Perlin Noise issue - c++

I've created a Perlin noise function. My issue is when I generate a terrain map from the noise it ends up blocky, nothing like the cloudlike images I've seen. I'm curious on what I'm doing wrong (if anything).
here's my code:
main.cpp
#include "PerlinNoise.h"
#include <stdio.h>
#include <SDL/SDL.h>
void DrawPixel(SDL_Surface *screen, int x, int y, Uint8 R, Uint8 G, Uint8 B);
SDL_Surface *Render_Noise(int w, int h, int r, int g, int b);
PerlinNoise noiseGen(2,.5,25);
int main(int argc, char **argv)
{
SDL_Init(SDL_INIT_EVERYTHING);
SDL_Surface *screen = SDL_SetVideoMode(500,500,32,SDL_SWSURFACE);
SDL_Surface *noise = Render_Noise(500,500,255,255,255);
SDL_SaveBMP(noise, "noise.bmp");
bool quit = false;
while(!quit)
{
SDL_Event e;
SDL_WaitEvent(&e);
switch(e.type)
{
case SDL_QUIT:
quit = true;
}
SDL_BlitSurface(noise,NULL,screen,NULL);
SDL_Flip(screen);
SDL_Delay(2000);
}
SDL_FreeSurface(noise);
SDL_Quit();
return 0;
}
void DrawPixel(SDL_Surface *screen, int x, int y, Uint8 R, Uint8 G, Uint8 B)
{
Uint32 color = SDL_MapRGB(screen->format, R, G, B);
if(SDL_MUSTLOCK(screen))
{
if(SDL_LockSurface(screen) < 0)
{
return;
}
}
switch(screen->format->BytesPerPixel)
{
case 1:
{
Uint8 *bufp;
bufp = (Uint8 *)screen->pixels + y*screen->pitch + x;
*bufp = color;
}
break;
case 2:
{
Uint16 *bufp;
bufp = (Uint16 *)screen->pixels + y*screen->pitch/2 + x;
*bufp = color;
}
break;
case 3:
{
Uint8 *bufp;
bufp = (Uint8 *)screen->pixels + y*screen->pitch + x;
*(bufp+screen->format->Rshift/8) = R;
*(bufp+screen->format->Bshift/8) = B;
*(bufp+screen->format->Gshift/8) = G;
}
break;
case 4:
{
Uint32 *bufp;
bufp = (Uint32 *)screen->pixels + y*screen->pitch/4 + x;
*bufp = color;
}
break;
}
if(SDL_MUSTLOCK(screen))
{
SDL_UnlockSurface(screen);
}
SDL_UpdateRect(screen, x, y, 1, 1);
}
SDL_Surface *Render_Noise(int w, int h, int r, int g, int b)
{
SDL_Surface *ret = SDL_CreateRGBSurface(SDL_SWSURFACE,w,h,32,0,0,0,0); //create an empty image
for(int y = 0; y < h; y++)
{
for(int x = 0; x < w; x++)
{
double getnoise = 0;
for(int a = 0; a < noiseGen.n; a++)
{
getnoise += noiseGen.generateNoise(x,y);
noiseGen.z = rand() % 100;
}
getnoise / noiseGen.n;
int color = (int)((getnoise * 128.0) + 128.0); //convert noise to 0-256 value
if (color > 255)
color = 255;
if (color < 0)
color = 0;
DrawPixel( ret, x, y, (int)((r/255.0) * (double)color), (int)((g/255.0) * (double)color), (int)((b/255.0) * (double)color) );
}
}
return ret;
}
perlinnoise.cpp
#include "PerlinNoise.h"
PerlinNoise::PerlinNoise(int octaves, double persistence, int zoom)
{
p = persistence;
n = octaves - 1;
z = zoom;
}
PerlinNoise::~PerlinNoise()
{
}
///<summary>Gets a random number using x and y as seeds </summary>
///<param name = x> A double value </param>
///<param name = y> A double value </param>
///<returns> A random number between -1.0 and 1.0 </returns>
inline double PerlinNoise::noise(double x, double y)
{
int n = x + y * 57;
n = (n << 13) ^ n;
return ( 1.0 - ( (n * (n * n * 15731 + 789221) + 1376312589) & 0x7fffffff) / 1073741824.0);
}
///<summary> Smooths out noise values </summary>
///<param name = x> a double value </param>
///<param name = y> a double value </param>
///<returns> a smoothed value between -1.0 and 1.0 </returns>
double PerlinNoise::smoothNoise(double x, double y)
{
double corners = (noise(x+1, y+1) + noise(x+1,y-1) + noise(x-1,y+1) + noise(x-1,y-1)) / 16;
double sides = (noise(x,y+1) + noise(x,y-1) + noise(x+1,y) + noise(x-1,y)) / 8;
double center = noise(x,y) / 4;
return corners + sides + center;
}
///<summary> Cosine Interpolation </summary>
///<param name = a> The low value to be interpolated </param>
///<param name = b> The high value to be interpolated </param>
///<param name = x> A value between -1.0 and 1.0 </param>
///<returns> Interpolated value between a and b </returns>
double PerlinNoise::cosineInterpolation(double a, double b, double x)
{
double ft = x * 3.1415927;
double f = (1.0 - cos(ft)) * .5;
return a * (1.0 - f) + b * f;
}
///<summary> Gets smoothed noise values and interpolates them </summary>
///<param name = x> a double value </param>
///<param name = y> a double value </param>
///<returns> a value between -1 and 1 that's been smoothed and interpolated </returns>
double PerlinNoise::interpolatedNoise(double x, double y)
{
double integer_x = (int)x;
double fractional_x = x - integer_x;
double integer_y = (int)y;
double fractional_y = y - integer_y;
double v1 = smoothNoise(integer_x, integer_y);
double v2 = smoothNoise(integer_x + 1, integer_y);
double v3 = smoothNoise(integer_x, integer_y + 1);
double v4 = smoothNoise(integer_x + 1, integer_y + 1);
double inter1 = cosineInterpolation(v1, v2, fractional_x);
double inter2 = cosineInterpolation(v3, v4, fractional_x);
return cosineInterpolation(inter1, inter2, fractional_y);
}
double PerlinNoise::generateNoise(double x, double y)
{
double total = 0;
for(int i = 0; i < n; i++)
{
frequency = pow(2.0,i);
amplitude = pow(p,i);
total = total + interpolatedNoise(x * frequency / z, y * frequency / z) * amplitude;
}
return total;
}

Found the problem, my persistence was much lower than it should be, upping that I got the cloudlike image I expected

Related

Scaling png font down

Is there a way to scale down with highest quality a font which is png image in opengl at startup? I tried gluScaleImage but there are many artefacts. Is there anything that uses lanczos or something like that? I don't want to write a shader or anything that does the scaling runtime.
This is based on an algorithm, I copied decades ago from the German c't Magazin, and still use it from time to time for similar issues like described by OP.
bool scaleDown(
const Image &imgSrc,
Image &imgDst,
int w, int h,
int align)
{
const int wSrc = imgSrc.w(), hSrc = imgSrc.h();
assert(w > 0 && w <= wSrc && h > 0 && h <= hSrc);
// compute scaling factors
const double sx = (double)wSrc / (double)w;
const double sy = (double)hSrc / (double)h;
const double sxy = sx * sy;
// prepare destination image
imgDst.resize(w, h, (w * 3 + align - 1) / align * align);
// cache some data
const uint8 *const dataSrc = imgSrc.data();
const int bPRSrc = imgSrc.bPR();
// perform scaling
for (int y = 0; y < h; ++y) {
const double yStart = sy * y;
const double yEnd = std::min(sy * (y + 1), (double)hSrc);
const int yStartInt = (int)yStart;
const int yEndInt = (int)yEnd - (yEndInt == yEnd);
const double tFrm = 1 + yStartInt - yStart, bFrm = yEnd - yEndInt;
for (int x = 0; x < w; ++x) {
const double xStart = sx * x;
const double xEnd = std::min(sx * (x + 1), (double)wSrc);
const int xStartInt = (int)xStart;
const int xEndInt = (int)xEnd - (xEndInt == xEnd);
double lFrm = 1 + xStartInt - xStart, rFrm = xEnd - xEndInt;
double pixel[3] = { 0.0, 0.0, 0.0 }; // values of target pixel
for (int i = yStartInt; i <= yEndInt; ++i) {
int jData = i * bPRSrc + xStartInt * 3;
for (int j = xStartInt; j <= xEndInt; ++j) {
double pixelAdd[3];
for (int k = 0; k < 3; ++k) {
pixelAdd[k] = (double)dataSrc[jData++] / sxy;
}
if (j == xStartInt) {
for (int k = 0; k < 3; ++k) pixelAdd[k] *= lFrm;
} else if (j == xEndInt) {
for (int k = 0; k < 3; ++k) pixelAdd[k] *= rFrm;
}
if (i == yStartInt) {
for (int k = 0; k < 3; ++k) pixelAdd[k] *= tFrm;
} else if (i == yEndInt) {
for (int k = 0; k < 3; ++k) pixelAdd[k] *= bFrm;
}
for (int k = 0; k < 3; ++k) pixel[k] += pixelAdd[k];
}
}
imgDst.setPixel(x, y,
(uint8)pixel[0], (uint8)pixel[1], (uint8)pixel[2]);
}
}
// done
return true;
}
If I got it right, this implements a bilinear interpolation.
