www.pudn.com > cximage602_full.rar > ximaint.cpp
// xImaInt.cpp : interpolation functions
/* 02/2004 - Branko Brevensek
* CxImage version 6.0.0 02/Feb/2008 - Davide Pizzolato - www.xdp.it
*/
#include "ximage.h"
#include "ximath.h"
#if CXIMAGE_SUPPORT_INTERPOLATION
////////////////////////////////////////////////////////////////////////////////
/**
* Recalculates coordinates according to specified overflow method.
* If pixel (x,y) lies within image, nothing changes.
*
* \param x, y - coordinates of pixel
* \param ofMethod - overflow method
*
* \return x, y - new coordinates (pixel (x,y) now lies inside image)
*
* \author ***bd*** 2.2004
*/
void CxImage::OverflowCoordinates(long &x, long &y, OverflowMethod const ofMethod)
{
if (IsInside(x,y)) return; //if pixel is within bounds, no change
switch (ofMethod) {
case OM_REPEAT:
//clip coordinates
x=max(x,0); x=min(x, head.biWidth-1);
y=max(y,0); y=min(y, head.biHeight-1);
break;
case OM_WRAP:
//wrap coordinates
x = x % head.biWidth;
y = y % head.biHeight;
if (x<0) x = head.biWidth + x;
if (y<0) y = head.biHeight + y;
break;
case OM_MIRROR:
//mirror pixels near border
if (x<0) x=((-x) % head.biWidth);
else if (x>=head.biWidth) x=head.biWidth-(x % head.biWidth + 1);
if (y<0) y=((-y) % head.biHeight);
else if (y>=head.biHeight) y=head.biHeight-(y % head.biHeight + 1);
break;
default:
return;
}//switch
}
////////////////////////////////////////////////////////////////////////////////
/**
* See OverflowCoordinates for integer version
* \author ***bd*** 2.2004
*/
void CxImage::OverflowCoordinates(float &x, float &y, OverflowMethod const ofMethod)
{
if (x>=0 && x=0 && y=head.biWidth) x=head.biWidth-((float)fmod(x, (float) head.biWidth) + 1);
if (y<0) y=(float)fmod(-y, (float) head.biHeight);
else if (y>=head.biHeight) y=head.biHeight-((float)fmod(y, (float) head.biHeight) + 1);
break;
default:
return;
}//switch
}
////////////////////////////////////////////////////////////////////////////////
/**
* Method return pixel color. Different methods are implemented for out of bounds pixels.
* If an image has alpha channel, alpha value is returned in .RGBReserved.
*
* \param x,y : pixel coordinates
* \param ofMethod : out-of-bounds method:
* - OF_WRAP - wrap over to pixels on other side of the image
* - OF_REPEAT - repeat last pixel on the edge
* - OF_COLOR - return input value of color
* - OF_BACKGROUND - return background color (if not set, return input color)
* - OF_TRANSPARENT - return transparent pixel
*
* \param rplColor : input color (returned for out-of-bound coordinates in OF_COLOR mode and if other mode is not applicable)
*
* \return color : color of pixel
* \author ***bd*** 2.2004
*/
RGBQUAD CxImage::GetPixelColorWithOverflow(long x, long y, OverflowMethod const ofMethod, RGBQUAD* const rplColor)
{
RGBQUAD color; //color to return
if ((!IsInside(x,y)) || pDib==NULL) { //is pixel within bouns?:
//pixel is out of bounds or no DIB
if (rplColor!=NULL)
color=*rplColor;
else {
color.rgbRed=color.rgbGreen=color.rgbBlue=255; color.rgbReserved=0; //default replacement colour: white transparent
}//if
if (pDib==NULL) return color;
//pixel is out of bounds:
switch (ofMethod) {
case OM_TRANSPARENT:
#if CXIMAGE_SUPPORT_ALPHA
if (AlphaIsValid()) {
//alpha transparency is supported and image has alpha layer
color.rgbReserved=0;
} else {
#endif //CXIMAGE_SUPPORT_ALPHA
//no alpha transparency
if (GetTransIndex()>=0) {
color=GetTransColor(); //single color transparency enabled (return transparent color)
}//if
#if CXIMAGE_SUPPORT_ALPHA
}//if
#endif //CXIMAGE_SUPPORT_ALPHA
return color;
case OM_BACKGROUND:
//return background color (if it exists, otherwise input value)
if (info.nBkgndIndex >= 0) {
if (head.biBitCount<24) color = GetPaletteColor((BYTE)info.nBkgndIndex);
else color = info.nBkgndColor;
}//if
return color;
case OM_REPEAT:
case OM_WRAP:
case OM_MIRROR:
OverflowCoordinates(x,y,ofMethod);
break;
default:
//simply return replacement color (OM_COLOR and others)
return color;
}//switch
}//if
//just return specified pixel (it's within bounds)
return BlindGetPixelColor(x,y);
}
////////////////////////////////////////////////////////////////////////////////
/**
* This method reconstructs image according to chosen interpolation method and then returns pixel (x,y).
