414 lines
8.8 KiB
C
414 lines
8.8 KiB
C
|
/** \file
|
||
|
|
* \brief Math Utilities
|
||
|
|
*
|
||
|
|
* See Copyright Notice in im_lib.h
|
||
|
|
*/
|
||
|
|
|
||
|
|
#ifndef __IM_MATH_H
|
||
|
|
#define __IM_MATH_H
|
||
|
|
|
||
|
|
#include <math.h>
|
||
|
|
#include "im_util.h"
|
||
|
|
|
||
|
|
#ifdef IM_DEFMATHFLOAT
|
||
|
|
inline float acosf(float _X) {return ((float)acos((double)_X)); }
|
||
|
|
inline float asinf(float _X) {return ((float)asin((double)_X)); }
|
||
|
|
inline float atanf(float _X) {return ((float)atan((double)_X)); }
|
||
|
|
inline float atan2f(float _X, float _Y) {return ((float)atan2((double)_X, (double)_Y)); }
|
||
|
|
inline float ceilf(float _X) {return ((float)ceil((double)_X)); }
|
||
|
|
inline float cosf(float _X) {return ((float)cos((double)_X)); }
|
||
|
|
inline float coshf(float _X) {return ((float)cosh((double)_X)); }
|
||
|
|
inline float expf(float _X) {return ((float)exp((double)_X)); }
|
||
|
|
inline float fabsf(float _X) {return ((float)fabs((double)_X)); }
|
||
|
|
inline float floorf(float _X) {return ((float)floor((double)_X)); }
|
||
|
|
inline float fmodf(float _X, float _Y) {return ((float)fmod((double)_X, (double)_Y)); }
|
||
|
|
inline float logf(float _X) {return ((float)log((double)_X)); }
|
||
|
|
inline float log10f(float _X) {return ((float)log10((double)_X)); }
|
||
|
|
inline float powf(float _X, float _Y) {return ((float)pow((double)_X, (double)_Y)); }
|
||
|
|
inline float sinf(float _X) {return ((float)sin((double)_X)); }
|
||
|
|
inline float sinhf(float _X) {return ((float)sinh((double)_X)); }
|
||
|
|
inline float sqrtf(float _X) {return ((float)sqrt((double)_X)); }
|
||
|
|
inline float tanf(float _X) {return ((float)tan((double)_X)); }
|
||
|
|
inline float tanhf(float _X) {return ((float)tanh((double)_X)); }
|
||
|
|
#endif
|
||
|
|
|
||
|
|
/** \defgroup math Math Utilities
|
||
|
|
* \par
|
||
|
|
* When converting between continuous and discrete use: \n
|
||
|
|
* Continuous = Discrete + 0.5 [Reconstruction/Interpolation] \n
|
||
|
|
* Discrete = Round(Continuous - 0.5) [Sampling/Quantization] \n
|
||
|
|
* \par
|
||
|
|
* Notice that must check min-max limits when converting from Continuous to Discrete.
|
||
|
|
* \par
|
||
|
|
* When converting between discrete and discrete use: \n
|
||
|
|
* integer src_size, dst_len, src_i, dst_i \n
|
||
|
|
* real factor = (real)(dst_size)/(real)(src_size) \n
|
||
|
|
* dst_i = Round(factor*(src_i + 0.5) - 0.5)
|
||
|
|
* \par
|
||
|
|
* See \ref im_math.h
|
||
|
|
* \ingroup util */
|
||
|
|
|
||
|
|
|
||
|
|
/** Round a real to the nearest integer.
|
||
|
|
* \ingroup math */
|
||
|
|
inline int imRound(float x)
|
||
|
|
{
|
||
|
|
return (int)(x < 0? x-0.5f: x+0.5f);
|
||
|
|
}
|
||
|
|
inline int imRound(double x)
|
||
|
|
{
|
||
|
|
return (int)(x < 0? x-0.5: x+0.5);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
inline T imAbs(const T& v)
|
||
|
|
{
|
||
|
|
if (v < 0)
|
||
|
|
return -1*v;
|
||
|
|
return v;
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Converts between two discrete grids.
|
||
|
|
* factor is "dst_size/src_size".
|
||
|
|
* \ingroup math */
|
||
|
|
inline int imResampleInt(int x, double factor)
|
||
|
|
{
|
||
|
|
double xr = factor*(x + 0.5) - 0.5;
|
||
|
|
return (int)(xr < 0? xr-0.5: xr+0.5); /* Round */
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Does Zero Order Decimation (Mean).
