kig/misc/cubic-common.h

   1 // Copyright (C)  2003  Dominique Devriese <devriese@kde.org>
   2
   3 // This program is free software; you can redistribute it and/or
   4 // modify it under the terms of the GNU General Public License
   5 // as published by the Free Software Foundation; either version 2
   6 // of the License, or (at your option) any later version.
   7
   8 // This program is distributed in the hope that it will be useful,
   9 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  10 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  11 // GNU General Public License for more details.
  12
  13 // You should have received a copy of the GNU General Public License
  14 // along with this program; if not, write to the Free Software
  15 // Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
  16 // 02111-1307, USA.
  17
  18 #ifndef KIG_MISC_CUBIC_COMMON_H
  19 #define KIG_MISC_CUBIC_COMMON_H
  20
  21 #include "common.h"
  22
  23 class Transformation;
  24
  25 /**
  26  * This class represents an equation of a cubic in the form
  27  * "a_{ijk} x_i x_j x_k = 0" (in homogeneous coordinates, i,j,k = 0,1,2),
  28  * i <= j <= k.
  29  * The coefficients are stored in lessicografic order.
  30  */
  31 class CubicCartesianData
  32 {
  33 public:
  34   double coeffs[10];
  35   explicit CubicCartesianData();
  36   CubicCartesianData( double a000, double a001, double a002,
  37                       double a011, double a012, double a022,
  38                       double a111, double a112, double a122,
  39                       double a222 )
  40     {
  41       coeffs[0] = a000;
  42       coeffs[1] = a001;
  43       coeffs[2] = a002;
  44       coeffs[3] = a011;
  45       coeffs[4] = a012;
  46       coeffs[5] = a022;
  47       coeffs[6] = a111;
  48       coeffs[7] = a112;
  49       coeffs[8] = a122;
  50       coeffs[9] = a222;
  51     };
  52   CubicCartesianData( const double incoeffs[10] );
  53
  54   static CubicCartesianData invalidData();
  55   bool valid() const;
  56 };
  57
  58 bool operator==( const CubicCartesianData& lhs, const CubicCartesianData& rhs );
  59
  60 /**
  61  * This function calcs a cartesian cubic equation such that the
  62  * given points are on the cubic.  There can be at most 9 and at
  63  * least 2 point.  If there are less than 9, than the coefficients
  64  * will be chosen to 1.0 if possible
  65  */
  66
  67 const CubicCartesianData calcCubicThroughPoints (
  68     const std::vector<Coordinate>& points );
  69
  70 const CubicCartesianData calcCubicCuspThroughPoints (
  71     const std::vector<Coordinate>& points );
  72
  73 const CubicCartesianData calcCubicNodeThroughPoints (
  74     const std::vector<Coordinate>& points );
  75
  76 double calcCubicYvalue ( double x, double ymin, double ymax,
  77                          int root, CubicCartesianData data,
  78                          bool& valid, int& numroots );
  79
  80 const Coordinate calcCubicLineIntersect( const CubicCartesianData& c,
  81                                          const LineData& l,
  82                                          int root, bool& valid );
  83
  84 void calcCubicLineRestriction ( CubicCartesianData data,
  85          Coordinate p1, Coordinate dir,
  86          double& a, double& b, double& c, double& d );
  87
  88 const CubicCartesianData calcCubicTransformation (
  89   const CubicCartesianData& data,
  90   const Transformation& t, bool& valid );
  91
  92 #endif