File:Zernike polynomials.png
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![File:Zernike polynomials.png](https://upload.wikimedia.org/wikipedia/commons/thumb/3/37/Zernike_polynomials.png/257px-Zernike_polynomials.png?20080507073139)
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[edit]DescriptionZernike polynomials.png | Image of the Zernike_polynomials values |
Date | |
Source | Own work |
Author | Rocchini |
Permission (Reusing this file) |
CC-BY 3.0 |
Other versions |
[edit]
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Source Code
[edit]Ther dirty C++ code:
#include <stdio.h>
#include <stdlib.h>
#include <math.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(-1.0,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
[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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This file is licensed under the Creative Commons Attribution 3.0 Unported license.
- 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.
You may select the license of your choice.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 07:31, 7 May 2008 | ![]() | 793 × 1,850 (476 KB) | Rocchini (talk | contribs) | {{Information |Description=Image of the Zernike_polynomials values |Source=self-made |Date=2008-05-07 |Author= Rocchini |Permission=CC-BY 3.0 }} |
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