* (x,y) can lie between actual image pixels. If (x,y) lies outside of image, method returns value
* according to overflow method.
* This method is very useful for geometrical image transformations, where destination pixel
* can often assume color value lying between source pixels.
*
* \param (x,y) - coordinates of pixel to return
* GPCI method recreates "analogue" image back from digital data, so x and y
* are float values and color value of point (1.1,1) will generally not be same
* as (1,1). Center of first pixel is at (0,0) and center of pixel right to it is (1,0).
* (0.5,0) is half way between these two pixels.
* \param inMethod - interpolation (reconstruction) method (kernel) to use:
* - IM_NEAREST_NEIGHBOUR - returns colour of nearest lying pixel (causes stairy look of
* processed images)
* - IM_BILINEAR - interpolates colour from four neighbouring pixels (softens image a bit)
* - IM_BICUBIC - interpolates from 16 neighbouring pixels (can produce "halo" artifacts)
* - IM_BICUBIC2 - interpolates from 16 neighbouring pixels (perhaps a bit less halo artifacts
than IM_BICUBIC)
* - IM_BSPLINE - interpolates from 16 neighbouring pixels (softens image, washes colours)
* (As far as I know, image should be prefiltered for this method to give
* good results... some other time :) )
* This method uses bicubic interpolation kernel from CXImage 5.99a and older
* versions.
* - IM_LANCZOS - interpolates from 12*12 pixels (slow, ringing artifacts)
*
* \param ofMethod - overflow method (see comments at GetPixelColorWithOverflow)
* \param rplColor - pointer to color used for out of borders pixels in OM_COLOR mode
* (and other modes if colour can't calculated in a specified way)
*
* \return interpolated color value (including interpolated alpha value, if image has alpha layer)
*
* \author ***bd*** 2.2004
*/
RGBQUAD CxImage::GetPixelColorInterpolated(
float x,float y,
InterpolationMethod const inMethod,
OverflowMethod const ofMethod,
RGBQUAD* const rplColor)
{
//calculate nearest pixel
int xi=(int)(x); if (x<0) xi--; //these replace (incredibly slow) floor (Visual c++ 2003, AMD Athlon)
int yi=(int)(y); if (y<0) yi--;
RGBQUAD color; //calculated colour
switch (inMethod) {
case IM_NEAREST_NEIGHBOUR:
return GetPixelColorWithOverflow((long)(x+0.5f), (long)(y+0.5f), ofMethod, rplColor);
default: {
//IM_BILINEAR: bilinear interpolation
if (xi<-1 || xi>=head.biWidth || yi<-1 || yi>=head.biHeight) { //all 4 points are outside bounds?:
switch (ofMethod) {
case OM_COLOR: case OM_TRANSPARENT: case OM_BACKGROUND:
//we don't need to interpolate anything with all points outside in this case
return GetPixelColorWithOverflow(-999, -999, ofMethod, rplColor);
default:
//recalculate coordinates and use faster method later on
OverflowCoordinates(x,y,ofMethod);
xi=(int)(x); if (x<0) xi--; //x and/or y have changed ... recalculate xi and yi
yi=(int)(y); if (y<0) yi--;
}//switch
}//if
//get four neighbouring pixels
if ((xi+1)=0 && (yi+1)=0 && head.biClrUsed==0) {
//all pixels are inside RGB24 image... optimize reading (and use fixed point arithmetic)
WORD wt1=(WORD)((x-xi)*256.0f), wt2=(WORD)((y-yi)*256.0f);
WORD wd=wt1*wt2>>8;
WORD wb=wt1-wd;
WORD wc=wt2-wd;
WORD wa=256-wt1-wc;
WORD wrr,wgg,wbb;
BYTE *pxptr=(BYTE*)info.pImage+yi*info.dwEffWidth+xi*3;
wbb=wa*(*pxptr++); wgg=wa*(*pxptr++); wrr=wa*(*pxptr++);
wbb+=wb*(*pxptr++); wgg+=wb*(*pxptr++); wrr+=wb*(*pxptr);
pxptr+=(info.dwEffWidth-5); //move to next row
wbb+=wc*(*pxptr++); wgg+=wc*(*pxptr++); wrr+=wc*(*pxptr++);
