771 lines
20 KiB
C++
771 lines
20 KiB
C++
#include <string>
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#include <fstream>
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#include <iostream>
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#include <sstream>
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#include <cmath>
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#include <cassert>
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#include <cstring>
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#include <chrono>
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#include <xmmintrin.h>
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using namespace std;
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template <typename T>
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struct TPoint {
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T x;
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T y;
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TPoint(T a, T b)
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: x(a)
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, y(b)
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{}
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};
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typedef TPoint<int> Point;
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typedef TPoint<double> DPoint; // absolute point, can be negative
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template<typename Elem, typename Traits, typename T>
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std::basic_ostream<Elem, Traits>& operator << (std::basic_ostream<Elem, Traits>& o, TPoint<T> const& p)
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{
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o << "(" << p.x << ", " << p.y << ")";
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return o;
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}
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struct Image {
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unsigned int width;
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unsigned int height;
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uint8_t* buffer;
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Image()
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: width(0)
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, height(0)
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, buffer(NULL)
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{}
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Image(unsigned int w, unsigned int h)
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{
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this->width = w;
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this->height = h;
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buffer = new uint8_t[width * height * 3];
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memset(buffer, 0, width * height * 3 * sizeof (uint8_t));
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}
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Image(string const& path)
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: Image()
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{
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ifstream is(path);
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if (!is.is_open())
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{
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cerr << "Cannot open file '" << path << "'" << endl;
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abort();
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}
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if (!this->read_header(is))
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{
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cerr << "Invalid header." << endl;
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abort();
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}
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if (!this->read_body(is))
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{
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delete buffer;
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buffer = nullptr;
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cerr << "Invalid header." << endl;
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abort();
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}
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}
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bool save(string const& path)
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{
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ofstream os(path);
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if (!os.is_open())
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{
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cerr << "Cannot open file '" << path << "'" << endl;
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return false;
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}
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this->write_header(os);
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this->write_body(os);
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return true;
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}
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void set_pixel(unsigned int x, unsigned int y, uint8_t r, uint8_t g, uint8_t b)
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{
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if (x >= width || y >= height)
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{
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// cerr << __LINE__ << " | Point (" << x << ", " << y << ") out of bounds" << endl;
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// cerr << " Image dimensions: " << width << " x " << height << endl;
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// assert(false);
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return;
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}
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int index = (y * width + x) * 3;
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buffer[index++] = r;
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buffer[index++] = g;
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buffer[index++] = b;
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}
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void set_pixel(Point const& p, uint8_t r, uint8_t g, uint8_t b)
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{
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this->set_pixel(p.x, p.y, r, g, b);
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}
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private:
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bool read_header(std::ifstream& istr)
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{
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// check magic
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if (istr.get() != 'P' )
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{
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return false;
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}
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char type = static_cast<char>(istr.get());
