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//
// "$Id$"
//
// Bezier curve functions for the Fast Light Tool Kit (FLTK).
//
// Copyright 1998-2005 by Bill Spitzak and others.
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Library General Public
// License as published by the Free Software Foundation; either
// version 2 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Library General Public License for more details.
//
// You should have received a copy of the GNU Library General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA.
//
// Please report all bugs and problems on the following page:
//
// http://www.fltk.org/str.php
//
// Utility for drawing Bezier curves, adding the points to
// the current fl_begin/fl_vertex/fl_end path.
// Incremental math implementation:
// I very much doubt this is optimal! From Foley/vanDam page 511.
// If anybody has a better algorithim, please send it!
#include <FL/fl_draw.H>
#include <math.h>
void fl_curve(double X0, double Y0,
double X1, double Y1,
double X2, double Y2,
double X3, double Y3) {
double x = fl_transform_x(X0,Y0);
double y = fl_transform_y(X0,Y0);
// draw point 0:
fl_transformed_vertex(x,y);
double x1 = fl_transform_x(X1,Y1);
double yy1 = fl_transform_y(X1,Y1);
double x2 = fl_transform_x(X2,Y2);
double y2 = fl_transform_y(X2,Y2);
double x3 = fl_transform_x(X3,Y3);
double y3 = fl_transform_y(X3,Y3);
// find the area:
double a = fabs((x-x2)*(y3-yy1)-(y-y2)*(x3-x1));
double b = fabs((x-x3)*(y2-yy1)-(y-y3)*(x2-x1));
if (b > a) a = b;
// use that to guess at the number of segments:
int n = int(sqrt(a)/4);
if (n > 1) {
if (n > 100) n = 100; // make huge curves not hang forever
double e = 1.0/n;
// calculate the coefficients of 3rd order equation:
double xa = (x3-3*x2+3*x1-x);
double xb = 3*(x2-2*x1+x);
double xc = 3*(x1-x);
// calculate the forward differences:
double dx1 = ((xa*e+xb)*e+xc)*e;
double dx3 = 6*xa*e*e*e;
double dx2 = dx3 + 2*xb*e*e;
// calculate the coefficients of 3rd order equation:
double ya = (y3-3*y2+3*yy1-y);
double yb = 3*(y2-2*yy1+y);
double yc = 3*(yy1-y);
// calculate the forward differences:
double dy1 = ((ya*e+yb)*e+yc)*e;
double dy3 = 6*ya*e*e*e;
double dy2 = dy3 + 2*yb*e*e;
// draw points 1 .. n-2:
for (int m=2; m<n; m++) {
x += dx1;
dx1 += dx2;
dx2 += dx3;
y += dy1;
dy1 += dy2;
dy2 += dy3;
fl_transformed_vertex(x,y);
}
// draw point n-1:
fl_transformed_vertex(x+dx1, y+dy1);
}
// draw point n:
fl_transformed_vertex(x3,y3);
}
//
// End of "$Id$".
//
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