wbb+=wd*(*pxptr++); wgg+=wd*(*pxptr++); wrr+=wd*(*pxptr);
color.rgbRed=(BYTE) (wrr>>8); color.rgbGreen=(BYTE) (wgg>>8); color.rgbBlue=(BYTE) (wbb>>8);
#if CXIMAGE_SUPPORT_ALPHA
if (pAlpha) {
WORD waa;
//image has alpha layer... we have to do the same for alpha data
pxptr=AlphaGetPointer(xi,yi); //pointer to first byte
waa=wa*(*pxptr++); waa+=wb*(*pxptr); //first two pixels
pxptr+=(head.biWidth-1); //move to next row
waa+=wc*(*pxptr++); waa+=wd*(*pxptr); //and second row pixels
color.rgbReserved=(BYTE) (waa>>8);
} else
#endif
{ //Alpha not supported or no alpha at all
color.rgbReserved = 0;
}
return color;
} else {
//default (slower) way to get pixels (not RGB24 or some pixels out of borders)
float t1=x-xi, t2=y-yi;
float d=t1*t2;
float b=t1-d;
float c=t2-d;
float a=1-t1-c;
RGBQUAD rgb11,rgb21,rgb12,rgb22;
rgb11=GetPixelColorWithOverflow(xi, yi, ofMethod, rplColor);
rgb21=GetPixelColorWithOverflow(xi+1, yi, ofMethod, rplColor);
rgb12=GetPixelColorWithOverflow(xi, yi+1, ofMethod, rplColor);
rgb22=GetPixelColorWithOverflow(xi+1, yi+1, ofMethod, rplColor);
//calculate linear interpolation
color.rgbRed=(BYTE) (a*rgb11.rgbRed+b*rgb21.rgbRed+c*rgb12.rgbRed+d*rgb22.rgbRed);
color.rgbGreen=(BYTE) (a*rgb11.rgbGreen+b*rgb21.rgbGreen+c*rgb12.rgbGreen+d*rgb22.rgbGreen);
color.rgbBlue=(BYTE) (a*rgb11.rgbBlue+b*rgb21.rgbBlue+c*rgb12.rgbBlue+d*rgb22.rgbBlue);
#if CXIMAGE_SUPPORT_ALPHA
if (AlphaIsValid())
color.rgbReserved=(BYTE) (a*rgb11.rgbReserved+b*rgb21.rgbReserved+c*rgb12.rgbReserved+d*rgb22.rgbReserved);
else
#endif
{ //Alpha not supported or no alpha at all
color.rgbReserved = 0;
}
return color;
}//if
}//default
case IM_BICUBIC:
case IM_BICUBIC2:
case IM_BSPLINE:
case IM_BOX:
case IM_HERMITE:
case IM_HAMMING:
case IM_SINC:
case IM_BLACKMAN:
case IM_BESSEL:
case IM_GAUSSIAN:
case IM_QUADRATIC:
case IM_MITCHELL:
case IM_CATROM:
case IM_HANNING:
case IM_POWER:
//bicubic interpolation(s)
if (((xi+2)<0) || ((xi-1)>=head.biWidth) || ((yi+2)<0) || ((yi-1)>=head.biHeight)) { //all points are outside bounds?:
switch (ofMethod) {
case OM_COLOR: case OM_TRANSPARENT: case OM_BACKGROUND:
//we don't need to interpolate anything with all points outside in this case
return GetPixelColorWithOverflow(-999, -999, ofMethod, rplColor);
break;
default:
//recalculate coordinates and use faster method later on
OverflowCoordinates(x,y,ofMethod);
xi=(int)(x); if (x<0) xi--; //x and/or y have changed ... recalculate xi and yi
yi=(int)(y); if (y<0) yi--;
}//switch
}//if
//some variables needed from here on
int xii,yii; //x any y integer indexes for loops
float kernel, kernelyc; //kernel cache
float kernelx[12], kernely[4]; //precalculated kernel values
float rr,gg,bb,aa; //accumulated color values
//calculate multiplication factors for all pixels
int i;
switch (inMethod) {
case IM_BICUBIC:
for (i=0; i<4; i++) {
kernelx[i]=KernelCubic((float)(xi+i-1-x));
kernely[i]=KernelCubic((float)(yi+i-1-y));
}//for i
break;
case IM_BICUBIC2:
for (i=0; i<4; i++) {
kernelx[i]=KernelGeneralizedCubic((float)(xi+i-1-x), -0.5);
kernely[i]=KernelGeneralizedCubic((float)(yi+i-1-y), -0.5);
}//for i
break;
case IM_BSPLINE:
for (i=0; i<4; i++) {
kernelx[i]=KernelBSpline((float)(xi+i-1-x));
kernely[i]=KernelBSpline((float)(yi+i-1-y));
}//for i
break;
case IM_BOX:
for (i=0; i<4; i++) {
kernelx[i]=KernelBox((float)(xi+i-1-x));
kernely[i]=KernelBox((float)(yi+i-1-y));
}//for i
break;
case IM_HERMITE:
for (i=0; i<4; i++) {