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if (type != '6')
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{
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return false;
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}
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if (istr.get() != '\n')
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{
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return false;
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}
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// skip comments
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while (istr.peek() == '#')
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{
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std::string line;
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std::getline(istr, line);
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}
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// get size
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istr >> width >> height;
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if (width == 0 || height == 0)
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{
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return false;
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}
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// get maxvalue
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if (istr.get() != '\n')
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{
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return false;
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}
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int max_value = -1;
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istr >> max_value;
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if (max_value > 255)
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{
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return false;
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}
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if (istr.get() != '\n')
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{
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return false;
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}
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// cout << "width: " << width << endl;
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// cout << "height: " << height << endl;
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return true;
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}
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bool write_header(std::ofstream& ostr)
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{
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ostr << "P6" << endl;
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ostr << width << " " << height << endl;
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ostr << "255" << endl;
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return true;
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}
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bool read_body(std::ifstream& istr)
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{
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unsigned int const nb_pixels = width * height;
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buffer = new uint8_t[nb_pixels * 3];
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uint8_t* buf_index = buffer;
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for (unsigned int i = 0; i < nb_pixels * 3; ++i)
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{
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*buf_index = istr.get();
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++buf_index;
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}
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return true;
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}
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bool write_body(std::ofstream& ostr)
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{
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unsigned int const nb_pixels = width * height;
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uint8_t* buf_index = buffer;
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for (unsigned int i = 0; i < nb_pixels * 3; ++i)
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{
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ostr << (char) *buf_index;
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++buf_index;
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}
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return true;
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}
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};
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//
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//
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// Trigonometry
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//
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DPoint convert_grid_coord(Image const& img, Point const& p)
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{
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return DPoint(p.x - img.width / 2.0f + 0.5, p.y - img.height / 2.0f + 0.5);
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}
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double convert_radian(Image const& img, Point const& p, double const ratio)
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{
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DPoint centered = convert_grid_coord(img, p);
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double const cos_value = centered.x * ratio;
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double const sin_value = - (centered.y * ratio);
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double angle = acos(cos_value);
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if (sin_value < 0)
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{
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angle = (2 * M_PI) - angle;
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}
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return angle;
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}
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DPoint convert_abs_coord(double const angle, double const ratio)
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{
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return DPoint(cos(angle) / ratio, - sin(angle) / ratio);
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}
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Point convert_img_coord(Image const& img, DPoint const& p)
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{
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int x = round(p.x + (img.width / 2.0f) - 0.5);
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int y = round(p.y + (img.height / 2.0f) - 0.5);
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return Point(x, y);
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}
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DPoint convert_img_coord_precision(Image const& img, DPoint const& p)
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{
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int x = p.x + (img.width / 2.0f) - 0.5;