I don't dare to call it a Minimal Complete Verifiable Example although this is what I intended to do.
The complete sample application:
A simplified class Image
image.h:
#ifndef IMAGE_H
#define IMAGE_H
#include <vector>
// convenience type for bytes
typedef unsigned char uint8;
// image helper class
class Image {
private: // variables:
int _w, _h; // image size
size_t _bPR; // bytes per row
std::vector<uint8> _data; // image data
public: // methods:
// constructor.
Image(): _w(0), _h(0), _bPR(0) { }
// destructor.
~Image() = default;
// copy constructor.
Image(const Image&) = delete; // = default; would work as well.
// copy assignment.
Image& operator=(const Image&) = delete; // = default; would work as well.
// returns width of image.
int w() const { return _w; }
// returns height of image.
int h() const { return _h; }
// returns bytes per row.
size_t bPR() const { return _bPR; }
// returns pointer to image data.
const uint8* data(
int y = 0) // row number
const {
return &_data[y * _bPR];
}
// returns data size (in bytes).
size_t size() const { return _data.size(); }
// clears image.
void clear();
// resizes image.
uint8* resize( // returns allocated buffer
int w, // image width
int h, // image height
int bPR); // bytes per row
// returns pixel.
int getPixel(
int x, // column
int y) // row
const;
// sets pixel.
void setPixel(
int x, // column
int y, // row
uint8 r, uint8 g, uint8 b);
// sets pixel.
void setPixel(
int x, // column
int y, // row
int value) // RGB value
{
setPixel(x, y, value & 0xff, value >> 8 & 0xff, value >> 16 & 0xff);
}
};
// helper functions:
inline uint8 getR(int value) { return value & 0xff; }
inline uint8 getG(int value) { return value >> 8 & 0xff; }
inline uint8 getB(int value) { return value >> 16 & 0xff; }
#endif // IMAGE_H
image.cc:
#include <cassert>
#include "image.h"
// clears image.
void Image::clear()
{
_data.clear(); _w = _h = _bPR = 0;
}
// allocates image data.
uint8* Image::resize( // returns allocated buffer
int w, // image width
int h, // image height
int bPR) // bits per row
{
assert(w >= 0 && 3 * w <= bPR);
assert(h >= 0);
_w = w; _h = h; _bPR = bPR;
const size_t size = h * bPR;
_data.resize(size);
return _data.data();
}
// returns pixel.
int Image::getPixel(
int x, // column
int y) // row
const {
assert(x >= 0 && x < _w);
assert(y >= 0 && y < _h);
const size_t offs = y * _bPR + 3 * x;
return _data[offs + 0]
| _data[offs + 1] << 8
| _data[offs + 2] << 16;
}
// sets pixel.
void Image::setPixel(
int x, // column
int y, // row
uint8 r, uint8 g, uint8 b) // R, G, B values
{
assert(x >= 0 && x < _w);
assert(y >= 0 && y < _h);
const size_t offs = y * _bPR + 3 * x;
_data[offs + 0] = r;
_data[offs + 1] = g;
_data[offs + 2] = b;
}
Image Scaling
imageScale.h:
#ifndef IMAGE_SCALE_H
#define IMAGE_SCALE_H
#include "image.h"
/* scales an image to a certain width and height.
*
* Note:
* imgSrc and imgDst may not be identical.
*/
bool scaleTo( // returns true if successful
const Image &imgSrc, // source image
Image &imgDst, // destination image
int w, int h, // destination width and height
int align = 4); // row alignment
/* scales an image about a certain horizontal/vertical scaling factor.
*
* Note:
* imgSrc and imgDst may not be identical.
*/
inline bool scaleXY( // returns true if successful
const Image &imgSrc, // source image
Image &imgDst, // destination image
double sX, // horizontal scaling factor (must be > 0 but not too large)
double sY, // vertical scaling factor (must be > 0 but not too large)
int align = 4) // row alignment
{
return sX > 0.0 && sY > 0.0
? scaleTo(imgSrc, imgDst,
(int)(sX * imgSrc.w()), (int)(sY * imgSrc.h()), align)
: false;
}
/* scales an image about a certain scaling factor.
*
* Note:
* imgSrc and imgDst may not be identical.
*/
inline bool scale( // returns true if successful
const Image &imgSrc, // source image
Image &imgDst, // destination image
double s, // scaling factor (must be > 0 but not too large)
int align = 4) // row alignment
{
return scaleXY(imgSrc, imgDst, s, s, align);
}
#endif // IMAGE_SCALE_H
imageScale.cc:
#include <cassert>
#include <algorithm>
#include "imageScale.h"
namespace {
template <typename VALUE>
VALUE clip(VALUE value, VALUE min, VALUE max)
{
return value < min ? min : value > max ? max : value;
}
bool scaleDown(
const Image &imgSrc,
Image &imgDst,
int w, int h,
int align)
{
const int wSrc = imgSrc.w(), hSrc = imgSrc.h();
assert(w > 0 && w <= wSrc && h > 0 && h <= hSrc);
// compute scaling factors
const double sx = (double)wSrc / (double)w;
const double sy = (double)hSrc / (double)h;
const double sxy = sx * sy;
// prepare destination image
imgDst.resize(w, h, (w * 3 + align - 1) / align * align);
// cache some data
const uint8 *const dataSrc = imgSrc.data();
const int bPRSrc = imgSrc.bPR();
// perform scaling
for (int y = 0; y < h; ++y) {
const double yStart = sy * y;
const double yEnd = std::min(sy * (y + 1), (double)hSrc);
const int yStartInt = (int)yStart;
const int yEndInt = (int)yEnd - (yEndInt == yEnd);
const double tFrm = 1 + yStartInt - yStart, bFrm = yEnd - yEndInt;
for (int x = 0; x < w; ++x) {
const double xStart = sx * x;
const double xEnd = std::min(sx * (x + 1), (double)wSrc);
const int xStartInt = (int)xStart;
const int xEndInt = (int)xEnd - (xEndInt == xEnd);
double lFrm = 1 + xStartInt - xStart, rFrm = xEnd - xEndInt;
double pixel[3] = { 0.0, 0.0, 0.0 }; // values of target pixel
for (int i = yStartInt; i <= yEndInt; ++i) {
int jData = i * bPRSrc + xStartInt * 3;
for (int j = xStartInt; j <= xEndInt; ++j) {
double pixelAdd[3];
for (int k = 0; k < 3; ++k) {
pixelAdd[k] = (double)dataSrc[jData++] / sxy;
}
if (j == xStartInt) {
for (int k = 0; k < 3; ++k) pixelAdd[k] *= lFrm;
} else if (j == xEndInt) {
for (int k = 0; k < 3; ++k) pixelAdd[k] *= rFrm;
}
if (i == yStartInt) {
for (int k = 0; k < 3; ++k) pixelAdd[k] *= tFrm;
} else if (i == yEndInt) {
for (int k = 0; k < 3; ++k) pixelAdd[k] *= bFrm;
}
for (int k = 0; k < 3; ++k) pixel[k] += pixelAdd[k];
}
}
imgDst.setPixel(x, y,
(uint8)pixel[0], (uint8)pixel[1], (uint8)pixel[2]);
}
}
// done
return true;
}
bool scaleUp(
const Image &imgSrc,
Image &imgDst,
int w, int h,
int align)
{
const int wSrc = imgSrc.w(), hSrc = imgSrc.h();
assert(w && w >= wSrc && h && h >= hSrc);
// compute scaling factors
const double sx = (double)wSrc / (double)w;
const double sy = (double)hSrc / (double)h;
// prepare destination image
imgDst.resize(w, h, (w * 3 + align - 1) / align * align);
// cache some data
const uint8 *const dataSrc = imgSrc.data();
const int bPRSrc = imgSrc.bPR();
// perform scaling
for (int y = 0; y < h; ++y) {
const double yStart = sy * y;
const double yEnd = std::min(sy * (y + 1), (double)hSrc - 1);
const int yStartInt = (int)yStart;
const int yEndInt = (int)yEnd;
if (yStartInt < yEndInt) {
const double bFract = clip((double)((yEnd - yEndInt) / sy), 0.0, 1.0);
const double tFract = 1.0 - bFract;
for (int x = 0; x < w; ++x) {
const double xStart = sx * x;
const double xEnd = std::min(sx * (x + 1), (double)wSrc - 1);
const int xStartInt = (int)xStart, xEndInt = (int)xEnd;
double pixel[4];
if (xStartInt < xEndInt) {
const double rFract
= clip((double)((xEnd - xEndInt) / sx), 0.0, 1.0);
const double lFract = 1.0 - rFract;
int jData = yStartInt * bPRSrc + xStartInt * 3;
for (int k = 0; k < 3; ++k) {
pixel[k] = tFract * lFract * dataSrc[jData++];
}
for (int k = 0; k < 3; ++k) {
pixel[k] += tFract * rFract * dataSrc[jData++];
}
jData = yEndInt * bPRSrc + xStartInt * 3;
for (int k = 0; k < 3; ++k) {
pixel[k] += bFract * lFract *dataSrc[jData++];
}
for (int k = 0; k < 3; ++k) {
pixel[k] += bFract * rFract *dataSrc[jData++];
}
} else {
int jData = yStartInt * bPRSrc + xStartInt * 3;
for (int k = 0; k < 3; ++k) {
pixel[k] = tFract * dataSrc[jData++];
}
jData = yEndInt * bPRSrc + xStartInt * 3;
for (int k = 0; k < 3; ++k) {
pixel[k] += bFract * dataSrc[jData++];
}
}
imgDst.setPixel(x, y,
(uint8)pixel[0], (uint8)pixel[1], (uint8)pixel[2]);
}
} else {
for (int x = 0; x < w; ++x) {
const double xStart = sx * x;
const double xEnd = std::min(sx * (x + 1), (double)wSrc - 1);
const int xStartInt = (int)xStart, xEndInt = (int)xEnd;
double pixel[3];
if (xStartInt < xEndInt) {
const double rFract
= clip((double)((xEnd - xEndInt) / sx), 0.0, 1.0);
const double lFract = 1.0 - rFract;
int jData = yStartInt * bPRSrc + xStartInt * 3;
for (int k = 0; k < 3; ++k) {
pixel[k] = lFract * dataSrc[jData++];
}
for (int k = 0; k < 3; ++k) {
pixel[k] += rFract * dataSrc[jData++];
}
} else {
int jData = yStartInt * bPRSrc + xStartInt * 3;
for (int k = 0; k < 3; ++k) pixel[k] = dataSrc[jData++];
}
imgDst.setPixel(x, y,
(uint8)pixel[0], (uint8)pixel[1], (uint8)pixel[2]);
}
}
}
// done
return true;
}
} // namespace
bool scaleTo(const Image &imgSrc, Image &imgDst, int w, int h, int align)
{
Image imgTmp;
return w <= 0 || h <= 0 ? false
: w >= imgSrc.w() && h >= imgSrc.h()
? scaleUp(imgSrc, imgDst, w, h, align)
: w <= imgSrc.w() && h <= imgSrc.h()
? scaleDown(imgSrc, imgDst, w, h, align)
: w >= imgSrc.w()
? scaleUp(imgSrc, imgTmp, w, imgSrc.h(), 1)
&& scaleDown(imgTmp, imgDst, w, h, align)
: scaleDown(imgSrc, imgTmp, w, imgSrc.h(), 1)
&& scaleUp(imgTmp, imgDst, w, h, align);
}
PPM file IO
imagePPM.h:
#ifndef IMAGE_PPM_H
#define IMAGE_PPM_H
#include <iostream>
#include "image.h"
// reads a binary PPM file.