kernelx[i]=KernelHermite((float)(xi+i-1-x));
kernely[i]=KernelHermite((float)(yi+i-1-y));
}//for i
break;
case IM_HAMMING:
for (i=0; i<4; i++) {
kernelx[i]=KernelHamming((float)(xi+i-1-x));
kernely[i]=KernelHamming((float)(yi+i-1-y));
}//for i
break;
case IM_SINC:
for (i=0; i<4; i++) {
kernelx[i]=KernelSinc((float)(xi+i-1-x));
kernely[i]=KernelSinc((float)(yi+i-1-y));
}//for i
break;
case IM_BLACKMAN:
for (i=0; i<4; i++) {
kernelx[i]=KernelBlackman((float)(xi+i-1-x));
kernely[i]=KernelBlackman((float)(yi+i-1-y));
}//for i
break;
case IM_BESSEL:
for (i=0; i<4; i++) {
kernelx[i]=KernelBessel((float)(xi+i-1-x));
kernely[i]=KernelBessel((float)(yi+i-1-y));
}//for i
break;
case IM_GAUSSIAN:
for (i=0; i<4; i++) {
kernelx[i]=KernelGaussian((float)(xi+i-1-x));
kernely[i]=KernelGaussian((float)(yi+i-1-y));
}//for i
break;
case IM_QUADRATIC:
for (i=0; i<4; i++) {
kernelx[i]=KernelQuadratic((float)(xi+i-1-x));
kernely[i]=KernelQuadratic((float)(yi+i-1-y));
}//for i
break;
case IM_MITCHELL:
for (i=0; i<4; i++) {
kernelx[i]=KernelMitchell((float)(xi+i-1-x));
kernely[i]=KernelMitchell((float)(yi+i-1-y));
}//for i
break;
case IM_CATROM:
for (i=0; i<4; i++) {
kernelx[i]=KernelCatrom((float)(xi+i-1-x));
kernely[i]=KernelCatrom((float)(yi+i-1-y));
}//for i
break;
case IM_HANNING:
for (i=0; i<4; i++) {
kernelx[i]=KernelHanning((float)(xi+i-1-x));
kernely[i]=KernelHanning((float)(yi+i-1-y));
}//for i
break;
case IM_POWER:
for (i=0; i<4; i++) {
kernelx[i]=KernelPower((float)(xi+i-1-x));
kernely[i]=KernelPower((float)(yi+i-1-y));
}//for i
break;
}//switch
rr=gg=bb=aa=0;
if (((xi+2)=1 && ((yi+2)=1) && !IsIndexed()) {
//optimized interpolation (faster pixel reads) for RGB24 images with all pixels inside bounds
BYTE *pxptr, *pxptra;
for (yii=yi-1; yii255) rr=255; if (rr<0) rr=0; color.rgbRed=(BYTE) rr;
if (gg>255) gg=255; if (gg<0) gg=0; color.rgbGreen=(BYTE) gg;
if (bb>255) bb=255; if (bb<0) bb=0; color.rgbBlue=(BYTE) bb;
#if CXIMAGE_SUPPORT_ALPHA
if (AlphaIsValid()) {
if (aa>255) aa=255; if (aa<0) aa=0; color.rgbReserved=(BYTE) aa;
} else
#endif
{ //Alpha not supported or no alpha at all
color.rgbReserved = 0;
}
return color;
case IM_LANCZOS:
//lanczos window (16*16) sinc interpolation
if (((xi+6)<0) || ((xi-5)>=head.biWidth) || ((yi+6)<0) || ((yi-5)>=head.biHeight)) {
//all points are outside bounds
switch (ofMethod) {
case OM_COLOR: case OM_TRANSPARENT: case OM_BACKGROUND:
//we don't need to interpolate anything with all points outside in this case
return GetPixelColorWithOverflow(-999, -999, ofMethod, rplColor);
break;
default:
//recalculate coordinates and use faster method later on
OverflowCoordinates(x,y,ofMethod);
xi=(int)(x); if (x<0) xi--; //x and/or y have changed ... recalculate xi and yi
yi=(int)(y); if (y<0) yi--;
}//switch
}//if
for (xii=xi-5; xii=0) && ((yi+6)=0) && !IsIndexed()) {
//optimized interpolation (faster pixel reads) for RGB24 images with all pixels inside bounds
BYTE *pxptr, *pxptra;
for (yii=yi-5; yii255) rr=255; if (rr<0) rr=0; color.rgbRed=(BYTE) rr;
if (gg>255) gg=255; if (gg<0) gg=0; color.rgbGreen=(BYTE) gg;
if (bb>255) bb=255; if (bb<0) bb=0; color.rgbBlue=(BYTE) bb;
#if CXIMAGE_SUPPORT_ALPHA
if (AlphaIsValid()) {
if (aa>255) aa=255; if (aa<0) aa=0; color.rgbReserved=(BYTE) aa;
} else
#endif
{ //Alpha not supported or no alpha at all
color.rgbReserved = 0;
}
return color;
}//switch
}
////////////////////////////////////////////////////////////////////////////////
/**
* Helper function for GetAreaColorInterpolated.