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int y = p.y + (img.height / 2.0f) - 0.5;
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return DPoint(x, y);
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}
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void convert_abs_to_polar_coord(DPoint const& p, double& angle, double& dist)
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{
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angle = atan2(-p.y, p.x);
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dist = sqrt(p.x * p.x + p.y * p.y);
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}
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DPoint convert_polar_to_grid_coord(double const angle, double const distance)
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{
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return DPoint(cos(angle) * distance, - (sin(angle) * distance));
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}
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double compute_ratio(Image const& img)
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{
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double const trigo_length = (sqrt(img.width * img.width + img.height * img.height) - 1) / 2;
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return 1.0f / trigo_length;
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}
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inline
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bool fequal(float a, float b, float sigma)
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{
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return abs(a - b) < sigma;
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}
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void compute_output_size(Image const& src, double const rotation, unsigned int& width, unsigned int& height)
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{
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double const ratio = compute_ratio(src);
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double min_w = 0;
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double max_w = 0;
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double min_h = 0;
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double max_h = 0;
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Point p(0, 0);
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double angle = convert_radian(src, p, ratio);
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DPoint tl = convert_abs_coord(angle + rotation, ratio);
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min_w = min(min_w, tl.x);
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max_w = max(max_w, tl.x);
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min_h = min(min_h, tl.y);
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max_h = max(max_h, tl.y);
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p = Point(src.width - 1, 0);
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angle = convert_radian(src, p, ratio);
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DPoint tr = convert_abs_coord(angle + rotation, ratio);
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min_w = min(min_w, tr.x);
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max_w = max(max_w, tr.x);
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min_h = min(min_h, tr.y);
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max_h = max(max_h, tr.y);
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p = Point(0, src.height - 1);
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angle = convert_radian(src, p, ratio);
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DPoint bl = convert_abs_coord(angle + rotation, ratio);
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min_w = min(min_w, bl.x);
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max_w = max(max_w, bl.x);
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min_h = min(min_h, bl.y);
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max_h = max(max_h, bl.y);
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p = Point(src.width - 1, src.height - 1);
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angle = convert_radian(src, p, ratio);
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DPoint br = convert_abs_coord(angle + rotation, ratio);
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min_w = min(min_w, br.x);
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max_w = max(max_w, br.x);
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min_h = min(min_h, br.y);
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max_h = max(max_h, br.y);
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width = (int) (max_w - min_w) + 1;
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height = (int) (max_h - min_h) + 1;
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}
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//
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//
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// Point rotation
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//
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Point rotate(Image const& src, Point const& p, double const ratio, double const rotation, Image const& rotated)
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{
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double angle = convert_radian(src, p, ratio);
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DPoint a_point = convert_abs_coord(angle + rotation, ratio);
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return convert_img_coord(rotated, a_point);
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}
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//
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//
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// Drawing
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//
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void draw_line(Image& img, unsigned int x1, unsigned int y1, unsigned int x2, unsigned int y2)
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{
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int x_inc = x1 <= x2 ? 1 : -1;
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unsigned int const y_min = min(y1, y2);
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unsigned int const y_max = max(y1, y2);
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double slope = (double) y2 - y1;
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if (x1 != x2)
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slope = ((double) y2 - y1) / abs((double) x2 - x1);
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int y_inc = slope > 0 ? 1 : -1;
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if (x1 == x2)
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{
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for (unsigned int runner = y1; runner != y2; runner+= y_inc)
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img.set_pixel(x1, runner, 255, 0, 0); // set line to red
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return;
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}
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if (y1 == y2)
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{
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for (unsigned int runner = x1; runner != x2; runner+= x_inc)
