] = \mathbf{C}[ [0,t] ]\f$ and
* \f$\mathbf{E}[ [0,1] ] = \mathbf{C}[ [t,1] ]\f$ */
std::pair<BezierCurveN, BezierCurveN> subdivide(Coord t) const {
std::pair<Bezier, Bezier> sx = inner[X].subdivide(t), sy = inner[Y].subdivide(t);
return std::make_pair(
BezierCurveN(sx.first, sy.first),
BezierCurveN(sx.second, sy.second));
}
virtual bool isDegenerate() const {
return BezierCurve::isDegenerate();
}
virtual bool isLineSegment() const {
return size() == 2;
}
virtual Curve *duplicate() const {
return new BezierCurveN(*this);
}
virtual Curve *portion(Coord f, Coord t) const {
if (degree == 1) {
return new BezierCurveN<1>(pointAt(f), pointAt(t));
} else {
return new BezierCurveN(Geom::portion(inner, f, t));
}
}
virtual Curve *reverse() const {
if (degree == 1) {
return new BezierCurveN<1>(finalPoint(), initialPoint());
} else {
return new BezierCurveN(Geom::reverse(inner));
}
}
virtual Curve *derivative() const;
virtual Coord nearestTime(Point const &p, Coord from = 0, Coord to = 1) const {
return BezierCurve::nearestTime(p, from, to);
}
virtual std::vector<CurveIntersection> intersect(Curve const &other, Coord eps = EPSILON) const {
// call super. this is implemented only to allow specializations
return BezierCurve::intersect(other, eps);
}
virtual int winding(Point const &p) const {
return Curve::winding(p);
}
virtual void feed(PathSink &sink, bool moveto_initial) const {
// call super. this is implemented only to allow specializations
BezierCurve::feed(sink, moveto_initial);
}
};
// BezierCurveN<0> is meaningless; specialize it out
template<> class BezierCurveN<0> : public BezierCurveN<1> { private: BezierCurveN();};
/** @brief Line segment.
* Line segments are Bezier curves of order 1. They have only two control points,
* the starting point and the ending point.
* @ingroup Curves */
typedef BezierCurveN<1> LineSegment;
/** @brief Quadratic (order 2) Bezier curve.
* @ingroup Curves */
typedef BezierCurveN<2> QuadraticBezier;
/** @brief Cubic (order 3) Bezier curve.
* @ingroup Curves */
typedef BezierCurveN<3> CubicBezier;
template <unsigned degree>
inline
Curve *BezierCurveN<degree>::derivative() const {
return new BezierCurveN<degree-1>(Geom::derivative(inner[X]), Geom::derivative(inner[Y]));
}
// optimized specializations
template <> inline bool BezierCurveN<1>::isDegenerate() const {
return inner[X][0] == inner[X][1] && inner[Y][0] == inner[Y][1];
}
template <> inline bool BezierCurveN<1>::isLineSegment() const { return true; }
template <> Curve *BezierCurveN<1>::derivative() const;
template <> Coord BezierCurveN<1>::nearestTime(Point const &, Coord, Coord) const;
template <> std::vector<CurveIntersection> BezierCurveN<1>::intersect(Curve const &, Coord) const;
template <> int BezierCurveN<1>::winding(Point const &) const;
template <> void BezierCurveN<1>::feed(PathSink &sink, bool moveto_initial) const;
template <> void BezierCurveN<2>::feed(PathSink &sink, bool moveto_initial) const;
template <> void BezierCurveN<3>::feed(PathSink &sink, bool moveto_initial) const;
inline Point middle_point(LineSegment const& _segment) {
return ( _segment.initialPoint() + _segment.finalPoint() ) / 2;
}
inline Coord length(LineSegment const& seg) {
return distance(seg.initialPoint(), seg.finalPoint());
}
Coord bezier_length(std::vector<Point> const &points, Coord tolerance = 0.01);
Coord bezier_length(Point p0, Point p1, Point p2, Coord tolerance = 0.01);
Coord bezier_length(Point p0, Point p1, Point p2, Point p3, Coord tolerance = 0.01);
} // end namespace Geom
#endif // LIB2GEOM_SEEN_BEZIER_CURVE_H
/*
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End:
*/
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