* Adds 'surf' portion of image pixel with color 'color' to (rr,gg,bb,aa).
*/
void CxImage::AddAveragingCont(RGBQUAD const &color, float const surf, float &rr, float &gg, float &bb, float &aa)
{
rr+=color.rgbRed*surf;
gg+=color.rgbGreen*surf;
bb+=color.rgbBlue*surf;
#if CXIMAGE_SUPPORT_ALPHA
aa+=color.rgbReserved*surf;
#endif
}
////////////////////////////////////////////////////////////////////////////////
/**
* This method is similar to GetPixelColorInterpolated, but this method also properly handles
* subsampling.
* If you need to sample original image with interval of more than 1 pixel (as when shrinking an image),
* you should use this method instead of GetPixelColorInterpolated or aliasing will occur.
* When area width and height are both less than pixel, this method gets pixel color by interpolating
* color of frame center with selected (inMethod) interpolation by calling GetPixelColorInterpolated.
* If width and height are more than 1, method calculates color by averaging color of pixels within area.
* Interpolation method is not used in this case. Pixel color is interpolated by averaging instead.
* If only one of both is more than 1, method uses combination of interpolation and averaging.
* Chosen interpolation method is used, but since it is averaged later on, there is little difference
* between IM_BILINEAR (perhaps best for this case) and better methods. IM_NEAREST_NEIGHBOUR again
* leads to aliasing artifacts.
* This method is a bit slower than GetPixelColorInterpolated and when aliasing is not a problem, you should
* simply use the later.
*
* \param xc, yc - center of (rectangular) area
* \param w, h - width and height of area
* \param inMethod - interpolation method that is used, when interpolation is used (see above)
* \param ofMethod - overflow method used when retrieving individual pixel colors
* \param rplColor - replacement colour to use, in OM_COLOR
*
* \author ***bd*** 2.2004
*/
RGBQUAD CxImage::GetAreaColorInterpolated(
float const xc, float const yc, float const w, float const h,
InterpolationMethod const inMethod,
OverflowMethod const ofMethod,
RGBQUAD* const rplColor)
{
RGBQUAD color; //calculated colour
if (h<=1 && w<=1) {
//both width and height are less than one... we will use interpolation of center point
return GetPixelColorInterpolated(xc, yc, inMethod, ofMethod, rplColor);
} else {
//area is wider and/or taller than one pixel:
CxRect2 area(xc-w/2.0f, yc-h/2.0f, xc+w/2.0f, yc+h/2.0f); //area
int xi1=(int)(area.botLeft.x+0.49999999f); //low x
int yi1=(int)(area.botLeft.y+0.49999999f); //low y
int xi2=(int)(area.topRight.x+0.5f); //top x
int yi2=(int)(area.topRight.y+0.5f); //top y (for loops)
float rr,gg,bb,aa; //red, green, blue and alpha components
rr=gg=bb=aa=0;
int x,y; //loop counters
float s=0; //surface of all pixels
float cps; //surface of current crosssection
if (h>1 && w>1) {
//width and height of area are greater than one pixel, so we can employ "ordinary" averaging
CxRect2 intBL, intTR; //bottom left and top right intersection
intBL=area.CrossSection(CxRect2(((float)xi1)-0.5f, ((float)yi1)-0.5f, ((float)xi1)+0.5f, ((float)yi1)+0.5f));
intTR=area.CrossSection(CxRect2(((float)xi2)-0.5f, ((float)yi2)-0.5f, ((float)xi2)+0.5f, ((float)yi2)+0.5f));
float wBL, wTR, hBL, hTR;
wBL=intBL.Width(); //width of bottom left pixel-area intersection
hBL=intBL.Height(); //height of bottom left...
wTR=intTR.Width(); //width of top right...
hTR=intTR.Height(); //height of top right...