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img.set_pixel(runner, y1, 255, 0, 0); // set line to red
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return;
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}
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unsigned int previous_y = y1;
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for (unsigned int i = x1, steps = 0; i != x2; i += x_inc, ++steps)
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{
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unsigned int y = slope * steps + y1;
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y = min(y, y_max);
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y = max(y, y_min);
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for (unsigned int runner = previous_y; runner != y; runner+= y_inc)
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img.set_pixel(i, runner, 255, 0, 0); // set line to red
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previous_y = y;
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}
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}
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void draw_line(Image& img, Point const& p1, Point const& p2)
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{
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draw_line(img, p1.x, p1.y, p2.x, p2.y);
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}
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void draw_outline(Image const& input, unsigned int degrees, string const& name)
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{
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double const rotation = (degrees / 180.0f) * M_PI;
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unsigned int w = 0;
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unsigned int h = 0;
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compute_output_size(input, rotation, w, h);
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cout << "rotation(" << degrees << ") -> " << w << " x " << h << endl;
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Image rotated(w, h);
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double const ratio = compute_ratio(input);
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Point tl = rotate(input, Point(0, 0), ratio, rotation, rotated);
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Point tr = rotate(input, Point(input.width - 1, 0), ratio, rotation, rotated);
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Point bl = rotate(input, Point(0, input.height - 1), ratio, rotation, rotated);
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Point br = rotate(input, Point(input.width - 1, input.height - 1), ratio, rotation, rotated);
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cout << tl << " " << tr << " " << bl << " " << br << endl;
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draw_line(rotated, tl, tr);
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draw_line(rotated, tr, br);
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draw_line(rotated, br, bl);
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draw_line(rotated, bl, tl);
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stringstream ss;
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ss << "check_lines_" << name << "_" << degrees << ".ppm";
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rotated.save(ss.str());
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}
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//
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//
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// Math approximation
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//
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void round_if_very_small(double& d)
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{
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if (abs(d) < 1.0e-10)
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d = 0.0;
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}
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//
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//
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// Image rotation
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//
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DPoint get_mapped_point(Image const& src, Point const& p, double const rotation)
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{
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DPoint const d = convert_grid_coord(src, p);
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double p_angle = 0;
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double dist = 0;
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convert_abs_to_polar_coord(d, p_angle, dist);
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return convert_polar_to_grid_coord(p_angle + rotation, dist);
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}
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inline
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void rotate_pixel(Image const& src, Image& rotated,
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DPoint const& src_rotated_point, Point const& rot_point,
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unsigned int const src_limit, unsigned int const rot_limit)
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{
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unsigned int src_index = ((int) src_rotated_point.y * src.width + (int) src_rotated_point.x) * 3;
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unsigned int rot_index = (rot_point.y * rotated.width + rot_point.x) * 3;
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// Out-of-bounds check
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if (src_index >= src_limit
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|| rot_index >= rot_limit)
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return;
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// Bilinear interpolation
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unsigned int src_index_1 = src_index;
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unsigned int src_index_2 = src_index_1 + 3;
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unsigned int src_index_3 = src_index_1 + 3 * src.width;
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unsigned int src_index_4 = src_index_3 + 3;
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if (src_index_4 >= src_limit)
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return;
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double x_delta = src_rotated_point.x - floor(src_rotated_point.x);
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round_if_very_small(x_delta);
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double y_delta = src_rotated_point.y - floor(src_rotated_point.y);
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round_if_very_small(y_delta);
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// SIMD
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__m128 const x_d = _mm_set_ps1(x_delta);
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__m128 const inv_x_d = _mm_set_ps1(1 - x_delta);
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__m128 top_left = _mm_set_ps(src.buffer[src_index_1], src.buffer[src_index_1 + 1], src.buffer[src_index_1 + 2], 0.0);
