File:Zernike polynomials2.png
![File:Zernike polynomials2.png](https://upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Zernike_polynomials2.png/600px-Zernike_polynomials2.png?20110723204259)
Size of this preview: 600 × 600 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 768 × 768 pixels | 1,024 × 1,024 pixels | 1,568 × 1,568 pixels.
Original file (1,568 × 1,568 pixels, file size: 478 KB, MIME type: image/png)
File information
Structured data
Captions
Captions
Add a one-line explanation of what this file represents
Summary
editDescriptionZernike polynomials2.png |
English: The Zernike_polynomials values |
Date | |
Source |
Own work (Original caption: " self-made ") |
Author | Rocchini (Zom-B at en.wikipedia) |
Other versions |
[edit]
|
Source Code
editThe dirty C++ code:
#include <stdio.h>
#include <stdlib.h>
static double fact( int n ) { // The factorial function!
double f = 1;
while(n>1)
f *= n--;
return f;
}
static inline unsigned char f2b( double f ) { // float to byte
if(f<0) f = 0; if(f>1) f = 1;
int i = f*256; if(i>255) i = 255;
return i;
}
void HSV2RGB(double h, double s, double v, unsigned char rgb[3] ) { // the classic hue scale
if (s == 0) {
rgb[0] = rgb[1] = rgb[2] = f2b(v);
} else {
double v_h = h * 6;
double v_i = floor(v_h);
double v_1 = v * (1 - s);
double v_2 = v * (1 - s * (v_h - v_i));
double v_3 = v * (1 - s * (1 - (v_h - v_i)));
double v_r,v_g,v_b;
if (v_i == 0) {v_r = v; v_g = v_3; v_b = v_1;}
else if (v_i == 1) {v_r = v_2; v_g = v; v_b = v_1;}
else if (v_i == 2) {v_r = v_1; v_g = v; v_b = v_3;}
else if (v_i == 3) {v_r = v_1; v_g = v_2; v_b = v ;}
else if (v_i == 4) {v_r = v_3; v_g = v_1; v_b = v ;}
else {v_r = v; v_g = v_1; v_b = v_2;};
rgb[0] = f2b(v_r);
rgb[1] = f2b(v_g);
rgb[2] = f2b(v_b);
}
}
double zernike_polynomials( int m, int n, double ro, double th ) { // the polynomial hitself
double Rmnro = 0;
bool even = m>=0;
if(m<0) m = -m;
if( (n-m)%2 ) return 0;
for(int k=0;k<=(n-m)/2;++k) {
Rmnro += pow(ro,n-2*k)*
( pow(-1,k) * fact(n-k) ) /
( fact( k) *
fact((n+m)/2-k) *
fact((n-m)/2-k)
);
}
if(even) return Rmnro * cos(m*th);
else return Rmnro * sin(m*th);
}
void main() {
const double NO_VALUE = 42; const int B = 64;
const int SX = 1024;
const int SY = 1024;
const int LX = 3; const int LY = 7;
int pairs[21][2] =
{
{ 0,0},
{-1,1},{ 1,1},
{-2,2},{ 0,2},{ 2,2},
{-3,3},{-1,3},{ 1,3},{ 3,3},
{-4,4},{-2,4},{ 0,4},{ 2,4},{ 4,4},
{-5,5},{-3,5},{-1,5},{ 1,5},{ 3,5},{ 5,5},
};
unsigned char * img = new unsigned char[LX*SX*LY*SY*3];
int ix,iy,q = 0;
for(iy=0;iy<LY;++iy) for(ix=0;ix<LX;++ix) {
int m = pairs[q][0];
int n = pairs[q][1];
for(int j=0;j<SY;++j) {
double y = double(SY/2-j)/(SY/2-B);
for(int i=0;i<SX;++i) {
double x = double(SX/2-i)/(SX/2-B);
double ro = sqrt(x*x+y*y);
double th = atan2(y,x);
double z = NO_VALUE;
if(ro<=1)
z = zernike_polynomials(m,n,ro,th);
unsigned char * rgb = img+3*( i+SX*(ix+LX*(j+SY*iy)) );
if(z == NO_VALUE )
rgb[0] = rgb[1] = rgb[2] = 255;
else {
if(z>=0) z = pow( z,0.8); // little enance
else z = -pow(-z,0.8);
z = (z+1)/2; // normalize
if(z<0) z = 0;
if(z>1) z = 1;
HSV2RGB( 2.0*z/3.0, 0.8, 0.9, rgb );
}
}
}
printf("%03d%%\n",q*100/(LX*LY)); ++q;
}
FILE * fp = fopen("c:\\temp\\zernike.ppm","wb");
fprintf(fp,"P6\n%d %d\n255\n",SX*LX,SY*LY);
fwrite(img,1,LX*SX*LY*SY*3,fp);
fclose(fp);
delete[] img;
}
Licensing
editThis is a retouched picture, which means that it has been digitally altered from its original version. Modifications: Made into pyramid shape. The original can be viewed here: Zernike polynomials.png: ![]()
|
Zom-B at en.wikipedia, the copyright holder of this work, hereby publishes it under the following license:
![w:en:Creative Commons](https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/CC_some_rights_reserved.svg/90px-CC_some_rights_reserved.svg.png)
![attribution](https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cc-by_new_white.svg/24px-Cc-by_new_white.svg.png)
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
Attribution: Zom-B at en.wikipedia
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
Original upload log
editThe original description page was here. All following user names refer to en.wikipedia.
- 2009-09-30 22:19 Zom-B 1568×1568× (489636 bytes) == Dettagli == {{Information |Description=Image of the Zernike_polynomials values |Source=self-made |Date=2008-05-07 |Author= [[User:Rocchini|Rocchini]] |Permission=CC-BY 3.0 }} {{RetouchedPicture|Made into pyramid shape|editor=|orig=Zernike_polynomials.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 20:42, 23 July 2011 | ![]() | 1,568 × 1,568 (478 KB) | Akkakk (talk | contribs) | {{Information |Description={{en|Image of the Zernike_polynomials values}} |Source=Transferred from [http://en.wikipedia.org en.wikipedia]<br/> (Original text : ''self-made'') |Date={{Date|2008|05|07}}<br/> ({{Date|2009|09|30}} (original upload date)) |Aut |
You cannot overwrite this file.
File usage on Commons
The following 8 pages use this file:
File usage on other wikis
The following other wikis use this file:
- Usage on ca.wikipedia.org
- Usage on en.wikipedia.org
- Usage on es.wikipedia.org
- Usage on fa.wikipedia.org
- Usage on fr.wikipedia.org
- Usage on it.wikipedia.org
- Usage on ja.wikipedia.org
- Usage on ms.wikipedia.org
- Usage on ru.wikipedia.org
- Usage on sr.wikipedia.org