bool readPPM( // returns true if successful
std::istream &in, // input stream (must be opened with std::ios::binary)
Image &img, // image to read into
int align = 4); // row alignment
// writes binary PPM file.
bool writePPM( // returns true if successful
std::ostream &out, // output stream (must be opened with std::ios::binary)
const Image &img); // image to write from
#endif // IMAGE_PPM_H
imagePPM.cc:
#include <sstream>
#include <string>
#include "imagePPM.h"
// reads a binary PPM file.
bool readPPM( // returns true if successful
std::istream &in, // input stream (must be opened with std::ios::binary)
Image &img, // image to read into
int align) // row alignment
{
// parse header
std::string buffer;
if (!getline(in, buffer)) return false;
if (buffer != "P6") {
std::cerr << "Wrong header! 'P6' expected.\n";
return false;
}
int w = 0, h = 0, t = 0;
for (int i = 0; i < 3;) {
if (!getline(in, buffer)) return false;
if (buffer.empty()) continue; // skip empty lines
if (buffer[0] == '#') continue; // skip comments
std::istringstream str(buffer);
switch (i) {
case 0:
if (!(str >> w)) continue;
++i;
case 1:
if (!(str >> h)) continue;
++i;
case 2:
if (!(str >> t)) continue;
++i;
}
}
if (t != 255) {
std::cerr << "Unsupported format! t = 255 expected.\n";
return false;
}
// allocate image buffer
uint8 *data = img.resize(w, h, (w * 3 + align - 1) / align * align);
// read data
for (int i = 0; i < h; ++i) {
if (!in.read((char*)data, 3 * img.w())) return false;
data += img.bPR();
}
// done
return true;
}
// writes binary PPM file.
bool writePPM( // returns true if successful
std::ostream &out, // output stream (must be opened with std::ios::binary)
const Image &img) // image to write from
{
// write header
if (!(out << "P6\n" << img.w() << ' ' << img.h() << " 255\n")) return false;
// write image data
for (size_t y = 0; y < img.h(); ++y) {
const uint8 *const data = img.data(y);
if (!out.write((const char*)data, 3 * img.w())) return false;
}
// done
return true;
}
The main application
scaleRGBImg.cc:
#include <iostream>
#include <fstream>
#include <string>
#include "image.h"
#include "imagePPM.h"
#include "imageScale.h"
int main(int argc, char **argv)
{
// read command line arguments
if (argc <= 3) {
std::cerr << "Missing arguments!\n";
std::cout
<< "Usage:\n"
<< " scaleRGBImg IN_FILE SCALE OUT_FILE\n";
return 1;
}
const std::string inFile = argv[1];
char *end;
const double s = std::strtod(argv[2], &end);
if (end == argv[2] || *end != '\0') {
std::cerr << "Invalid scale factor '" << argv[2] << "'!\n";
return 1;
}
if (s <= 0.0) {
std::cerr << "Invalid scale factor " << s << "!\n";
return 1;
}
const std::string outFile = argv[3];
// read image
Image imgSrc;
{ std::ifstream fIn(inFile.c_str(), std::ios::binary);
if (!readPPM(fIn, imgSrc)) {
std::cerr << "Reading '" << inFile << "' failed!\n";
return 1;
}
}
// scale image
Image imgDst;
if (!scale(imgSrc, imgDst, s)) {
std::cerr << "Scaling failed!\n";
return 1;
}
// write image
{ std::ofstream fOut(outFile.c_str(), std::ios::binary);
if (!writePPM(fOut, imgDst) || (fOut.close(), !fOut.good())) {
std::cerr << "Writing '" << outFile << "' failed!\n";
return 1;
}
}
// done
return 0;
}
Test
Compiled in cygwin64:
$ g++ -std=c++11 -o scaleRGBImg scaleRGBImg.cc image.cc imagePPM.cc imageScale.cc
$
A sample image test.ppm for a test – converted to PPM in GIMP:
Test with the sample image:
$ for I in 0.8 0.6 0.4 0.2 ; do echo ./scaleRGBImg test.ppm $I test.$I.ppm ; done
./scaleRGBImg test.ppm 0.8 test.0.8.ppm
./scaleRGBImg test.ppm 0.6 test.0.6.ppm
./scaleRGBImg test.ppm 0.4 test.0.4.ppm
./scaleRGBImg test.ppm 0.2 test.0.2.ppm
$ for I in 0.8 0.6 0.4 0.2 ; do ./scaleRGBImg test.ppm $I test.$I.ppm ; done
$
This is what came out:
test.0.8.ppm:
test.0.6.ppm:
test.0.4.ppm:
test.0.2.ppm:

bool variable behaves strangely in opengl fragment shader

I am using OpenGL version 4.2. I am calling a function inside another function in OpenGL fragment shader where the inner function (pix2loc) returns a bool variable as function argument and then the outer function (pix2ang) uses this bool variable to take a decision. More precisely, I have:
void pix2ang (int order_, bool is_nest, int pix, out double theta, out double phi)
{
double z, sth;
bool have_sth;
pix2loc (order_, is_nest, pix, z, phi, sth, have_sth);
if(have_sth)
theta = atan(float(sth),float(z));
else
theta = acos(float(z));
}
where the function pix2loc returns boolean variable have_sth as function argument as follows:
void pix2loc (int order_, bool is_nest, int pix, out double z, out double phi, out double sth, out bool have_sth)
{
.....
if <condition true>
have_sth = true;
else
have_sth = false;
}
I noticed that inside pix2ang have_sth does not work as expected, but if I inverse the if statements and change it to
if(!have_sth)
theta = acos(float(z));
else
theta = atan(float(sth),float(z));
then it works as expected. This makes the code un-reliable and I don't exactly understand what the problem is.
Ok. I decided to write the whole function of pix2loc such that it may help to understand the problem.