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__m128 top_right = _mm_set_ps(src.buffer[src_index_2], src.buffer[src_index_2 + 1], src.buffer[src_index_2 + 2], 0.0);
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top_left = _mm_mul_ps(top_left, inv_x_d);
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top_right = _mm_mul_ps(top_right, x_d);
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top_left = _mm_add_ps(top_left, top_right);
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__m128 bottom_left = _mm_set_ps(src.buffer[src_index_3], src.buffer[src_index_3 + 1], src.buffer[src_index_3 + 2], 0.0);
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__m128 bottom_right = _mm_set_ps(src.buffer[src_index_4], src.buffer[src_index_4 + 1], src.buffer[src_index_4 + 2], 0.0);
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bottom_left = _mm_mul_ps(bottom_left, inv_x_d);
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bottom_right = _mm_mul_ps(bottom_right, x_d);
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bottom_left = _mm_add_ps(bottom_left, bottom_right);
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__m128 const y_d = _mm_set_ps1(y_delta);
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__m128 const inv_y_d = _mm_set_ps1(1 - y_delta);
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top_left = _mm_mul_ps(top_left, inv_y_d);
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bottom_left = _mm_mul_ps(bottom_left, y_d);
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top_left = _mm_add_ps(top_left, bottom_left);
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// convert float values to uint8_t
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rotated.buffer[rot_index] = top_left[3];
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rotated.buffer[rot_index + 1] = top_left[2];
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rotated.buffer[rot_index + 2] = top_left[1];
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}
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Image rotate(Image const& src, double angle)
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{
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double const rotation = (angle / 180.0f) * M_PI;
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unsigned int w = 0;
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unsigned int h = 0;
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compute_output_size(src, rotation, w, h);
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Image rotated(w, h);
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// corner points in rotated image
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// TODO: add one ligne for smooth border
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DPoint const tl_grid = get_mapped_point(src, Point(0, 0), rotation);
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Point const tl = convert_img_coord(rotated, tl_grid);
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DPoint const tr_grid = get_mapped_point(src, Point(src.width - 1, 0), rotation);
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Point const tr = convert_img_coord(rotated, tr_grid);
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DPoint const bl_grid = get_mapped_point(src, Point(0, src.height - 1), rotation);
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Point const bl = convert_img_coord(rotated, bl_grid);
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// corner points in source image
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DPoint src_tl = get_mapped_point(rotated, tl, -rotation);
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src_tl = convert_img_coord_precision(src, src_tl);
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DPoint src_origin = get_mapped_point(rotated, Point(0, 0), -rotation);
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DPoint src_delta_x = get_mapped_point(rotated, Point(1, 0), -rotation);
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DPoint src_delta_y = get_mapped_point(rotated, Point(0, 1), -rotation);
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src_delta_x.x = src_delta_x.x - src_origin.x;
|
|
src_delta_x.y = src_delta_x.y - src_origin.y;
|
|
round_if_very_small(src_delta_x.x);
|
|
round_if_very_small(src_delta_x.y);
|
|
src_delta_y.x = src_delta_y.x - src_origin.x;
|
|
src_delta_y.y = src_delta_y.y - src_origin.y;
|
|
round_if_very_small(src_delta_y.x);
|
|
round_if_very_small(src_delta_y.y);
|
|
// cout << "src delta x = " << src_delta_x << endl;
|
|
// cout << "src delta y = " << src_delta_y << endl;
|
|
|
|
|
|
// // steps for first column in source image (y)
|
|
int origin_nb_steps = max(abs(bl.x - tl.x), abs(bl.y - tl.y));
|
|
// // steps for line in source image (x)
|
|
int line_nb_steps = max(abs(tr.x - tl.x), abs(tr.y - tl.y));
|
|
|
|
// steps for first column in rotated image (y)
|
|
DPoint rotated_step((bl.x - tl.x) / (float) origin_nb_steps, (bl.y - tl.y) / (float) origin_nb_steps);
|
|
|
|
// steps for line in rotated image (x)
|
|
DPoint bresenham((tr.x - tl.x) / (float) line_nb_steps, (tr.y - tl.y) / (float) line_nb_steps);
|
|
|
|
unsigned int const src_limit = src.width * src.height * 3;
|
|
unsigned int const rot_limit = rotated.width * rotated.height * 3;
|
|
|
|
for (int y_i = 0; y_i <= (int) origin_nb_steps; ++y_i)
|
|
{
|
|
// first column origin
|
|
Point const rot_origin(tl.x + y_i * rotated_step.x, tl.y + y_i * rotated_step.y);
|
|
|
|
Point previous = rot_origin;
|
|
|
|
for (int x_i = 0; x_i <= (int) line_nb_steps; ++x_i)
|
|
{
|
|
Point rot_point(rot_origin.x + x_i * bresenham.x, rot_origin.y + x_i * bresenham.y);
|
|
|
|
Point const delta(rot_point.x - tl.x, rot_point.y - tl.y);
|
|
DPoint src_rotated_point(src_tl.x + delta.x * src_delta_x.x + delta.y * src_delta_y.x,
|
|
src_tl.y + delta.x * src_delta_x.y + delta.y * src_delta_y.y);
|
|
|
|
rotate_pixel(src, rotated, src_rotated_point, rot_point, src_limit, rot_limit);
|
|
|
|
if (previous.x != rot_point.x && previous.y != rot_point.y)
|
|
{
|
|
int y_slope = rot_point.y > previous.y ? 1 : -1;
|
|
int tmp_y = rot_point.y;
|
|
rot_point.y = previous.y;
|
|
|
|
src_rotated_point.x -= y_slope * src_delta_y.x;
|
|
src_rotated_point.y -= y_slope * src_delta_y.y;
|
|
|
|
rotate_pixel(src, rotated, src_rotated_point, rot_point, src_limit, rot_limit);
|
|
|
|
rot_point.y = tmp_y;
|
|
}
|
|
|
|
previous = rot_point;
|
|
}
|
|
}
|
|
|
|
return rotated;
|
|
}
|
|
|
|
|
|
|
|
//
|
|
//
|
|
// Check
|
|
//
|
|
|
|
bool check_points()
|
|
{
|
|
Image five(5, 5);
|
|
Point origin(0, 0);
|
|
DPoint d1 = convert_grid_coord(five, origin);
|
|
assert(d1.x == -2);
|
|
assert(d1.y == -2);
|
|
|
|
return true;
|
|
}
|
|
|
|
bool check_trigo()
|
|
{
|
|
Image square(500, 500);
|
|
double const ratio = compute_ratio(square);
|
|
double const sigma = 1.0e-2;
|
|
if (!fequal(ratio, 1 / 707.106, sigma))
|
|
{
|
|
cerr << __LINE__ << " | Invalid ratio: " << ratio << " != " << 1 / 707.106 << endl;
|
|
return false;
|
|
}
|
|
|
|
// Check that the origin of a square image is at sqrt(2) / 2
|
|
double const angle = convert_radian(square, Point(0, 0), ratio);
|
|
|
|
if (!fequal(angle, 3 * M_PI / 4, sigma))
|
|
{
|
|
cerr << __LINE__ << " | Invalid angle value: " << angle << " != " << 3 * M_PI / 4 << endl;
|
|
return false;
|
|
}
|
|
|
|
// Check that we can reverse the origin point.
