src/2geom/curve.h

	curve.h revision 1f37e9d97c3bb8cf02b2cc80af8dcfc9aba7c7b4
/*
 * Abstract Curve Type
 *
 * Authors:
 *      MenTaLguY <mental@rydia.net>
 *      Marco Cecchetti <mrcekets at gmail.com>
 *
 * Copyright 2007-2008  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 _2GEOM_CURVE_H_
#define _2GEOM_CURVE_H_


#include <2geom/coord.h>
#include <2geom/point.h>
#include <2geom/interval.h>
#include <2geom/nearest-point.h>
#include <2geom/sbasis.h>
#include <2geom/d2.h>
#include <2geom/matrix.h>
#include <2geom/exception.h>

#include <vector>


namespace Geom
{

class Curve;

struct CurveHelpers {
protected:
  static int root_winding(Curve const &c, Point p);
};

class Curve : private CurveHelpers {
public:
  virtual ~Curve() {}

  virtual Point initialPoint() const = 0;
  virtual Point finalPoint() const = 0;

  /* isDegenerate returns true if the curve has "zero length".
   * For a bezier curve this means for example that all handles are at the same point */
  virtual bool isDegenerate() const = 0;

  virtual Curve *duplicate() const = 0;

  virtual Rect boundsFast() const = 0;
  virtual Rect boundsExact() const = 0;
  virtual Rect boundsLocal(Interval i, unsigned deg) const = 0;
  Rect boundsLocal(Interval i) const { return boundsLocal(i, 0); }

  virtual std::vector<double> roots(double v, Dim2 d) const = 0;

  virtual int winding(Point p) const { return root_winding(*this, p); }

  //mental: review these
  virtual Curve *portion(double f, double t) const = 0;
  virtual Curve *reverse() const { return portion(1, 0); }
  virtual Curve *derivative() const = 0;

  virtual void setInitial(Point v) = 0;
  virtual void setFinal(Point v) = 0;

  virtual
  double nearestPoint( Point const& p, double from = 0, double to = 1 ) const
  {
      return nearest_point(p, toSBasis(), from, to);
  }

  virtual
  std::vector<double>
  allNearestPoints( Point const& p, double from = 0, double to = 1 ) const
  {
      return all_nearest_points(p, toSBasis(), from, to);
  }

  /*
  Path operator*=(Matrix)
  This is not possible, because:
  A Curve can be many things, for example a HLineSegment.
  Such a segment cannot be transformed and stay a HLineSegment in general (take for example rotations).
  This means that these curves become a different type of curve, hence one should use "transformed(Matrix).
  */

  virtual Curve *transformed(Matrix const &m) const = 0;

  virtual Point pointAt(Coord t) const { return pointAndDerivatives(t, 0).front(); }
  virtual Coord valueAt(Coord t, Dim2 d) const { return pointAt(t)[d]; }
  virtual Point operator() (double t)  const { return pointAt(t); }

  /* pointAndDerivatives returns a vector that looks like the following:
   *  [ point at t, 1st derivative at t, 2nd derivative at t, ... , n'th derivative at t] */
  virtual std::vector<Point> pointAndDerivatives(Coord t, unsigned n) const = 0;

  /* unitTangentAt returns the unit vector tangent to the curve at position t
   * (in the direction of increasing t). The method uses l'Hopital's rule when the derivative
   * is (0,0), parameter n determines the maximum nr of iterations (for when higher derivatives are also (0,0) ).
   * Point(0,0) is returned if no non-zero derivative could be found.
   * Note that unitTangentAt(1) will probably not give the desired result. Probably one should do:
   *    Curve * c_reverse = c.reverse();
   *    Point tangent = - c_reverse->unitTangentAt(0);
   *    delete c_reverse;
   */
  virtual Point unitTangentAt(Coord t, unsigned n = 3) const
  {
    for (unsigned deriv_n = 1; deriv_n <= n; deriv_n++) {
      Point deriv = pointAndDerivatives(t, deriv_n)[deriv_n];
      Coord length = deriv.length();
      if ( ! are_near(length, 0) ) {
         // length of derivative is non-zero, so return unit vector
         return deriv / length;
      }
    }
    return Point (0,0);
  };

  virtual D2<SBasis> toSBasis() const = 0;
  virtual bool operator==(Curve const &c) const { return this == &c;}
};

inline
Coord nearest_point(Point const& p, Curve const& c)
{
    return c.nearestPoint(p);
}

} // end namespace Geom


#endif // _2GEOM_CURVE_H_


/*
  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:encoding=utf-8:textwidth=99 :