|
||
|
|
* \ingroup math */
|
||
|
|
template <class T, class TU>
|
||
|
|
inline T imZeroOrderDecimation(int width, int height, T *map, double xl, double yl, double box_width, double box_height, TU Dummy)
|
||
|
|
{
|
||
|
|
int x0,x1,y0,y1;
|
||
|
|
(void)Dummy;
|
||
|
|
|
||
|
|
x0 = (int)floor(xl - box_width/2.0 - 0.5) + 1;
|
||
|
|
y0 = (int)floor(yl - box_height/2.0 - 0.5) + 1;
|
||
|
|
x1 = (int)floor(xl + box_width/2.0 - 0.5);
|
||
|
|
y1 = (int)floor(yl + box_height/2.0 - 0.5);
|
||
|
|
|
||
|
|
if (x0 == x1) x1++;
|
||
|
|
if (y0 == y1) y1++;
|
||
|
|
|
||
|
|
x0 = x0<0? 0: x0>width-1? width-1: x0;
|
||
|
|
y0 = y0<0? 0: y0>height-1? height-1: y0;
|
||
|
|
x1 = x1<0? 0: x1>width-1? width-1: x1;
|
||
|
|
y1 = y1<0? 0: y1>height-1? height-1: y1;
|
||
|
|
|
||
|
|
TU Value;
|
||
|
|
int Count = 0;
|
||
|
|
|
||
|
|
Value = 0;
|
||
|
|
|
||
|
|
for (int y = y0; y <= y1; y++)
|
||
|
|
{
|
||
|
|
for (int x = x0; x <= x1; x++)
|
||
|
|
{
|
||
|
|
Value += map[y*width+x];
|
||
|
|
Count++;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if (Count == 0)
|
||
|
|
{
|
||
|
|
Value = 0;
|
||
|
|
return (T)Value;
|
||
|
|
}
|
||
|
|
|
||
|
|
return (T)(Value/double(Count));
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Does Bilinear Decimation.
|
||
|
|
* \ingroup math */
|
||
|
|
template <class T, class TU>
|
||
|
|
inline T imBilinearDecimation(int width, int height, T *map, double xl, double yl, double box_width, double box_height, TU Dummy)
|
||
|
|
{
|
||
|
|
int x0,x1,y0,y1;
|
||
|
|
(void)Dummy;
|
||
|
|
|
||
|
|
x0 = (int)floor(xl - box_width/2.0 - 0.5) + 1;
|
||
|
|
y0 = (int)floor(yl - box_height/2.0 - 0.5) + 1;
|
||
|
|
x1 = (int)floor(xl + box_width/2.0 - 0.5);
|
||
|
|
y1 = (int)floor(yl + box_height/2.0 - 0.5);
|
||
|
|
|
||
|
|
if (x0 == x1) x1++;
|
||
|
|
if (y0 == y1) y1++;
|
||
|
|
|
||
|
|
x0 = x0<0? 0: x0>width-1? width-1: x0;
|
||
|
|
y0 = y0<0? 0: y0>height-1? height-1: y0;
|
||
|
|
x1 = x1<0? 0: x1>width-1? width-1: x1;
|
||
|
|
y1 = y1<0? 0: y1>height-1? height-1: y1;
|
||
|
|
|
||
|
|
TU Value, LineValue;
|
||
|
|
double dxr, dyr;
|
||
|
|
double LineNorm, Norm;
|
||
|
|
|
||
|
|
Value = 0;
|
||
|
|
Norm = 0;
|
||
|
|
|
||
|
|
for (int y = y0; y <= y1; y++)
|
||
|
|
{
|
||
|
|
dyr = yl - (y+0.5);
|
||
|
|
if (dyr < 0) dyr *= -1;
|
||
|
|
|
||
|
|
LineValue = 0;
|
||
|
|
LineNorm = 0;
|
||
|
|
|
||
|
|
for (int x = x0; x <= x1; x++)
|
||
|
|
{
|
||
|
|
dxr = xl - (x+0.5);
|
||
|
|
if (dxr < 0) dxr *= -1;
|
||
|
|
|
||
|
|
LineValue += map[y*width+x] * dxr;
|
||
|
|
LineNorm += dxr;
|
||
|
|
}
|
||
|
|
|
||
|
|
Value += LineValue * dyr;
|
||
|
|
Norm += dyr * LineNorm;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (Norm == 0)
|
||
|
|
{
|
||
|
|
Value = 0;
|
||
|
|
return (T)Value;
|
||
|
|
}
|
||
|
|
|
||
|
|
return (T)(Value/Norm);
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Does Zero Order Interpolation (Nearest Neighborhood).
