| DRC | 2ff39b8 | 2011-07-28 08:38:59 +0000 | [diff] [blame] | 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 | // |