1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
|
//
// Bézier curve functions for the Fast Light Tool Kit (FLTK).
//
// Copyright 1998-2010 by Bill Spitzak and others.
//
// This library is free software. Distribution and use rights are outlined in
// the file "COPYING" which should have been included with this file. If this
// file is missing or damaged, see the license at:
//
// https://www.fltk.org/COPYING.php
//
// Please see the following page on how to report bugs and issues:
//
// https://www.fltk.org/bugs.php
//
/**
\file fl_curve.cxx
\brief Utility for drawing Bézier 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 algorithm, please send it!
*/
#include <FL/fl_draw.H>
#include <math.h>
/**
\cond DriverDev
\addtogroup DriverDeveloper
\{
*/
/** see fl_curve() */
void Fl_Graphics_Driver::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 y1 = 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-y1)-(y-y2)*(x3-x1));
double b = fabs((x-x3)*(y2-y1)-(y-y3)*(x2-x1));
if (b > a) a = b;
// use that to guess at the number of segments:
int nSeg = int(sqrt(a)/4);
if (nSeg > 1) {
if (nSeg > 100) nSeg = 100; // make huge curves not hang forever
if (nSeg < 9) nSeg = 9; // make tiny curevs look bearable
double e = 1.0/nSeg;
// 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*y1-y);
double yb = 3*(y2-2*y1+y);
double yc = 3*(y1-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 .. nSeg-2:
for (int i=2; i<nSeg; i++) {
x += dx1;
dx1 += dx2;
dx2 += dx3;
y += dy1;
dy1 += dy2;
dy2 += dy3;
fl_transformed_vertex(x,y);
}
// draw point nSeg-1:
fl_transformed_vertex(x+dx1, y+dy1);
}
// draw point nSeg:
fl_transformed_vertex(x3,y3);
}
/**
\}
\endcond
*/
|
