common_math.h

matlab一些常用的处理模块

/******************************************************************************
 * 光学字符识别程序
 * 文件名：common_math.h
 * 功能  ：通用的数学函数
 * modified by [e-mail]
******************************************************************************/

#ifndef COMMON_MATH_H
#define COMMON_MATH_H

#include <math.h>
#include <limits.h>
#include <float.h>
#include <complex>

using std::min;
using std::complex;

// 检查两个浮点数是否相等
inline bool is_equal( float x, float y )
{
	return fabs( x - y ) < 100.0 * FLT_EPSILON;
}

// 检验一个浮点数是否为0
inline bool is_null( float x )
{
	return is_equal( x, 0 );
}

// 考虑机器精度
inline bool specify( float &x, float y )
{
	if ( is_equal( x, y ) ) 
	{
		x = y;
		return true;
	}
	return false;
}

// 转换弧度为角度
inline double radtodeg( double rad )
{
	return 180*rad / M_PI;
}

// 转换角度到弧度
inline double degtorad( double deg )
{
	return M_PI * deg/180;
}

// 归一化角度
inline double normalize_angle_2pi( double rad )
{
	register double res = fmod( rad, 2*M_PI );
	
	if( res < 0 )
		res += 2*M_PI;
	
	return res;
}

// 归一化角度
inline double normalize_angle_pi( double rad )
{
	register double res = fmod( rad, 2*M_PI );
	
	if( res < -M_PI )
		res += 2*M_PI;
	else if( res > M_PI )
		res -= 2*M_PI;

	return res;
}

// 归一化角度
inline double normalize_line_angle( double rad )
{
	register double res = fmod( rad, M_PI );
	
	if( res < -M_PI/2 )
		res += M_PI;
	else if( res > M_PI/2 )
		res -= M_PI;

	return res;
}

// 归一化角度
inline double normalize_inner_angle( double rad )
{
	register double inner_angle = normalize_angle_2pi( rad );
	
	if( inner_angle > M_PI )
		inner_angle = 2*M_PI-inner_angle;
	
	return inner_angle;
}

// 归一化角度
inline double normalize_straight_line_angle( double rad )
{
	register double inner_angle = normalize_angle_2pi( rad );
	
	if( inner_angle >= M_PI )
		inner_angle -= M_PI;
	
	return inner_angle;
}

// 计算角度差
inline float min_angle_between( float angle1, float angle2, float periodicity )
{
	return angle2 > angle1 ? min( angle2 - angle1, angle1 - angle2 + periodicity)
			       : min( angle1 - angle2, angle2 - angle1 + periodicity);
}

// 计算线性方程的参数
inline void straight_line_params( float x1, float y1, float x2, float y2, float &A, float &B, float &C )
{
	A = y1 - y2;
	B = x2 - x1;
	C = -x1*A - y1*B;
}

// 计算线性方差参数 (Ax+By+C=0)
inline int intersect_lines( float x1,  float y1, float x2, float y2,
			    float X1,  float Y1, float X2, float Y2,
			    float &x0, float &y0)
{
	float A1, B1, C1, A2, B2, C2;
	straight_line_params( x1, y1, x2, y2, A1, B1, C1 );
	straight_line_params( X1, Y1, X2, Y2, A2, B2, C2 );
	
	float divisor = A1*B2 - A2*B1;
	
	if( is_null( divisor ) )
		return -1;

	if( is_null( A1*X1 + B1*Y1 + C1 ) && is_null( A1*X2 + B1*Y2 + C1 ) )
		return 1;
	
	x0 = static_cast<float>( B1*C2 - B2*C1 ) / divisor;
	y0 = static_cast<float>( C1*A2 - C2*A1 ) / divisor;

	return 0;
}

// 返回x的signum
template<class T> inline int signum( T x )
{
	if( x < 0 )
		return -1;
	
	else if( x > 0 )
		return 1;
	
	return 0;
}

// 强制数值到某个范围中
inline bool assure_range( float lower_boundary, float upper_boundary, float &value )
{
	if( value > upper_boundary )
		value = upper_boundary;
	
	else if( value < lower_boundary )
		value = lower_boundary;
	
	else
		return true;
	
	return false;
}

// 保证范围
inline bool assure_range( int lower_boundary, int upper_boundary, int &value )
{
	float fvalue = static_cast<float>( value );	
	bool retval = assure_range( static_cast<float>( lower_boundary ), static_cast<float>( upper_boundary ), fvalue );
	value = static_cast<int>( fvalue );
	
	return retval;
}

// 计算点 (x1,y1) 到点 (x2,y2) 的欧几里得距离，T为实数或浮点数
template<class T> inline float euklidian_distance( T x1, T y1, T x2, T y2 )
{
	register T dx = x1 - x2;
	register T dy = y1 - y2;
	return sqrt( dx*dx + dy*dy );
}

// 判断点 (x,y) 是否在线段 (p1_x,p1_y) - (p2_x,p2_y) 上
template<class T> inline bool is_part_of( T p1_x,T p1_y, T p2_x,T p2_y, T x,T y )
{
	return	euklidian_distance( p1_x, p1_y, x, y ) + euklidian_distance( p2_x, p2_y, x, y ) <
		euklidian_distance( p1_x, p1_y, p2_x, p2_y ) + FLT_EPSILON*10.0;
}	

// 计算线段 ((x1,y1),(x2,y2)) 与 ((x2,y2),(x3,y3))之间的角度
template<class T> float angle_between( T x1, T y1, T x2, T y2, T x3, T y3 )
{
	complex<float> v1( x3-x2, y3-y2 ), v2( x1-x2, y1-y2 );

	return normalize_angle_pi( arg( v2 ) - arg( v1 ) );
}

#endif