void pix2loc (int order_, bool is_nest, int pix, out double z, out double phi, out double sth, out bool have_sth)
{
int nside_ = int(1)<<order_;
int npface_ = nside_<<order_;
int ncap_ = (npface_-nside_)<<1;
int npix_ = 12*npface_;
double fact2_ = 4./npix_;
double fact1_ = (nside_<<1)*fact2_;
have_sth=false;
if (!is_nest)
{
if (pix<ncap_) // North Polar cap
{
int iring = (1+int(isqrt(1+2*pix)))>>1; // counted from North pole
int iphi = (pix+1) - 2*iring*(iring-1);
double tmp=(iring*iring)*fact2_;
z = 1.0 - tmp;
if (z>0.99) { sth=sqrt(tmp*(2.-tmp)); have_sth=true; }
phi = (iphi-0.5) * halfpi/iring;
}
else if (pix<(npix_-ncap_)) // Equatorial region
{
int nl4 = 4*nside_;
int ip = pix - ncap_;
int tmp = (order_>=0) ? ip>>(order_+2) : ip/nl4;
int iring = tmp + nside_;
int iphi = ip-nl4*tmp+1;
// 1 if iring+nside is odd, 1/2 otherwise
double fodd = bool((iring+nside_)&1) ? 1. : 0.5;
z = (2*nside_-iring)*fact1_;
phi = (iphi-fodd) * pi*0.75*fact1_;
}
else // South Polar cap
{
int ip = npix_ - pix;
int iring = (1+int(isqrt(2*ip-1)))>>1; // counted from South pole
int iphi = 4*iring + 1 - (ip - 2*iring*(iring-1));
double tmp=(iring*iring)*fact2_;
z = tmp - 1.0;
if (z<-0.99) { sth=sqrt(tmp*(2.-tmp)); have_sth=true; }
phi = (iphi-0.5) * halfpi/iring;
}
}
else
{
int face_num, ix, iy;
nest2xyf(order_, pix,ix,iy,face_num);
int jr = (int(jrll[face_num])<<order_) - ix - iy - 1;
int nr;
if (jr<nside_)
{
nr = jr;
double tmp=(nr*nr)*fact2_;
z = 1 - tmp;
if (z>0.99) { sth=sqrt(tmp*(2.-tmp)); have_sth=true; }
}
else if (jr > 3*nside_)
{
nr = nside_*4-jr;
double tmp=(nr*nr)*fact2_;
z = tmp - 1;
if (z<-0.99) { sth=sqrt(tmp*(2.-tmp)); have_sth=true; }
}
else
{
nr = nside_;
z = (2*nside_-jr)*fact1_;
}
int tmp=int(jpll[face_num])*nr+ix-iy;
if (tmp<0) tmp+=8*nr;
phi = (nr==nside_) ? 0.75*halfpi*tmp*fact1_ : (0.5*halfpi*tmp)/nr;
}
}
where pi, halfpi, jrll and jpll are constant variable defined in the begining of the fragment shader as
#version 420 core
const double pi = 3.141592653589793;
const double halfpi = 0.5 * pi;
const int jrll[] = { 2,2,2,2,3,3,3,3,4,4,4,4 };
const int jpll[] = { 1,3,5,7,0,2,4,6,1,3,5,7 };

How to to find smallest (optimized) distance between two vectors in C++

I'm translating Python's version of 'page_dewarper' (https://mzucker.github.io/2016/08/15/page-dewarping.html) into C++. I'm going to use dlib, which is a fantastic tool, that helped me in a few optimization problems before. In line 748 of Github repo (https://github.com/mzucker/page_dewarp/blob/master/page_dewarp.py) Matt uses optimize function from Scipy, to find the minimal distance between two vectors. I think, my C++ equivalent should be solve_least_squares_lm() or solve_least_squares(). I'll give a concrete example to analyze.
My data:
a) dstpoints is a vector with OpenCV points - std::vector<cv::Point2f> (I have 162 points in this example, they are not changing),
b) ppts is also std::vector<cv::Point2f> and the same size as dstpoints.
std::vector<cv::Point2f> ppts = project_keypoints(params, input);
It is dependent on:
- dlib::column_vector 'input' is 2*162=324 long and is not changing,
- dlib::column_vector 'params' is 189 long and its values should be changed to get the minimal value of variable 'suma', something like this:
double suma = 0.0;
for (int i=0; i<dstpoints_size; i++)
{
suma += pow(dstpoints[i].x - ppts[i].x, 2);
suma += pow(dstpoints[i].y - ppts[i].y, 2);
}
I'm looking for 'params' vector that will give me the smallest value of 'suma' variable. Least squares algorithm seems to be a good option to solve it: http://dlib.net/dlib/optimization/optimization_least_squares_abstract.h.html#solve_least_squares, but I don't know if it is good for my case.
I think, my problem is that for every different 'params' vector I get different 'ppts' vector, not only single value, and I don't know if solve_least_squares function can match my example.
I must calculate residual for every point. I think, my 'list' from aforementioned link should be something like this:
(ppts[i].x - dstpoints[i].x, ppts[i].y - dstpoints[i].y, ppts[i+1].x - dstpoints[i+1].x, ppts[i+1].y - dstpoints[i+1].y, etc.)
, where 'ppts' vector depends on 'params' vector and then this problem can be solved with least squares algorithm. I don't know how to create data_samples with these assumptions, because it requires dlib::input_vector for every sample, as it is shown in example: http://dlib.net/least_squares_ex.cpp.html.
Am I thinking right?
I'm doing the same thing this days. My solution is writing a Powell Class by myself. It works, but really slowly. The program takes 2 minutes in dewarping linguistics_thesis.jpg.
I don't know what cause the program running so slowly. Maybe because of the algorithm or the code has some extra loop. I'm a Chinese student and my school only have java lessons. So it is normal if you find some extra codes in my codes.
Here is my Powell class.
using namespace std;
using namespace cv;
class MyPowell
{
public:
vector<vector<double>> xi;
vector<double> pcom;
vector<double> xicom;
vector<Point2d> dstpoints;
vector<double> myparams;
vector<double> params;
vector<Point> keypoint_index;
Point2d dst_br;
Point2d dims;
int N;
int itmax;
int ncom;
int iter;
double fret, ftol;
int usingAorB;
MyPowell(vector<Point2d> &dstpoints, vector<double> &params, vector<Point> &keypoint_index);
MyPowell(Point2d &dst_br, vector<double> &params, Point2d & dims);
MyPowell();
double obj(vector<double> &params);
void powell(vector<double> &p, vector<vector<double>> &xi, double ftol, double &fret);
double sign(double a);// , double b);
double sqr(double a);
void linmin(vector<double> &p, vector<double> &xit, int n, double &fret);
void mnbrak(double & ax, double & bx, double & cx,
double & fa, double & fb, double & fc);
double f1dim(double x);
double brent(double ax, double bx, double cx, double & xmin, double tol);
vector<double> usePowell();
void erase(vector<double>& pbar, vector<double> &prr, vector<double> &pr);
};
#include"Powell.h"
MyPowell::MyPowell(vector<Point2d> &dstpoints, vector<double>& params, vector<Point> &keypoint_index)
{
this->dstpoints = dstpoints;
this->myparams = params;
this->keypoint_index = keypoint_index;
N = params.size();
itmax = N * N;
usingAorB = 1;
}
MyPowell::MyPowell(Point2d & dst_br, vector<double>& params, Point2d & dims)
{
this->dst_br = dst_br;
this->myparams.push_back(dims.x);
this->myparams.push_back(dims.y);
this->params = params;
this->dims = dims;
N = 2;
itmax = N * 1000;
usingAorB = 2;
}
MyPowell::MyPowell()
{
usingAorB = 3;
}
double MyPowell::obj(vector<double> &myparams)
{
if (1 == usingAorB)
{
vector<Point2d> ppts = Dewarp::projectKeypoints(keypoint_index, myparams);
double total = 0;
for (int i = 0; i < ppts.size(); i++)
{
double x = dstpoints[i].x - ppts[i].x;
double y = dstpoints[i].y - ppts[i].y;
total += (x * x + y * y);
}
return total;
}
else if(2 == usingAorB)
{
dims.x = myparams[0];
dims.y = myparams[1];
//cout << "dims.x " << dims.x << " dims.y " << dims.y << endl;
vector<Point2d> vdims = { dims };
vector<Point2d> proj_br = Dewarp::projectXY(vdims, params);
double total = 0;
double x = dst_br.x - proj_br[0].x;
double y = dst_br.y - proj_br[0].y;
total += (x * x + y * y);
return total;
}
return 0;
}
void MyPowell::powell(vector<double> &x, vector<vector<double>> &direc, double ftol, double &fval)
{
vector<double> x1;
vector<double> x2;
vector<double> direc1;
int myitmax = 20;
if(N>500)
myitmax = 10;
else if (N > 300)
{
myitmax = 15;
}
double fx2, t, fx, dum, delta;
fval = obj(x);
int bigind;
for (int j = 0; j < N; j++)
{
x1.push_back(x[j]);
}
int iter = 0;
while (true)
{
do
{
do
{
iter += 1;
fx = fval;
bigind = 0;
delta = 0.0;
for (int i = 0; i < N; i++)
{
direc1 = direc[i];
fx2 = fval;
linmin(x, direc1, N, fval);
if (fabs(fx2 - fval) > delta)
{
delta = fabs(fx2 - fval);
bigind = i;
}
}
if (2.0 * fabs(fx - fval) <= ftol * (fabs(fx) + fabs(fval)) + 1e-7)
{
erase(direc1, x2, x1);
return;
}
if (iter >= itmax)
{
cout << "powell exceeding maximum iterations" << endl;
return;
}
if (!x2.empty())
{
x2.clear();
}
for (int j = 0; j < N; j++)
{
x2.push_back(2.0*x[j] - x1[j]);
direc1[j] = x[j] - x1[j];
x1[j] = x[j];
}
myitmax--;
cout << fx2 << endl;
fx2 = obj(x2);
if (myitmax < 0)
return;
} while (fx2 >= fx);
dum = fx - 2 * fval + fx2;
t = 2.0*dum*pow((fx - fval - delta), 2) - delta * pow((fx - fx2), 2);
} while (t >= 0.0);
linmin(x, direc1, N, fval);
direc[bigind] = direc1;
