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/*
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 1998 - 2000 - ENPC - Jean-Philipe Chancelier
* Copyright (C) 2006 - INRIA - Jean-Baptiste Silvy
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
*/
/*------------------------------------------------------------------------
* Graphic library
--------------------------------------------------------------------------*/
#ifndef __SCIMATH_H__
#define __SCIMATH_H__
#include <stdlib.h>
#include "dynlib_graphics.h"
#include "BOOL.h"
#include "core_math.h"
#ifdef _MSC_VER
#include <float.h>
#define finite(x) _finite(x)
#else /* _MSC_VER */
/** This should only be provided when finite prototype is missing **/
/** XXX : to be tested **/
#ifndef __cplusplus
int finite (double);
#endif
#endif /* _MSC_VER */
#ifdef _MSC_VER
#include <float.h>
#define ISNAN(x) _isnan(x)
#else
#define ISNAN(x) isnan(x)
#endif
#define PI0 (int *) 0
#define PD0 (double *) 0
#define SMDOUBLE 1.e-200 /* Smalest number to avoid dividing by zero */
/* angle conversion */
#define PI_OVER_180 0.01745329251994329576913914624236578987393
#define _180_OVER_PI 57.29577951308232087665461840231273527024
#define DEG2RAD(x) ((x) * PI_OVER_180 )
#define RAD2DEG(x) ((x) * _180_OVER_PI )
#define round(a) (int)(((a)<0.0)?(a)-.5:(a)+.5)
#define EPSILON 1.0e-13
#define linint(x) ((int) floor(x + 0.5 ))
#define inint(x) ((int) floor(x + 0.5 ))
#if (defined(sun) || defined(SYSV))
#include <ieeefp.h>
#endif
#if defined(_MSC_VER)
#define M_PI 3.14159265358979323846
#else
#if defined(HAVE_VALUES_H)
#include <values.h>
#else
#if defined(HAVE_LIMITS_H)
#include <limits.h>
#endif
#endif
#endif
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
GRAPHICS_IMPEXP double Mini(const double vect[], int n) ;
GRAPHICS_IMPEXP double Maxi(const double vect[], int n) ;
/* prototypes */
/*----------------------------------------------------------------------------*/
/************************************************************************/
/* 2D algorithms */
/************************************************************************/
/* perform the rotation of point from to point dest with angle in radian */
GRAPHICS_IMPEXP void rotate2D( double from[2], double center[2], double angle, double dest[2] ) ;
/* perform the rotation of point from to point to. */
/* the angle is directly given with its sine and cosine for speed */
GRAPHICS_IMPEXP void rotate2Dim( double from[2] ,
double center[2] ,
double cosAngle ,
double sinAngle ,
double dest[2] ) ;
/* perform the translation of point from to point dest with vector trans */
GRAPHICS_IMPEXP void translate2D( double from[2], double trans[2], double dest[2] ) ;
/* perform the translation of point from to point dest with vector trans given in pixels.*/
GRAPHICS_IMPEXP void iTranslate2D( int from[2], int trans[2], int dest[2] ) ;
/**
* Normalize a 2d vector.
*/
GRAPHICS_IMPEXP void normalize2d( double vect[2] ) ;
/**
* Normalize a 2d vector in pixels coordinates.
*/
GRAPHICS_IMPEXP void iNormalize2d( int vect[2] ) ;
/**
* Perform the substraction of vect1 and vect2 and store it in res
*/
GRAPHICS_IMPEXP void vectSubstract2D(const double vect1[2], const double vect2[], double res[2]);
/**
* substraction of two vector
* @param res result of v1 + v2
*/
GRAPHICS_IMPEXP void vectAdd2D(const double v1[2], const double v2[2], double res[2]);
/**
* Multiply a vector by a scalar
* @param res scalar.v
*/
GRAPHICS_IMPEXP void scalarMult2D(const double v[2], const double scalar, double res[2]);
/**
* return the scalar product of two 2d vectors.
*/
#define DOT_PROD_2D(v1,v2) ( ((v1)[0]) * ((v2)[0]) + ((v1)[1]) * ((v2)[1]) )
/**
* Square norm of a vector
*/
#define SQUARE_NORM_2D(v) ( DOT_PROD_2D((v),(v)) )
/**
* Norm of a 2D vector
*/
#define NORM_2D(v) ( sqrt( SQUARE_NORM_2D(v) ) )
/**
* Compute wether the point lies within the triangle defined by A, B and C
*/
GRAPHICS_IMPEXP BOOL isPointInTriangle(const double point[2], const double a[2],
const double b[2], const double c[2]);
/**
* Compute wether p1 and p2 are on the same side of line (A,B).
