1 /*****************************************************************************
5 ** Purpose: Header file containing definitions for numerical app
6 ** Programmer: Kevin Rosenberg
7 ** Date Started: Nov 84
9 ** This is part of the CTSim program
10 ** Copyright (C) 1983-2000 Kevin Rosenberg
12 ** $Id: kmath.h,v 1.15 2000/06/18 10:27:11 kevin Exp $
14 ** This program is free software; you can redistribute it and/or modify
15 ** it under the terms of the GNU General Public License (version 2) as
16 ** published by the Free Software Foundation.
18 ** This program is distributed in the hope that it will be useful,
19 ** but WITHOUT ANY WARRANTY; without even the implied warranty of
20 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21 ** GNU General Public License for more details.
23 ** You should have received a copy of the GNU General Public License
24 ** along with this program; if not, write to the Free Software
25 ** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26 ******************************************************************************/
34 #define PI 3.14159265358979323846
35 #define HALFPI 1.57079632679489661923 /* PI divided by 2 */
36 #define QUARTPI 0.78539816339744830962 /* PI divided by 4 */
37 #define I_PI 0.31830988618379067154 /* Inverse of PI */
38 #define I_PID2 0.63661977236758134308 /* Inverse of PID2 */
40 #define TWOPI 6.28318530717958647692
41 #define SQRT2 1.414213562373095049
43 #define F_EPSILON 1.0E-6
44 #define D_EPSILON 1.0E-10
46 #define ASSUMEDZERO 1E-10
48 typedef double GRFMTX_2D[3][3];
49 typedef double GRFMTX_3D[4][4];
52 convertDegreesToRadians (double x)
53 { return (x * (PI/180.)); }
56 convertRadiansToDegrees (double x)
57 { return (x*(180./PI)); }
60 inline T nearest (double x)
61 { return (x > 0 ? static_cast<T>(x+0.5) : static_cast<T>(x-0.5)); }
64 inline T clamp (T value, T lowerBounds, T upperBounds)
65 { return (value >= upperBounds ? upperBounds : (value <= lowerBounds ? lowerBounds : value )); }
68 inline T lineLength (T x1, T y1, T x2, T y2)
69 { return static_cast<T>( sqrt ((x2-x1)*(x2-x1) + (y2-y1)*(y2-y1)) ); }
72 inline void minmax_array (const T* array, const int n, T& min, T& max)
76 for (int i = 1; i < n; i++)
79 else if (array[i] > max)
84 int clip_rect(double *x1, double *y1, double *x2, double *y2, const double rect[4]);
85 int clip_segment(double *x1, double *y1, double *x2, double *y2, const double u, const double v);
86 int clip_sector(double *x1, double *y1, double *x2, double *y2, const double u, const double v);
87 int clip_circle(double *x1, double *y1, double *x2, double *y2, const double cx, const double cy, const double radius, double t1, double t2);
88 int clip_triangle(double *x1, double *y1, double *x2, double *y2, const double u, const double v, const int clip_xaxis);
91 double norm_ang(double theta);
94 void indent_mtx2(GRFMTX_2D m);
95 void xlat_mtx2(GRFMTX_2D m, const double x, const double y);
96 void scale_mtx2(GRFMTX_2D m, const double sx, const double sy);
97 void rot_mtx2(GRFMTX_2D m, const double theta);
98 void mult_mtx2(GRFMTX_2D m1, GRFMTX_2D m2, GRFMTX_2D result);
99 void xform_mtx2(GRFMTX_2D m, double *x, double *y);
100 void rotate2d(double x[], double y[], int pts, double angle);
101 void xlat2d(double x[], double y[], int pts, double xoffset, double yoffset);
102 void scale2d(double x[], double y[], int pts, double xfact, double yfact);
105 double simpson(const double xmin, const double xmax, const double *y, const int np);