109 lines
2.7 KiB
C++
109 lines
2.7 KiB
C++
//
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// Bézier curve functions for the Fast Light Tool Kit (FLTK).
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//
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// Copyright 1998-2010 by Bill Spitzak and others.
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//
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// This library is free software. Distribution and use rights are outlined in
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// the file "COPYING" which should have been included with this file. If this
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// file is missing or damaged, see the license at:
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//
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// https://www.fltk.org/COPYING.php
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//
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// Please see the following page on how to report bugs and issues:
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//
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// https://www.fltk.org/bugs.php
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//
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/**
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\file fl_curve.cxx
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\brief Utility for drawing Bézier curves, adding the points to the
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current fl_begin/fl_vertex/fl_end path.
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Incremental math implementation:
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I very much doubt this is optimal! From Foley/vanDam page 511.
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If anybody has a better algorithm, please send it!
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*/
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#include <FL/fl_draw.H>
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#include <math.h>
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/**
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\cond DriverDev
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\addtogroup DriverDeveloper
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\{
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*/
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/** see fl_curve() */
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void Fl_Graphics_Driver::curve(double X0, double Y0,
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double X1, double Y1,
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double X2, double Y2,
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double X3, double Y3) {
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double x = fl_transform_x(X0,Y0);
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double y = fl_transform_y(X0,Y0);
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// draw point 0:
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fl_transformed_vertex(x,y);
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double x1 = fl_transform_x(X1,Y1);
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double y1 = fl_transform_y(X1,Y1);
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double x2 = fl_transform_x(X2,Y2);
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double y2 = fl_transform_y(X2,Y2);
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double x3 = fl_transform_x(X3,Y3);
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double y3 = fl_transform_y(X3,Y3);
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// find the area:
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double a = fabs((x-x2)*(y3-y1)-(y-y2)*(x3-x1));
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double b = fabs((x-x3)*(y2-y1)-(y-y3)*(x2-x1));
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if (b > a) a = b;
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// use that to guess at the number of segments:
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int nSeg = int(sqrt(a)/4);
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if (nSeg > 1) {
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if (nSeg > 100) nSeg = 100; // make huge curves not hang forever
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if (nSeg < 9) nSeg = 9; // make tiny curevs look bearable
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double e = 1.0/nSeg;
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// calculate the coefficients of 3rd order equation:
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double xa = (x3-3*x2+3*x1-x);
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double xb = 3*(x2-2*x1+x);
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double xc = 3*(x1-x);
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// calculate the forward differences:
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double dx1 = ((xa*e+xb)*e+xc)*e;
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double dx3 = 6*xa*e*e*e;
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double dx2 = dx3 + 2*xb*e*e;
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// calculate the coefficients of 3rd order equation:
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double ya = (y3-3*y2+3*y1-y);
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double yb = 3*(y2-2*y1+y);
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double yc = 3*(y1-y);
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// calculate the forward differences:
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double dy1 = ((ya*e+yb)*e+yc)*e;
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double dy3 = 6*ya*e*e*e;
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double dy2 = dy3 + 2*yb*e*e;
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// draw points 1 .. nSeg-2:
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for (int i=2; i<nSeg; i++) {
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x += dx1;
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dx1 += dx2;
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dx2 += dx3;
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y += dy1;
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dy1 += dy2;
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dy2 += dy3;
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fl_transformed_vertex(x,y);
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}
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// draw point nSeg-1:
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fl_transformed_vertex(x+dx1, y+dy1);
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}
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// draw point nSeg:
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fl_transformed_vertex(x3,y3);
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}
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/**
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\}
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\endcond
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*/
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