AddAveragingCont(GetPixelColorWithOverflow(xi1,yi1,ofMethod,rplColor), wBL*hBL, rr, gg, bb, aa); //bottom left pixel
AddAveragingCont(GetPixelColorWithOverflow(xi2,yi1,ofMethod,rplColor), wTR*hBL, rr, gg, bb, aa); //bottom right pixel
AddAveragingCont(GetPixelColorWithOverflow(xi1,yi2,ofMethod,rplColor), wBL*hTR, rr, gg, bb, aa); //top left pixel
AddAveragingCont(GetPixelColorWithOverflow(xi2,yi2,ofMethod,rplColor), wTR*hTR, rr, gg, bb, aa); //top right pixel
//bottom and top row
for (x=xi1+1; x255) rr=255; if (rr<0) rr=0; color.rgbRed=(BYTE) rr;
if (gg>255) gg=255; if (gg<0) gg=0; color.rgbGreen=(BYTE) gg;
if (bb>255) bb=255; if (bb<0) bb=0; color.rgbBlue=(BYTE) bb;
#if CXIMAGE_SUPPORT_ALPHA
if (AlphaIsValid()) {
if (aa>255) aa=255; if (aa<0) aa=0; color.rgbReserved=(BYTE) aa;
}//if
#endif
}//if
return color;
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelBSpline(const float x)
{
if (x>2.0f) return 0.0f;
// thanks to Kristian Kratzenstein
float a, b, c, d;
float xm1 = x - 1.0f; // Was calculatet anyway cause the "if((x-1.0f) < 0)"
float xp1 = x + 1.0f;
float xp2 = x + 2.0f;
if ((xp2) <= 0.0f) a = 0.0f; else a = xp2*xp2*xp2; // Only float, not float -> double -> float
if ((xp1) <= 0.0f) b = 0.0f; else b = xp1*xp1*xp1;
if (x <= 0) c = 0.0f; else c = x*x*x;
if ((xm1) <= 0.0f) d = 0.0f; else d = xm1*xm1*xm1;
return (0.16666666666666666667f * (a - (4.0f * b) + (6.0f * c) - (4.0f * d)));
/* equivalent
if (x < -2.0)
return(0.0f);
if (x < -1.0)
return((2.0f+x)*(2.0f+x)*(2.0f+x)*0.16666666666666666667f);
if (x < 0.0)
return((4.0f+x*x*(-6.0f-3.0f*x))*0.16666666666666666667f);
if (x < 1.0)
return((4.0f+x*x*(-6.0f+3.0f*x))*0.16666666666666666667f);
if (x < 2.0)
return((2.0f-x)*(2.0f-x)*(2.0f-x)*0.16666666666666666667f);
return(0.0f);
*/
}
////////////////////////////////////////////////////////////////////////////////
/**
* Bilinear interpolation kernel:
\verbatim
/
| 1-t , if 0 <= t <= 1
h(t) = | t+1 , if -1 <= t < 0
| 0 , otherwise
\
\endverbatim
* ***bd*** 2.2004
*/
float CxImage::KernelLinear(const float t)
{
// if (0<=t && t<=1) return 1-t;
// if (-1<=t && t<0) return 1+t;
// return 0;
//
if (t < -1.0f)
return 0.0f;
if (t < 0.0f)
return 1.0f+t;
if (t < 1.0f)
return 1.0f-t;
return 0.0f;
}
////////////////////////////////////////////////////////////////////////////////
/**
* Bicubic interpolation kernel (a=-1):
\verbatim
/
| 1-2|t|**2+|t|**3 , if |t| < 1
h(t) = | 4-8|t|+5|t|**2-|t|**3 , if 1<=|t|<2
| 0 , otherwise
\
\endverbatim
* ***bd*** 2.2004
*/
float CxImage::KernelCubic(const float t)
{
float abs_t = (float)fabs(t);
float abs_t_sq = abs_t * abs_t;
if (abs_t<1) return 1-2*abs_t_sq+abs_t_sq*abs_t;
if (abs_t<2) return 4 - 8*abs_t +5*abs_t_sq - abs_t_sq*abs_t;
return 0;
}
////////////////////////////////////////////////////////////////////////////////
/**
* Bicubic kernel (for a=-1 it is the same as BicubicKernel):
\verbatim
/
| (a+2)|t|**3 - (a+3)|t|**2 + 1 , |t| <= 1
h(t) = | a|t|**3 - 5a|t|**2 + 8a|t| - 4a , 1 < |t| <= 2
| 0 , otherwise
\
\endverbatim
* Often used values for a are -1 and -1/2.