}
}
double MyPowell::sign(double a)//, double b)
{
if (a > 0.0)
{
return 1;
}
else
{
if (a < 0.0)
{
return -1;
}
}
return 0;
}
double MyPowell::sqr(double a)
{
return a * a;
}
void MyPowell::linmin(vector<double>& p, vector<double>& xit, int n, double &fret)
{
double tol = 1e-2;
ncom = n;
pcom = p;
xicom = xit;
double ax = 0.0;
double xx = 1.0;
double bx = 0.0;
double fa, fb, fx, xmin;
mnbrak(ax, xx, bx, fa, fx, fb);
fret = brent(ax, xx, bx, xmin, tol);
for (int i = 0; i < n; i++)
{
xit[i] = (xmin * xit[i]);
p[i] += xit[i];
}
}
void MyPowell::mnbrak(double & ax, double & bx, double & cx,
double & fa, double & fb, double & fc)
{
const double GOLD = 1.618034, GLIMIT = 110.0, TINY = 1e-20;
double val, fw, tmp2, tmp1, w, wlim;
double denom;
fa = f1dim(ax);
fb = f1dim(bx);
if (fb > fa)
{
val = ax;
ax = bx;
bx = val;
val = fb;
fb = fa;
fa = val;
}
cx = bx + GOLD * (bx - ax);
fc = f1dim(cx);
int iter = 0;
while (fb >= fc)
{
tmp1 = (bx - ax) * (fb - fc);
tmp2 = (bx - cx) * (fb - fa);
val = tmp2 - tmp1;
if (fabs(val) < TINY)
{
denom = 2.0*TINY;
}
else
{
denom = 2.0*val;
}
w = bx - ((bx - cx)*tmp2 - (bx - ax)*tmp1) / (denom);
wlim = bx + GLIMIT * (cx - bx);
if ((bx - w) * (w - cx) > 0.0)
{
fw = f1dim(w);
if (fw < fc)
{
ax = bx;
fa = fb;
bx = w;
fb = fw;
return;
}
else if (fw > fb)
{
cx = w;
fc = fw;
return;
}
w = cx + GOLD * (cx - bx);
fw = f1dim(w);
}
else
{
if ((cx - w)*(w - wlim) >= 0.0)
{
fw = f1dim(w);
if (fw < fc)
{
bx = cx;
cx = w;
w = cx + GOLD * (cx - bx);
fb = fc;
fc = fw;
fw = f1dim(w);
}
}
else if ((w - wlim)*(wlim - cx) >= 0.0)
{
w = wlim;
fw = f1dim(w);
}
else
{
w = cx + GOLD * (cx - bx);
fw = f1dim(w);
}
}
ax = bx;
bx = cx;
cx = w;
fa = fb;
fb = fc;
fc = fw;
}
}
double MyPowell::f1dim(double x)
{
vector<double> xt;
for (int j = 0; j < ncom; j++)
{
xt.push_back(pcom[j] + x * xicom[j]);
}
return obj(xt);
}
double MyPowell::brent(double ax, double bx, double cx, double & xmin, double tol = 1.48e-8)
{
const double CGOLD = 0.3819660, ZEPS = 1.0e-4;
int itmax = 500;
double a = MIN(ax, cx);
double b = MAX(ax, cx);
double v = bx;
double w = v, x = v;
double deltax = 0.0;
double fx = f1dim(x);
double fv = fx;
double fw = fx;
double rat = 0, u = 0, fu;
int iter;
int done;
double dx_temp, xmid, tol1, tol2, tmp1, tmp2, p;
for (iter = 0; iter < 500; iter++)
{
xmid = 0.5 * (a + b);
tol1 = tol * fabs(x) + ZEPS;
tol2 = 2.0*tol1;
if (fabs(x - xmid) <= (tol2 - 0.5*(b - a)))
break;
done = -1;
if (fabs(deltax) > tol1)
{
tmp1 = (x - w) * (fx - fv);
tmp2 = (x - v) * (fx - fw);
p = (x - v) * tmp2 - (x - w) * tmp1;
tmp2 = 2.0 * (tmp2 - tmp1);
if (tmp2 > 0.0)
p = -p;
tmp2 = fabs(tmp2);
dx_temp = deltax;
deltax = rat;
if ((p > tmp2 * (a - x)) && (p < tmp2 * (b - x)) &&
fabs(p) < fabs(0.5 * tmp2 * dx_temp))
{
rat = p / tmp2;
u = x + rat;
if ((u - a) < tol2 || (b - u) < tol2)
{
rat = fabs(tol1) * sign(xmid - x);
}
done = 0;
}
}
if(done)
{
if (x >= xmid)
{
deltax = a - x;
}
else
{
deltax = b - x;
}
rat = CGOLD * deltax;
}
if (fabs(rat) >= tol1)
{
u = x + rat;
}
else
{
u = x + fabs(tol1) * sign(rat);
}
fu = f1dim(u);
if (fu > fx)
{
if (u < x)
{
a = u;
}
else
{
b = u;
}
if (fu <= fw || w == x)
{
v = w;
w = u;
fv = fw;
fw = fu;
}
else if (fu <= fv || v == x || v == w)
{
v = u;
fv = fu;
}
}
else
{
if (u >= x)
a = x;
else
b = x;
v = w;
w = x;
x = u;
fv = fw;
fw = fx;
fx = fu;
}
}
if(iter > itmax)
cout << "\n Brent exceed maximum iterations.\n\n";
xmin = x;
return fx;
}
vector<double> MyPowell::usePowell()
{
ftol = 1e-4;
vector<vector<double>> xi;
for (int i = 0; i < N; i++)
{
vector<double> xii;
for (int j = 0; j < N; j++)
{
xii.push_back(0);
}
xii[i]=(1.0);
xi.push_back(xii);
}
double fret = 0;
powell(myparams, xi, ftol, fret);
//for (int i = 0; i < xi.size(); i++)
//{
// double a = obj(xi[i]);
// if (fret > a)
// {
// fret = a;
// myparams = xi[i];
// }
//}
cout << "final result" << fret << endl;
return myparams;
}
void MyPowell::erase(vector<double>& pbar, vector<double>& prr, vector<double>& pr)
{
for (int i = 0; i < pbar.size(); i++)
{
pbar[i] = 0;
}
for (int i = 0; i < prr.size(); i++)
{
prr[i] = 0;
}
for (int i = 0; i < pr.size(); i++)
{
pr[i] = 0;
}
}
I used PRAXIS library, because it doesn't need derivative information and is fast.
I modified the code a little to my needs and now it is faster than original version written in Python.

Adding unused formal parameters to C++ method results in different behavior

When I add some extra formal parameters double tmin=0.0, double tmax=0.0 to the constructor of the Ray in the code below, I always obtain a wrong image with a white top border. These formal parameters currently contribute in no way (i.e. are unused) to the code. So how is it possible to obtain a different image?
System specifications:
OS: Windows 8.1
Compiler: MSVC 2015
Code:
#include "stdafx.h"
#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <random>
std::default_random_engine generator(606418532);
std::uniform_real_distribution<double> distribution = std::uniform_real_distribution<double>(0.0, 1.0);
double erand48(unsigned short *x) {
return distribution(generator);
}
#define M_PI 3.14159265358979323846
struct Vector3 {
double x, y, z;
Vector3(double x_ = 0, double y_ = 0, double z_ = 0) { x = x_; y = y_; z = z_; }
Vector3 operator+(const Vector3 &b) const { return Vector3(x + b.x, y + b.y, z + b.z); }
Vector3 operator-(const Vector3 &b) const { return Vector3(x - b.x, y - b.y, z - b.z); }
Vector3 operator*(double b) const { return Vector3(x*b, y*b, z*b); }
Vector3 mult(const Vector3 &b) const { return Vector3(x*b.x, y*b.y, z*b.z); }
Vector3& norm() { return *this = *this * (1 / sqrt(x*x + y*y + z*z)); }
double Dot(const Vector3 &b) const { return x*b.x + y*b.y + z*b.z; } // cross:
Vector3 operator%(Vector3&b) { return Vector3(y*b.z - z*b.y, z*b.x - x*b.z, x*b.y - y*b.x); }
};
//struct Ray { Vector3 o, d; Ray(const Vector3 &o_, const Vector3 &d_, double tmin=0.0, double tmax=0.0) : o(o_), d(d_) {} };
struct Ray { Vector3 o, d; Ray(const Vector3 &o_, const Vector3 &d_) : o(o_), d(d_) {} };
enum Reflection_t { DIFFUSE, SPECULAR, REFRACTIVE };
struct Sphere {
double rad; // radius
Vector3 p, e, f; // position, emission, color
Reflection_t reflection_t; // reflection type (DIFFuse, SPECular, REFRactive)
Sphere(double rad_, Vector3 p_, Vector3 e_, Vector3 f_, Reflection_t reflection_t) :
rad(rad_), p(p_), e(e_), f(f_), reflection_t(reflection_t) {}
double intersect(const Ray &r) const {
Vector3 op = p - r.o;
double t, eps = 1e-4, b = op.Dot(r.d), det = b*b - op.Dot(op) + rad*rad;
if (det<0) return 0; else det = sqrt(det);
return (t = b - det)>eps ? t : ((t = b + det)>eps ? t : 0);
}
};
Sphere spheres[] = {
Sphere(1e5, Vector3(1e5 + 1,40.8,81.6), Vector3(),Vector3(.75,.25,.25),DIFFUSE),//Left
Sphere(1e5, Vector3(-1e5 + 99,40.8,81.6),Vector3(),Vector3(.25,.25,.75),DIFFUSE),//Rght
Sphere(1e5, Vector3(50,40.8, 1e5), Vector3(),Vector3(.75,.75,.75),DIFFUSE),//Back
Sphere(1e5, Vector3(50,40.8,-1e5 + 170), Vector3(),Vector3(), DIFFUSE),//Frnt
Sphere(1e5, Vector3(50, 1e5, 81.6), Vector3(),Vector3(.75,.75,.75),DIFFUSE),//Botm
Sphere(1e5, Vector3(50,-1e5 + 81.6,81.6),Vector3(),Vector3(.75,.75,.75),DIFFUSE),//Top
Sphere(16.5,Vector3(27,16.5,47), Vector3(),Vector3(1,1,1)*.999, SPECULAR),//Mirr
Sphere(16.5,Vector3(73,16.5,78), Vector3(),Vector3(1,1,1)*.999, REFRACTIVE),//Glas
Sphere(600, Vector3(50,681.6 - .27,81.6),Vector3(12,12,12), Vector3(), DIFFUSE) //Lite
};
inline double clamp(double x) { return x<0 ? 0 : x>1 ? 1 : x; }
inline int toInt(double x) { return int(pow(clamp(x), 1 / 2.2) * 255 + .5); }
inline bool intersect(const Ray &r, double &t, int &id) {
double n = sizeof(spheres) / sizeof(Sphere), d, inf = t = 1e20;
for (int i = int(n); i--;) if ((d = spheres[i].intersect(r)) && d<t) { t = d; id = i; }
return t<inf;
}
Vector3 radiance(const Ray &r_, int depth_, unsigned short *Xi) {
double t; // distance to intersection
int id = 0; // id of intersected object
Ray r = r_;
int depth = depth_;
Vector3 cl(0, 0, 0); // accumulated color
Vector3 cf(1, 1, 1); // accumulated reflectance
while (1) {
if (!intersect(r, t, id)) return cl; // if miss, return black
const Sphere &obj = spheres[id]; // the hit object
Vector3 x = r.o + r.d*t, n = (x - obj.p).norm(), nl = n.Dot(r.d)<0 ? n : n*-1, f = obj.f;
double p = f.x>f.y && f.x>f.z ? f.x : f.y>f.z ? f.y : f.z; // max refl
cl = cl + cf.mult(obj.e);
if (++depth>5) if (erand48(Xi)<p) f = f*(1 / p); else return cl; //R.R.