|
||
|
|
* \ingroup math */
|
||
|
|
template <class T>
|
||
|
|
inline T imZeroOrderInterpolation(int width, int height, T *map, double xl, double yl)
|
||
|
|
{
|
||
|
|
int x0 = imRound(xl-0.5);
|
||
|
|
int y0 = imRound(yl-0.5);
|
||
|
|
x0 = x0<0? 0: x0>width-1? width-1: x0;
|
||
|
|
y0 = y0<0? 0: y0>height-1? height-1: y0;
|
||
|
|
return map[y0*width + x0];
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Does Bilinear Interpolation.
|
||
|
|
* \ingroup math */
|
||
|
|
template <class T>
|
||
|
|
inline T imBilinearInterpolation(int width, int height, T *map, double xl, double yl)
|
||
|
|
{
|
||
|
|
int x0, y0, x1, y1;
|
||
|
|
double t, u;
|
||
|
|
|
||
|
|
if (xl < 0.5)
|
||
|
|
{
|
||
|
|
x1 = x0 = 0;
|
||
|
|
t = 0;
|
||
|
|
}
|
||
|
|
else if (xl >= width-0.5)
|
||
|
|
{
|
||
|
|
x1 = x0 = width-1;
|
||
|
|
t = 0;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
x0 = (int)(xl-0.5);
|
||
|
|
x1 = x0+1;
|
||
|
|
t = xl - (x0+0.5);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (yl < 0.5)
|
||
|
|
{
|
||
|
|
y1 = y0 = 0;
|
||
|
|
u = 0;
|
||
|
|
}
|
||
|
|
else if (yl >= height-0.5)
|
||
|
|
{
|
||
|
|
y1 = y0 = height-1;
|
||
|
|
u = 0;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
y0 = (int)(yl-0.5);
|
||
|
|
y1 = y0+1;
|
||
|
|
u = yl - (y0+0.5);
|
||
|
|
}
|
||
|
|
|
||
|
|
T fll = map[y0*width + x0];
|
||
|
|
T fhl = map[y0*width + x1];
|
||
|
|
T flh = map[y1*width + x0];
|
||
|
|
T fhh = map[y1*width + x1];
|
||
|
|
|
||
|
|
return (T)((fhh - flh - fhl + fll) * u * t +
|
||
|
|
(fhl - fll) * t +
|
||
|
|
(flh - fll) * u +
|
||
|
|
fll);
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Does Bicubic Interpolation.
|
||
|
|
* \ingroup math */
|
||
|
|
template <class T, class TU>
|
||
|
|
inline T imBicubicInterpolation(int width, int height, T *map, double xl, double yl, TU Dummy)
|
||
|
|
{
|
||
|
|
int X[4], Y[4];
|
||
|
|
double t, u;
|
||
|
|
(void)Dummy;
|
||
|
|
|
||
|
|
if (xl >= width-0.5)
|
||
|
|
{
|
||
|
|
X[3] = X[2] = X[1] = width-1;
|
||
|
|
X[0] = X[1]-1;
|
||
|
|
t = 0;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
X[1] = (int)(xl-0.5);
|
||
|
|
if (X[1] < 0) X[1] = 0;
|
||
|
|
|
||
|
|
X[0] = X[1]-1;
|
||
|
|
X[2] = X[1]+1;
|
||
|
|
X[3] = X[1]+2;
|
||
|
|
|
||
|
|
if (X[0] < 0) X[0] = 0;
|
||
|
|
if (X[3] > width-1) X[3] = width-1;
|
||
|
|
|
||
|
|
t = xl - (X[1]+0.5);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (yl >= height-0.5)
|
||
|
|
{
|
||
|
|
Y[3] = Y[2] = Y[1] = height-1;
|
||
|
|
Y[0] = Y[1]-1;
|
||
|
|
u = 0;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
Y[1] = (int)(yl-0.5);
|
||
|
|
if (Y[1] < 0) Y[1] = 0;
|
||
|
|
|
||
|
|
Y[0] = Y[1]-1;
|
||
|
|
Y[2] = Y[1]+1;
|
||
|
|
Y[3] = Y[1]+2;
|
||
|
|
|
||
|
|
if (Y[0] < 0) Y[0] = 0;
|
||
|
|
if (Y[3] > height-1) Y[3] = height-1;
|
||
|
|
|
||
|
|
u = yl - (Y[1]+0.5);
|
||
|
|
}
|
||
|
|
|