*/
GRAPHICS_IMPEXP BOOL areOnSameSideOfLine(const double p1[2], const double p2[2],
const double a[2], const double b[2]);
/************************************************************************/
/* 3D algorithms */
/************************************************************************/
/**
* Scalar product of 2 vectors in 3D
*/
#define DOT_PROD_3D(v1,v2) ( ((v1)[0]) * ((v2)[0]) + ((v1)[1]) * ((v2)[1]) + ((v1)[2]) * ((v2)[2]) )
/**
* Cross product of two vector
* @param res v1^v2
*/
GRAPHICS_IMPEXP void crossProduct( const double v1[3], const double v2[3], double res[3] ) ;
/**
* Square norm of a 3D vector
*/
#define SQUARE_NORM_3D(v) ( DOT_PROD_3D((v),(v)) )
/**
* Norm of a 3D vector
*/
#define NORM_3D(v) ( sqrt( SQUARE_NORM_3D(v) ) )
/**
* substraction of two vector
* @param res result of v1 - v2
*/
GRAPHICS_IMPEXP void vectSubstract3D(const double v1[3], const double v2[3], double res[3]);
/**
* substraction of two vector
* @param res result of v1 + v2
*/
GRAPHICS_IMPEXP void vectAdd3D(const double v1[3], const double v2[3], double res[3]);
/**
* Multiply a vector by a scalar
* @param res scalar.v
*/
GRAPHICS_IMPEXP void scalarMult3D(const double v[3], double scalar, double res[3]);
/**
* Normalize a 3D vector
*/
GRAPHICS_IMPEXP void normalize3D( double vect[3] ) ;
/**
* Set a 4x4 matrix to identity.
*/
GRAPHICS_IMPEXP void setToIdentity(double mat4D[4][4]);
/**
* Compute the product mat4D*vect3D and store the result in res.
*/
GRAPHICS_IMPEXP void mat4DMult(const double mat4D[4][4], const double vect3D[3], double res[3]);
/*----------------------------------------------------------------------------*/
/* check if two values can be considered equal given an accurracy */
/* the x == y test is put to avoid division by 0 */
#define SAFE_EQUAL2(x,y,acc) ( Abs( (x) - (y) ) / Max( Abs( (x) + (y) ), EPSILON ) < (acc) )
#define SAFE_EQUAL(x,y,acc) ( (x) == (y) ) || ( Abs( (x) - (y) ) < (acc) * Max( Abs( (x) ), Abs( (y) ) ) )
/* test if a value if lesser than an other or just sligthy greater */
#define SAFE_LT(x,y,acc) ( (x) == (y) || ( (x) - (y) ) < (acc) * Max( Abs( (x) ), Abs( (y) ) ) )
#define SAFE_GT(x,y,acc) ( (x) == (y) || ( (y) - (x) ) < (acc) * Max( Abs( (x) ), Abs( (y) ) ) )
/*----------------------------------------------------------------------------*/
/*----------------------------------------------------------------------------*/
/* truncate an int to a 16 bits integer. Overflow value are truncated to the min */
/* and max of 16 bits integer. */
#define INT_2_16B(i) ( (i) > INT16MAX ? (INT16MAX) : ( (i) < INT16MIN ? INT16MIN : ((SCIINT16) i)) )
/*----------------------------------------------------------------------------*/
/*----------------------------------------------------------------------------*/
/* truncate an int to a char. Overflow value are truncated to the min */
/* and max of char integer. */
#define INT_2_UCHAR(i) ( (i) > UCHAR_MAX ? (UCHAR_MAX) : ( (i) < 0 ? 0 : ((char) i)) )
/*----------------------------------------------------------------------------*/
/*----------------------------------------------------------------------------*/
/* truncate a float or double to an int. Overflow value are truncated to the min */
/* and max of 32 bits integer. */
#define FLOAT_2_INT(f) ( (f) > INT_MAX ? (INT_MAX) : ( (f) < INT_MIN ? (INT_MIN) : ( inint( f ) ) ) )
/*----------------------------------------------------------------------------*/
/*----------------------------------------------------------------------------*/
/* return the number of digits of a positive int (ie for 10236 it is 5 ) */
/* the added 0.5 is to avoid trouble with 10^i which could become 9.999999999 */
#define GET_NB_DIGITS_POS(i) ( (i) == 0 ? 1 : ((int) floor( log10( (i) + 0.5 ) ) ) + 1 )
/*----------------------------------------------------------------------------*/
/*----------------------------------------------------------------------------*/
/* return the number of digits of an int (ie for 10236 it is 5 or -102 it is 4 ) */
/* For negative values, the length is increased by 1 because of the '-' sign" */
#define GET_NB_DIGITS(i) ( (i) > 0 ? GET_NB_DIGITS_POS(i) : GET_NB_DIGITS_POS(-i) + 1 )
/*----------------------------------------------------------------------------*/
#endif /* SCI_MATH.HG */
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