cf = cf.mult(f);
if (obj.reflection_t == DIFFUSE) { // Ideal DIFFUSE reflection
double r1 = 2 * M_PI*erand48(Xi), r2 = erand48(Xi), r2s = sqrt(r2);
Vector3 w = nl, u = ((fabs(w.x)>.1 ? Vector3(0, 1) : Vector3(1)) % w).norm(), v = w%u;
Vector3 d = (u*cos(r1)*r2s + v*sin(r1)*r2s + w*sqrt(1 - r2)).norm();
r = Ray(x, d);
continue;
}
else if (obj.reflection_t == SPECULAR) {
r = Ray(x, r.d - n * 2 * n.Dot(r.d));
continue;
}
Ray reflRay(x, r.d - n * 2 * n.Dot(r.d));
bool into = n.Dot(nl)>0;
double nc = 1, nt = 1.5, nnt = into ? nc / nt : nt / nc, ddn = r.d.Dot(nl), cos2t;
if ((cos2t = 1 - nnt*nnt*(1 - ddn*ddn))<0) {
r = reflRay;
continue;
}
Vector3 tdir = (r.d*nnt - n*((into ? 1 : -1)*(ddn*nnt + sqrt(cos2t)))).norm();
double a = nt - nc, b = nt + nc, R0 = a*a / (b*b), c = 1 - (into ? -ddn : tdir.Dot(n));
double Re = R0 + (1 - R0)*c*c*c*c*c, Tr = 1 - Re, P = .25 + .5*Re, RP = Re / P, TP = Tr / (1 - P);
if (erand48(Xi)<P) {
cf = cf*RP;
r = reflRay;
}
else {
cf = cf*TP;
r = Ray(x, tdir);
}
continue;
}
}
int main(int argc, char *argv[]) {
int w = 512, h = 384, samps = argc == 2 ? atoi(argv[1]) / 4 : 1; // # samples
Ray cam(Vector3(50, 52, 295.6), Vector3(0, -0.042612, -1).norm()); // cam pos, dir
Vector3 cx = Vector3(w*.5135 / h), cy = (cx%cam.d).norm()*.5135, r, *c = new Vector3[w*h];
#pragma omp parallel for schedule(dynamic, 1) private(r) // OpenMP
for (int y = 0; y<h; y++) { // Loop over image rows
fprintf(stderr, "\rRendering (%d spp) %5.2f%%", samps * 4, 100.*y / (h - 1));
for (unsigned short x = 0, Xi[3] = { 0,0,y*y*y }; x<w; x++) // Loop cols
for (int sy = 0, i = (h - y - 1)*w + x; sy<2; sy++) // 2x2 subpixel rows
for (int sx = 0; sx<2; sx++, r = Vector3()) { // 2x2 subpixel cols
for (int s = 0; s<samps; s++) {
double r1 = 2 * erand48(Xi), dx = r1<1 ? sqrt(r1) - 1 : 1 - sqrt(2 - r1);
double r2 = 2 * erand48(Xi), dy = r2<1 ? sqrt(r2) - 1 : 1 - sqrt(2 - r2);
Vector3 d = cx*(((sx + .5 + dx) / 2 + x) / w - .5) +
cy*(((sy + .5 + dy) / 2 + y) / h - .5) + cam.d;
r = r + radiance(Ray(cam.o + d * 140, d.norm()), 0, Xi)*(1. / samps);
} // Camera rays are pushed ^^^^^ forward to start in interior
c[i] = c[i] + Vector3(clamp(r.x), clamp(r.y), clamp(r.z))*.25;
}
}
FILE *fp;
fopen_s(&fp, "image.ppm", "w"); // Write image to PPM file.
fprintf(fp, "P3\n%d %d\n%d\n", w, h, 255);
for (int i = 0; i<w*h; i++)
fprintf(fp, "%d %d %d ", toInt(c[i].x), toInt(c[i].y), toInt(c[i].z));
}
First Ray structure:
struct Ray { Vector3 o, d; Ray(const Vector3 &o_, const Vector3 &d_) : o(o_), d(d_) {} };
Results in:
Second Ray structure:
struct Ray { Vector3 o, d; Ray(const Vector3 &o_, const Vector3 &d_, double tmin=0.0, double tmax=0.0) : o(o_), d(d_) {} };
Results in:
The last image has a noticeable white top border which is not present in the first image.
Edit:
I used
size_t n = sizeof(spheres) / sizeof(Sphere);
Now I obtain the same images, but I also checked if the original int(n) could differ from 9 which is never the case.
Ok this is from the Debug build, which is different from the Release build.
Sounds like a memory error, looking quickly at your code I'm sceptical of this line:
for (int i = int(n); i--;) if ((d = spheres[i].intersect(r)) && d<t)
I suspect accessing sphere[i] is out of bounds, perhaps you should try sphere[i-1]. You could also try compiling your code with a compiler that adds extra code for debugging/sanitising/checking memory addresses.

opencv: Rigid Transformation between two 3D point clouds

I have two 3D point clouds, and I'd like to use opencv to find the rigid transformation matrix (translation, rotation, constant scaling among all 3 axes).
I've found an estimateRigidTransformation function, but it's only for 2D points apparently
In addition, I've found estimateAffine3D, but it doesn't seem to support rigid transformation mode.
Do I need to just write my own rigid transformation function?
I did not find the required functionality in OpenCV so I have written my own implementation. Based on ideas from OpenSFM.
cv::Vec3d
CalculateMean(const cv::Mat_<cv::Vec3d> &points)
{
cv::Mat_<cv::Vec3d> result;
cv::reduce(points, result, 0, CV_REDUCE_AVG);
return result(0, 0);
}
cv::Mat_<double>
FindRigidTransform(const cv::Mat_<cv::Vec3d> &points1, const cv::Mat_<cv::Vec3d> points2)
{
/* Calculate centroids. */
cv::Vec3d t1 = -CalculateMean(points1);
cv::Vec3d t2 = -CalculateMean(points2);
cv::Mat_<double> T1 = cv::Mat_<double>::eye(4, 4);
T1(0, 3) = t1[0];
T1(1, 3) = t1[1];
T1(2, 3) = t1[2];
cv::Mat_<double> T2 = cv::Mat_<double>::eye(4, 4);
T2(0, 3) = -t2[0];
T2(1, 3) = -t2[1];
T2(2, 3) = -t2[2];
/* Calculate covariance matrix for input points. Also calculate RMS deviation from centroid
* which is used for scale calculation.
*/
cv::Mat_<double> C(3, 3, 0.0);
double p1Rms = 0, p2Rms = 0;
for (int ptIdx = 0; ptIdx < points1.rows; ptIdx++) {
cv::Vec3d p1 = points1(ptIdx, 0) + t1;
cv::Vec3d p2 = points2(ptIdx, 0) + t2;
p1Rms += p1.dot(p1);
p2Rms += p2.dot(p2);
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
C(i, j) += p2[i] * p1[j];
}
}
}
cv::Mat_<double> u, s, vh;
cv::SVD::compute(C, s, u, vh);
cv::Mat_<double> R = u * vh;
if (cv::determinant(R) < 0) {
R -= u.col(2) * (vh.row(2) * 2.0);
}
double scale = sqrt(p2Rms / p1Rms);
R *= scale;
cv::Mat_<double> M = cv::Mat_<double>::eye(4, 4);
R.copyTo(M.colRange(0, 3).rowRange(0, 3));
cv::Mat_<double> result = T2 * M * T1;
result /= result(3, 3);
return result.rowRange(0, 3);
}
I've found PCL to be a nice adjunct to OpenCV. Take a look at their Iterative Closest Point (ICP) example. The provided example registers the two point clouds and then displays the rigid transformation.