||
|
|
double CX[4], CY[4];
|
||
|
|
|
||
|
|
// Optimize calculations
|
||
|
|
{
|
||
|
|
double c, c2, c3;
|
||
|
|
|
||
|
|
#define C0 (-c3 + 2.0f*c2 - c)
|
||
|
|
#define C1 ( c3 - 2.0f*c2 + 1.0)
|
||
|
|
#define C2 (-c3 + c2 + c)
|
||
|
|
#define C3 ( c3 - c2)
|
||
|
|
|
||
|
|
c = t;
|
||
|
|
c2 = c*c; c3 = c2*c;
|
||
|
|
CX[0] = C0; CX[1] = C1; CX[2] = C2; CX[3] = C3;
|
||
|
|
|
||
|
|
c = u;
|
||
|
|
c2 = c*c; c3 = c2*c;
|
||
|
|
CY[0] = C0; CY[1] = C1; CY[2] = C2; CY[3] = C3;
|
||
|
|
|
||
|
|
#undef C0
|
||
|
|
#undef C1
|
||
|
|
#undef C2
|
||
|
|
#undef C3
|
||
|
|
}
|
||
|
|
|
||
|
|
TU LineValue, Value;
|
||
|
|
double LineNorm, Norm;
|
||
|
|
|
||
|
|
Value = 0;
|
||
|
|
Norm = 0;
|
||
|
|
|
||
|
|
for (int y = 0; y < 4; y++)
|
||
|
|
{
|
||
|
|
LineValue = 0;
|
||
|
|
LineNorm = 0;
|
||
|
|
|
||
|
|
for (int x = 0; x < 4; x++)
|
||
|
|
{
|
||
|
|
LineValue += map[Y[y]*width+X[x]] * CX[x];
|
||
|
|
LineNorm += CX[x];
|
||
|
|
}
|
||
|
|
|
||
|
|
Value += LineValue * CY[y];
|
||
|
|
Norm += CY[y] * LineNorm;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (Norm == 0)
|
||
|
|
{
|
||
|
|
Value = 0;
|
||
|
|
return (T)Value;
|
||
|
|
}
|
||
|
|
|
||
|
|
Value = (Value/Norm);
|
||
|
|
|
||
|
|
int size = sizeof(T);
|
||
|
|
if (size == 1)
|
||
|
|
return (T)(Value<=(TU)0? (TU)0: Value<=(TU)255? Value: (TU)255);
|
||
|
|
else
|
||
|
|
return (T)(Value);
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Calculates minimum and maximum values.
|
||
|
|
* \ingroup math */
|
||
|
|
template <class T>
|
||
|
|
inline void imMinMax(const T *map, int count, T& min, T& max, int absolute = 0)
|
||
|
|
{
|
||
|
|
if (absolute)
|
||
|
|
min = imAbs(map[0]);
|
||
|
|
else
|
||
|
|
min = map[0];
|
||
|
|
|
||
|
|
max = min;
|
||
|
|
for (int i = 1; i < count; i++)
|
||
|
|
{
|
||
|
|
T value;
|
||
|
|
if (absolute)
|
||
|
|
value = imAbs(map[i]);
|
||
|
|
else
|
||
|
|
value = map[i];
|
||
|
|
|
||
|
|
if (value > max)
|
||
|
|
max = value;
|
||
|
|
else if (value < min)
|
||
|
|
min = value;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Calculates minimum and maximum values
|
||
|
|
* with additional considerations for data type conversion and normalized operations.
|
||
|
|
* \ingroup math */
|
||
|
|
template <class T>
|
||
|
|
inline void imMinMaxType(const T *map, int count, T& min, T& max, int absolute = 0)
|
||
|
|
{
|
||
|
|
int size_of = sizeof(imbyte);
|
||
|
|
if (sizeof(T) == size_of)
|
||
|
|
{
|
||
|
|
/* for imbyte is always the maximum interval */
|
||
|
|
min = 0;
|
||
|
|
max = 255;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
imMinMax(map, count, min, max, absolute);
|
||
|
|
|
||
|
|
/* if equal define a minimum interval */
|
||
|
|
if (min == max)
|
||
|
|
{
|
||
|
|
max = min + 1;
|
||
|
|
|
||
|
|
if (min != 0)
|
||
|
|
min = min - 1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif
|