src/fl_curve.cxx

   1 //
   2 // "$Id: fl_curve.cxx 7903 2010-11-28 21:06:39Z matt $"
   3 //
   4 // Bezier curve functions for the Fast Light Tool Kit (FLTK).
   5 //
   6 // Copyright 1998-2010 by Bill Spitzak and others.
   7 //
   8 // This library is free software; you can redistribute it and/or
   9 // modify it under the terms of the GNU Library General Public
  10 // License as published by the Free Software Foundation; either
  11 // version 2 of the License, or (at your option) any later version.
  12 //
  13 // This library is distributed in the hope that it will be useful,
  14 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  15 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  16 // Library General Public License for more details.
  17 //
  18 // You should have received a copy of the GNU Library General Public
  19 // License along with this library; if not, write to the Free Software
  20 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
  21 // USA.
  22 //
  23 // Please report all bugs and problems on the following page:
  24 //
  25 //     http://www.fltk.org/str.php
  26 //
  27
  28 /**
  29   \file fl_curve.cxx
  30   \brief Utility for drawing Bezier curves, adding the points to the
  31          current fl_begin/fl_vertex/fl_end path.
  32
  33   Incremental math implementation:
  34   I very much doubt this is optimal!  From Foley/vanDam page 511.
  35   If anybody has a better algorithm, please send it!
  36 */
  37
  38 #include <FL/fl_draw.H>
  39 #include <math.h>
  40
  41 void Fl_Graphics_Driver::curve(double X0, double Y0,
  42               double X1, double Y1,
  43               double X2, double Y2,
  44               double X3, double Y3) {
  45
  46   double x = fl_transform_x(X0,Y0);
  47   double y = fl_transform_y(X0,Y0);
  48
  49   // draw point 0:
  50   fl_transformed_vertex(x,y);
  51
  52   double x1 = fl_transform_x(X1,Y1);
  53   double yy1 = fl_transform_y(X1,Y1);
  54   double x2 = fl_transform_x(X2,Y2);
  55   double y2 = fl_transform_y(X2,Y2);
  56   double x3 = fl_transform_x(X3,Y3);
  57   double y3 = fl_transform_y(X3,Y3);
  58
  59   // find the area:
  60   double a = fabs((x-x2)*(y3-yy1)-(y-y2)*(x3-x1));
  61   double b = fabs((x-x3)*(y2-yy1)-(y-y3)*(x2-x1));
  62   if (b > a) a = b;
  63
  64   // use that to guess at the number of segments:
  65   int n = int(sqrt(a)/4);
  66   if (n > 1) {
  67     if (n > 100) n = 100; // make huge curves not hang forever
  68
  69     double e = 1.0/n;
  70
  71     // calculate the coefficients of 3rd order equation:
  72     double xa = (x3-3*x2+3*x1-x);
  73     double xb = 3*(x2-2*x1+x);
  74     double xc = 3*(x1-x);
  75     // calculate the forward differences:
  76     double dx1 = ((xa*e+xb)*e+xc)*e;
  77     double dx3 = 6*xa*e*e*e;
  78     double dx2 = dx3 + 2*xb*e*e;
  79
  80     // calculate the coefficients of 3rd order equation:
  81     double ya = (y3-3*y2+3*yy1-y);
  82     double yb = 3*(y2-2*yy1+y);
  83     double yc = 3*(yy1-y);
  84     // calculate the forward differences:
  85     double dy1 = ((ya*e+yb)*e+yc)*e;
  86     double dy3 = 6*ya*e*e*e;
  87     double dy2 = dy3 + 2*yb*e*e;
  88
  89     // draw points 1 .. n-2:
  90     for (int m=2; m<n; m++) {
  91       x += dx1;
  92       dx1 += dx2;
  93       dx2 += dx3;
  94       y += dy1;
  95       dy1 += dy2;
  96       dy2 += dy3;
  97       fl_transformed_vertex(x,y);
  98     }
  99
 100     // draw point n-1:
 101     fl_transformed_vertex(x+dx1, y+dy1);
 102   }
 103
 104   // draw point n:
 105   fl_transformed_vertex(x3,y3);
 106 }
 107
 108 //
 109 // End of "$Id: fl_curve.cxx 7903 2010-11-28 21:06:39Z matt $".
 110 //