Here's my rmsd code:
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <assert.h>
typedef struct
{
float m[4][4];
} MATRIX;
#define vdiff2(a,b) ( ((a)[0]-(b)[0]) * ((a)[0]-(b)[0]) + \
((a)[1]-(b)[1]) * ((a)[1]-(b)[1]) + \
((a)[2]-(b)[2]) * ((a)[2]-(b)[2]) )
static double alignedrmsd(float *v1, float *v2, int N);
static void centroid(float *ret, float *v, int N);
static int getalignmtx(float *v1, float *v2, int N, MATRIX *mtx);
static void crossproduct(float *ans, float *pt1, float *pt2);
static void mtx_root(MATRIX *mtx);
static int almostequal(MATRIX *a, MATRIX *b);
static void mulpt(MATRIX *mtx, float *pt);
static void mtx_mul(MATRIX *ans, MATRIX *x, MATRIX *y);
static void mtx_identity(MATRIX *mtx);
static void mtx_trans(MATRIX *mtx, float x, float y, float z);
static int mtx_invert(float *mtx, int N);
static float absmaxv(float *v, int N);
/*
calculate rmsd between two structures
Params: v1 - first set of points
v2 - second set of points
N - number of points
mtx - return for transfrom matrix used to align structures
Returns: rmsd score
Notes: mtx can be null. Transform will be rigid. Inputs must
be previously aligned for sequence alignment
*/
double rmsd(float *v1, float *v2, int N, float *mtx)
{
float cent1[3];
float cent2[3];
MATRIX tmtx;
MATRIX tempmtx;
MATRIX move1;
MATRIX move2;
int i;
double answer;
float *temp1 = 0;
float *temp2 = 0;
int err;
assert(N > 3);
temp1 = malloc(N * 3 * sizeof(float));
temp2 = malloc(N * 3 * sizeof(float));
if(!temp1 || !temp2)
goto error_exit;
centroid(cent1, v1, N);
centroid(cent2, v2, N);
for(i=0;i<N;i++)
{
temp1[i*3+0] = v1[i*3+0] - cent1[0];
temp1[i*3+1] = v1[i*3+1] - cent1[1];
temp1[i*3+2] = v1[i*3+2] - cent1[2];
temp2[i*3+0] = v2[i*3+0] - cent2[0];
temp2[i*3+1] = v2[i*3+1] - cent2[1];
temp2[i*3+2] = v2[i*3+2] - cent2[2];
}
err = getalignmtx(temp1, temp2, N, &tmtx);
if(err == -1)
goto error_exit;
mtx_trans(&move1, -cent2[0], -cent2[1], -cent2[2]);
mtx_mul(&tempmtx, &move1, &tmtx);
mtx_trans(&move2, cent1[0], cent1[1], cent1[2]);
mtx_mul(&tmtx, &tempmtx, &move2);
memcpy(temp2, v2, N * sizeof(float) * 3);
for(i=0;i<N;i++)
mulpt(&tmtx, temp2 + i * 3);
answer = alignedrmsd(v1, temp2, N);
free(temp1);
free(temp2);
if(mtx)
memcpy(mtx, &tmtx.m, 16 * sizeof(float));
return answer;
error_exit:
free(temp1);
free(temp2);
if(mtx)
{
for(i=0;i<16;i++)
mtx[i] = 0;
}
return sqrt(-1.0);
}
/*
calculate rmsd between two aligned structures (trivial)
Params: v1 - first structure
v2 - second structure
N - number of points
Returns: rmsd
*/
static double alignedrmsd(float *v1, float *v2, int N)
{
double answer =0;
int i;
for(i=0;i<N;i++)
answer += vdiff2(v1 + i *3, v2 + i * 3);
return sqrt(answer/N);
}
/*
compute the centroid
*/
static void centroid(float *ret, float *v, int N)
{
int i;
ret[0] = 0;
ret[1] = 0;
ret[2] = 0;
for(i=0;i<N;i++)
{
ret[0] += v[i*3+0];
ret[1] += v[i*3+1];
ret[2] += v[i*3+2];
}
ret[0] /= N;
ret[1] /= N;
ret[2] /= N;
}
/*
get the matrix needed to align two structures
Params: v1 - reference structure
v2 - structure to align
N - number of points
mtx - return for rigid body alignment matrix
Notes: only calculates rotation part of matrix.
assumes input has been aligned to centroids
*/
static int getalignmtx(float *v1, float *v2, int N, MATRIX *mtx)
{
MATRIX A = { {{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,1}} };
MATRIX At;
MATRIX Ainv;
MATRIX temp;
float tv[3];
float tw[3];
float tv2[3];
float tw2[3];
int k, i, j;
int flag = 0;
float correction;
correction = absmaxv(v1, N * 3) * absmaxv(v2, N * 3);
for(k=0;k<N;k++)
for(i=0;i<3;i++)
for(j=0;j<3;j++)
A.m[i][j] += (v1[k*3+i] * v2[k*3+j])/correction;
while(flag < 3)
{
for(i=0;i<4;i++)
for(j=0;j<4;j++)
At.m[i][j] = A.m[j][i];
memcpy(&Ainv, &A, sizeof(MATRIX));
/* this will happen if all points are in a plane */
if( mtx_invert((float *) &Ainv, 4) == -1)
{
if(flag == 0)
{
crossproduct(tv, v1, v1+3);
crossproduct(tw, v2, v2+3);
}
else
{
crossproduct(tv2, tv, v1);
crossproduct(tw2, tw, v2);
memcpy(tv, tv2, 3 * sizeof(float));
memcpy(tw, tw2, 3 * sizeof(float));
}
for(i=0;i<3;i++)
for(j=0;j<3;j++)
A.m[i][j] += tv[i] * tw[j];
flag++;
}
else
flag = 5;
}
if(flag != 5)
return -1;
mtx_mul(&temp, &At, &A);
mtx_root(&temp);
mtx_mul(mtx, &temp, &Ainv);
return 0;
}
/*
get the crossproduct of two vectors.
Params: ans - return pinter for answer.
pt1 - first vector
pt2 - second vector.
Notes: crossproduct is at right angles to the two vectors.
*/
static void crossproduct(float *ans, float *pt1, float *pt2)
{
ans[0] = pt1[1] * pt2[2] - pt1[2] * pt2[1];
ans[1] = pt1[0] * pt2[2] - pt1[2] * pt2[0];
ans[2] = pt1[0] * pt2[1] - pt1[1] * pt2[0];
}
/*
Denman-Beavers square root iteration
*/
static void mtx_root(MATRIX *mtx)
{
MATRIX Y = *mtx;
MATRIX Z;
MATRIX Y1;
MATRIX Z1;
MATRIX invY;
MATRIX invZ;
MATRIX Y2;
int iter = 0;
int i, ii;
mtx_identity(&Z);
do
{
invY = Y;
invZ = Z;
if( mtx_invert((float *) &invY, 4) == -1)
return;
if( mtx_invert((float *) &invZ, 4) == -1)
return;
for(i=0;i<4;i++)
for(ii=0;ii<4;ii++)
{
Y1.m[i][ii] = 0.5 * (Y.m[i][ii] + invZ.m[i][ii]);
Z1.m[i][ii] = 0.5 * (Z.m[i][ii] + invY.m[i][ii]);
}
Y = Y1;
Z = Z1;
mtx_mul(&Y2, &Y, &Y);
}
while(!almostequal(&Y2, mtx) && iter++ < 20 );
*mtx = Y;
}
/*
Check two matrices for near-enough equality
Params: a - first matrix
b - second matrix
Returns: 1 if almost equal, else 0, epsilon 0.0001f.
*/
static int almostequal(MATRIX *a, MATRIX *b)
{
int i, ii;
float epsilon = 0.001f;
for(i=0;i<4;i++)
for(ii=0;ii<4;ii++)
if(fabs(a->m[i][ii] - b->m[i][ii]) > epsilon)
return 0;
return 1;
}
/*
multiply a point by a matrix.
Params: mtx - matrix
pt - the point (transformed)
*/
static void mulpt(MATRIX *mtx, float *pt)
{
float ans[4] = {0};
int i;
int ii;
for(i=0;i<4;i++)
{
for(ii=0;ii<3;ii++)
{
ans[i] += pt[ii] * mtx->m[ii][i];
}
ans[i] += mtx->m[3][i];
}
pt[0] = ans[0];
pt[1] = ans[1];
pt[2] = ans[2];
}
/*
multiply two matrices.
Params: ans - return pointer for answer.
x - first matrix
y - second matrix.
Notes: ans may not be equal to x or y.
*/
static void mtx_mul(MATRIX *ans, MATRIX *x, MATRIX *y)
{
int i;
int ii;
int iii;
for(i=0;i<4;i++)
for(ii=0;ii<4;ii++)
{
ans->m[i][ii] = 0;
for(iii=0;iii<4;iii++)
ans->m[i][ii] += x->m[i][iii] * y->m[iii][ii];
}
}
/*
create an identity matrix.
Params: mtx - return pointer.