*/
float CxImage::KernelGeneralizedCubic(const float t, const float a)
{
float abs_t = (float)fabs(t);
float abs_t_sq = abs_t * abs_t;
if (abs_t<1) return (a+2)*abs_t_sq*abs_t - (a+3)*abs_t_sq + 1;
if (abs_t<2) return a*abs_t_sq*abs_t - 5*a*abs_t_sq + 8*a*abs_t - 4*a;
return 0;
}
////////////////////////////////////////////////////////////////////////////////
/**
* Lanczos windowed sinc interpolation kernel with radius r.
\verbatim
/
h(t) = | sinc(t)*sinc(t/r) , if |t| r) return 0;
if (t==0) return 1;
float pit=PI*t;
float pitd=pit/r;
return (float)((sin(pit)/pit) * (sin(pitd)/pitd));
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelBox(const float x)
{
if (x < -0.5f)
return 0.0f;
if (x < 0.5f)
return 1.0f;
return 0.0f;
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelHermite(const float x)
{
if (x < -1.0f)
return 0.0f;
if (x < 0.0f)
return (-2.0f*x-3.0f)*x*x+1.0f;
if (x < 1.0f)
return (2.0f*x-3.0f)*x*x+1.0f;
return 0.0f;
// if (fabs(x)>1) return 0.0f;
// return(0.5f+0.5f*(float)cos(PI*x));
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelHanning(const float x)
{
if (fabs(x)>1) return 0.0f;
return (0.5f+0.5f*(float)cos(PI*x))*((float)sin(PI*x)/(PI*x));
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelHamming(const float x)
{
if (x < -1.0f)
return 0.0f;
if (x < 0.0f)
return 0.92f*(-2.0f*x-3.0f)*x*x+1.0f;
if (x < 1.0f)
return 0.92f*(2.0f*x-3.0f)*x*x+1.0f;
return 0.0f;
// if (fabs(x)>1) return 0.0f;
// return(0.54f+0.46f*(float)cos(PI*x));
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelSinc(const float x)
{
if (x == 0.0)
return(1.0);
return((float)sin(PI*x)/(PI*x));
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelBlackman(const float x)
{
//if (fabs(x)>1) return 0.0f;
return (0.42f+0.5f*(float)cos(PI*x)+0.08f*(float)cos(2.0f*PI*x));
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelBessel_J1(const float x)
{
double p, q;
register long i;
static const double
Pone[] =
{
0.581199354001606143928050809e+21,
-0.6672106568924916298020941484e+20,
0.2316433580634002297931815435e+19,
-0.3588817569910106050743641413e+17,
0.2908795263834775409737601689e+15,
-0.1322983480332126453125473247e+13,
0.3413234182301700539091292655e+10,
-0.4695753530642995859767162166e+7,
0.270112271089232341485679099e+4
},
Qone[] =
{
0.11623987080032122878585294e+22,
0.1185770712190320999837113348e+20,
0.6092061398917521746105196863e+17,
0.2081661221307607351240184229e+15,
0.5243710262167649715406728642e+12,
0.1013863514358673989967045588e+10,
0.1501793594998585505921097578e+7,
0.1606931573481487801970916749e+4,
0.1e+1
};
p = Pone[8];
q = Qone[8];
for (i=7; i >= 0; i--)
{
p = p*x*x+Pone[i];
q = q*x*x+Qone[i];
}
return (float)(p/q);
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelBessel_P1(const float x)
{
double p, q;
register long i;
static const double
Pone[] =
{
0.352246649133679798341724373e+5,
0.62758845247161281269005675e+5,
0.313539631109159574238669888e+5,
0.49854832060594338434500455e+4,
0.2111529182853962382105718e+3,
0.12571716929145341558495e+1
},
Qone[] =
{
0.352246649133679798068390431e+5,
0.626943469593560511888833731e+5,
0.312404063819041039923015703e+5,
0.4930396490181088979386097e+4,