*/
static void mtx_identity(MATRIX *mtx)
{
int i;
int ii;
for(i=0;i<4;i++)
for(ii=0;ii<4;ii++)
{
if(i==ii)
mtx->m[i][ii] = 1.0f;
else
mtx->m[i][ii] = 0;
}
}
/*
create a translation matrix.
Params: mtx - return pointer for matrix.
x - x translation.
y - y translation.
z - z translation
*/
static void mtx_trans(MATRIX *mtx, float x, float y, float z)
{
mtx->m[0][0] = 1;
mtx->m[0][1] = 0;
mtx->m[0][2] = 0;
mtx->m[0][3] = 0;
mtx->m[1][0] = 0;
mtx->m[1][1] = 1;
mtx->m[1][2] = 0;
mtx->m[1][3] = 0;
mtx->m[2][0] = 0;
mtx->m[2][1] = 0;
mtx->m[2][2] = 1;
mtx->m[2][3] = 0;
mtx->m[3][0] = x;
mtx->m[3][1] = y;
mtx->m[3][2] = z;
mtx->m[3][3] = 1;
}
/*
matrix invert routine
Params: mtx - the matrix in raw format, in/out
N - width and height
Returns: 0 on success, -1 on fail
*/
static int mtx_invert(float *mtx, int N)
{
int indxc[100]; /* these 100s are the only restriction on matrix size */
int indxr[100];
int ipiv[100];
int i, j, k;
int irow, icol;
double big;
double pinv;
int l, ll;
double dum;
double temp;
assert(N <= 100);
for(i=0;i<N;i++)
ipiv[i] = 0;
for(i=0;i<N;i++)
{
big = 0.0;
/* find biggest element */
for(j=0;j<N;j++)
if(ipiv[j] != 1)
for(k=0;k<N;k++)
if(ipiv[k] == 0)
if(fabs(mtx[j*N+k]) >= big)
{
big = fabs(mtx[j*N+k]);
irow = j;
icol = k;
}
ipiv[icol]=1;
if(irow != icol)
for(l=0;l<N;l++)
{
temp = mtx[irow * N + l];
mtx[irow * N + l] = mtx[icol * N + l];
mtx[icol * N + l] = temp;
}
indxr[i] = irow;
indxc[i] = icol;
/* if biggest element is zero matrix is singular, bail */
if(mtx[icol* N + icol] == 0)
goto error_exit;
pinv = 1.0/mtx[icol * N + icol];
mtx[icol * N + icol] = 1.0;
for(l=0;l<N;l++)
mtx[icol * N + l] *= pinv;
for(ll=0;ll<N;ll++)
if(ll != icol)
{
dum = mtx[ll * N + icol];
mtx[ll * N + icol] = 0.0;
for(l=0;l<N;l++)
mtx[ll * N + l] -= mtx[icol * N + l]*dum;
}
}
/* unscramble matrix */
for (l=N-1;l>=0;l--)
{
if (indxr[l] != indxc[l])
for (k=0;k<N;k++)
{
temp = mtx[k * N + indxr[l]];
mtx[k * N + indxr[l]] = mtx[k * N + indxc[l]];
mtx[k * N + indxc[l]] = temp;
}
}
return 0;
error_exit:
return -1;
}
/*
get the asolute maximum of an array
*/
static float absmaxv(float *v, int N)
{
float answer;
int i;
for(i=0;i<N;i++)
if(answer < fabs(v[i]))
answer = fabs(v[i]);
return answer;
}
#include <stdio.h>
/*
debug utlitiy
*/
static void printmtx(FILE *fp, MATRIX *mtx)
{
int i, ii;
for(i=0;i<4;i++)
{
for(ii=0;ii<4;ii++)
fprintf(fp, "%f, ", mtx->m[i][ii]);
fprintf(fp, "\n");
}
}
int rmsdmain(void)
{
float one[4*3] = {0,0,0, 1,0,0, 2,1,0, 0,3,1};
float two[4*3] = {0,0,0, 0,1,0, 1,2,0, 3,0,1};
MATRIX mtx;
double diff;
int i;
diff = rmsd(one, two, 4, (float *) &mtx.m);
printf("%f\n", diff);
printmtx(stdout, &mtx);
for(i=0;i<4;i++)
{
mulpt(&mtx, two + i * 3);
printf("%f %f %f\n", two[i*3], two[i*3+1], two[i*3+2]);
}
return 0;
}
I took #vagran's implementation and added RANSAC on top of it, since estimateRigidTransform2d does it and it was helpful for me since my data is noisy. (Note: This code doesn't have constant scaling along all 3 axes; you can add it back in easily by comparing to vargran's).
cv::Vec3f CalculateMean(const cv::Mat_<cv::Vec3f> &points)
{
if(points.size().height == 0){
return 0;
}
assert(points.size().width == 1);
double mx = 0.0;
double my = 0.0;
double mz = 0.0;
int n_points = points.size().height;
for(int i = 0; i < n_points; i++){
double x = double(points(i)[0]);
double y = double(points(i)[1]);
double z = double(points(i)[2]);
mx += x;
my += y;
mz += z;
}
return cv::Vec3f(mx/n_points, my/n_points, mz/n_points);
}
cv::Mat_<double>
FindRigidTransform(const cv::Mat_<cv::Vec3f> &points1, const cv::Mat_<cv::Vec3f> points2)
{
/* Calculate centroids. */
cv::Vec3f t1 = CalculateMean(points1);
cv::Vec3f t2 = CalculateMean(points2);
cv::Mat_<double> T1 = cv::Mat_<double>::eye(4, 4);
T1(0, 3) = double(-t1[0]);
T1(1, 3) = double(-t1[1]);
T1(2, 3) = double(-t1[2]);
cv::Mat_<double> T2 = cv::Mat_<double>::eye(4, 4);
T2(0, 3) = double(t2[0]);
T2(1, 3) = double(t2[1]);
T2(2, 3) = double(t2[2]);
/* Calculate covariance matrix for input points. Also calculate RMS deviation from centroid
* which is used for scale calculation.
*/
cv::Mat_<double> C(3, 3, 0.0);
for (int ptIdx = 0; ptIdx < points1.rows; ptIdx++) {
cv::Vec3f p1 = points1(ptIdx) - t1;
cv::Vec3f p2 = points2(ptIdx) - t2;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
C(i, j) += double(p2[i] * p1[j]);
}
}
}
cv::Mat_<double> u, s, vt;
cv::SVD::compute(C, s, u, vt);
cv::Mat_<double> R = u * vt;
if (cv::determinant(R) < 0) {
R -= u.col(2) * (vt.row(2) * 2.0);
}
cv::Mat_<double> M = cv::Mat_<double>::eye(4, 4);
R.copyTo(M.colRange(0, 3).rowRange(0, 3));
cv::Mat_<double> result = T2 * M * T1;
result /= result(3, 3);
return result;
}
cv::Mat_<double> RANSACFindRigidTransform(const cv::Mat_<cv::Vec3f> &points1, const cv::Mat_<cv::Vec3f> &points2)
{
cv::Mat points1Homo;
cv::convertPointsToHomogeneous(points1, points1Homo);
int iterations = 100;
int min_n_points = 3;
int n_points = points1.size().height;
std::vector<int> range(n_points);
cv::Mat_<double> best;
int best_inliers = -1;
// inlier points should be projected within this many units
float threshold = .02;
std::iota(range.begin(), range.end(), 0);
auto gen = std::mt19937{std::random_device{}()};
for(int i = 0; i < iterations; i++) {
std::shuffle(range.begin(), range.end(), gen);
cv::Mat_<cv::Vec3f> points1subset(min_n_points, 1, cv::Vec3f(0,0,0));
cv::Mat_<cv::Vec3f> points2subset(min_n_points, 1, cv::Vec3f(0,0,0));
for(int j = 0; j < min_n_points; j++) {
points1subset(j) = points1(range[j]);
points2subset(j) = points2(range[j]);
}
cv::Mat_<float> rigidT = FindRigidTransform(points1subset, points2subset);
cv::Mat_<float> rigidT_float = cv::Mat::eye(4, 4, CV_32F);
rigidT.convertTo(rigidT_float, CV_32F);
std::vector<int> inliers;
for(int j = 0; j < n_points; j++) {
cv::Mat_<float> t1_3d = rigidT_float * cv::Mat_<float>(points1Homo.at<cv::Vec4f>(j));
if(t1_3d(3) == 0) {
continue; // Avoid 0 division
}
float dx = (t1_3d(0)/t1_3d(3) - points2(j)[0]);
float dy = (t1_3d(1)/t1_3d(3) - points2(j)[1]);
float dz = (t1_3d(2)/t1_3d(3) - points2(j)[2]);
float square_dist = dx * dx + dy * dy + dz * dz;
if(square_dist < threshold * threshold){
inliers.push_back(j);
}
}
int n_inliers = inliers.size();
if(n_inliers > best_inliers) {
best_inliers = n_inliers;
best = rigidT;
}
}
return best;
}
#vagran Thanks for the code! Seems to work very well.
I do have a little terminology suggestion though. Since you are estimating and applying a scale during the transformation, it is a 7-parameter transformation, or Helmert / similarity transformation. And in a rigid transformation, no scaling is applied because all Euclidiean distances need to be reserved.
I would've added this as comment, but don't have enough points.. D: sorry for that.
rigid transformation: https://en.wikipedia.org/wiki/Rigid_transformation
Helmert transformation: https://www.researchgate.net/publication/322841143_Parameter_estimation_in_3D_affine_and_similarity_transformation_implementation_of_variance_component_estimation