0.2030775189134759322293574e+3,
0.1e+1
};
p = Pone[5];
q = Qone[5];
for (i=4; i >= 0; i--)
{
p = p*(8.0/x)*(8.0/x)+Pone[i];
q = q*(8.0/x)*(8.0/x)+Qone[i];
}
return (float)(p/q);
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelBessel_Q1(const float x)
{
double p, q;
register long i;
static const double
Pone[] =
{
0.3511751914303552822533318e+3,
0.7210391804904475039280863e+3,
0.4259873011654442389886993e+3,
0.831898957673850827325226e+2,
0.45681716295512267064405e+1,
0.3532840052740123642735e-1
},
Qone[] =
{
0.74917374171809127714519505e+4,
0.154141773392650970499848051e+5,
0.91522317015169922705904727e+4,
0.18111867005523513506724158e+4,
0.1038187585462133728776636e+3,
0.1e+1
};
p = Pone[5];
q = Qone[5];
for (i=4; i >= 0; i--)
{
p = p*(8.0/x)*(8.0/x)+Pone[i];
q = q*(8.0/x)*(8.0/x)+Qone[i];
}
return (float)(p/q);
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelBessel_Order1(float x)
{
float p, q;
if (x == 0.0)
return (0.0f);
p = x;
if (x < 0.0)
x=(-x);
if (x < 8.0)
return(p*KernelBessel_J1(x));
q = (float)sqrt(2.0f/(PI*x))*(float)(KernelBessel_P1(x)*(1.0f/sqrt(2.0f)*(sin(x)-cos(x)))-8.0f/x*KernelBessel_Q1(x)*
(-1.0f/sqrt(2.0f)*(sin(x)+cos(x))));
if (p < 0.0f)
q = (-q);
return (q);
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelBessel(const float x)
{
if (x == 0.0f)
return(PI/4.0f);
return(KernelBessel_Order1(PI*x)/(2.0f*x));
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelGaussian(const float x)
{
return (float)(exp(-2.0f*x*x)*0.79788456080287f/*sqrt(2.0f/PI)*/);
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelQuadratic(const float x)
{
if (x < -1.5f)
return(0.0f);
if (x < -0.5f)
return(0.5f*(x+1.5f)*(x+1.5f));
if (x < 0.5f)
return(0.75f-x*x);
if (x < 1.5f)
return(0.5f*(x-1.5f)*(x-1.5f));
return(0.0f);
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelMitchell(const float x)
{
#define KM_B (1.0f/3.0f)
#define KM_C (1.0f/3.0f)
#define KM_P0 (( 6.0f - 2.0f * KM_B ) / 6.0f)
#define KM_P2 ((-18.0f + 12.0f * KM_B + 6.0f * KM_C) / 6.0f)
#define KM_P3 (( 12.0f - 9.0f * KM_B - 6.0f * KM_C) / 6.0f)
#define KM_Q0 (( 8.0f * KM_B + 24.0f * KM_C) / 6.0f)
#define KM_Q1 ((-12.0f * KM_B - 48.0f * KM_C) / 6.0f)
#define KM_Q2 (( 6.0f * KM_B + 30.0f * KM_C) / 6.0f)
#define KM_Q3 (( -1.0f * KM_B - 6.0f * KM_C) / 6.0f)
if (x < -2.0)
return(0.0f);
if (x < -1.0)
return(KM_Q0-x*(KM_Q1-x*(KM_Q2-x*KM_Q3)));
if (x < 0.0f)
return(KM_P0+x*x*(KM_P2-x*KM_P3));
if (x < 1.0f)
return(KM_P0+x*x*(KM_P2+x*KM_P3));
if (x < 2.0f)
return(KM_Q0+x*(KM_Q1+x*(KM_Q2+x*KM_Q3)));
return(0.0f);
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelCatrom(const float x)
{
if (x < -2.0)
return(0.0f);
if (x < -1.0)
return(0.5f*(4.0f+x*(8.0f+x*(5.0f+x))));
if (x < 0.0)
return(0.5f*(2.0f+x*x*(-5.0f-3.0f*x)));
if (x < 1.0)
return(0.5f*(2.0f+x*x*(-5.0f+3.0f*x)));
if (x < 2.0)
return(0.5f*(4.0f+x*(-8.0f+x*(5.0f-x))));
return(0.0f);
}
////////////////////////////////////////////////////////////////////////////////
float CxImage::KernelPower(const float x, const float a)
{
if (fabs(x)>1) return 0.0f;
return (1.0f - (float)fabs(pow(x,a)));
}
////////////////////////////////////////////////////////////////////////////////
#endif