|
|
DPoint const abs_reverse_point = convert_abs_coord(angle, ratio);
|
|
Point const reverse_point = convert_img_coord(square, abs_reverse_point);
|
|
if (!fequal(0.0, reverse_point.x, sigma)
|
|
|| !fequal(0.0, reverse_point.y, sigma))
|
|
{
|
|
cerr << __LINE__ << "Reverse origin fail" << endl;
|
|
cerr << " " << reverse_point << " != (0, 0)" << endl;
|
|
cerr << " abs point " << abs_reverse_point << endl;
|
|
return false;
|
|
}
|
|
|
|
// Check that when rotating the origin by 45 degrees
|
|
double const rotation = M_PI / 4; // 45 degrees
|
|
unsigned int w = 0;
|
|
unsigned int h = 0;
|
|
compute_output_size(square, rotation, w, h);
|
|
|
|
if (!fequal(w, square.width * sqrt(2), sigma * square.width)
|
|
|| !fequal(h, square.height * sqrt(2), sigma * square.height))
|
|
{
|
|
cerr << "Invalid rotated image dimensions " << w << " x " << h << endl;
|
|
cerr << " expected " << (int) ceil(square.width * sqrt(2)) << " x " << (int) ceil(square.height * sqrt(2)) << endl;
|
|
return false;
|
|
}
|
|
|
|
|
|
Image rotated(w, h);
|
|
|
|
DPoint const a_p45 = convert_abs_coord(angle + rotation, ratio);
|
|
Point const p45 = convert_img_coord(rotated, a_p45);
|
|
if (!fequal(0, p45.x, sigma))
|
|
{
|
|
cerr << __LINE__ << " > Rotation origin by 45 degrees:" << endl;
|
|
cerr << " invalid x value: " << p45.x << " != " << 0 << endl;
|
|
cerr << " absolute point: " << a_p45 << endl;
|
|
cerr << " relative point: " << p45 << endl;
|
|
return false;
|
|
}
|
|
if (!fequal(p45.y, (h - 1) / 2.0f, sigma))
|
|
{
|
|
cerr << __LINE__ << " > Rotation origin by 45 degrees:" << endl;
|
|
cerr << "Invalid y value: " << p45.y << " != " << (h - 1) / 2.0f << endl;
|
|
cerr << " absolute point: " << a_p45 << endl;
|
|
cerr << " relative point: " << p45 << endl;
|
|
return false;
|
|
}
|
|
|
|
// Polar coordinates
|
|
{
|
|
DPoint const d(-42.5, 37.5);
|
|
double angle = 0;
|
|
double dist = 0;
|
|
convert_abs_to_polar_coord(d, angle, dist);
|
|
DPoint const reversed = convert_polar_to_grid_coord(angle, dist);
|
|
if (!fequal(d.x, reversed.x, sigma)
|
|
|| !fequal(d.y, reversed.y, sigma))
|
|
{
|
|
cerr << __LINE__ << " > Reverse polar coordinates:" << endl;
|
|
cerr << reversed << " != " << d << endl;
|
|
cerr << "polar (" << angle << ", " << dist << ")" << endl;
|
|
return false;
|
|
}
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
bool check_90(string const& path)
|
|
{
|
|
Image const src(path);
|
|
Image const rotated = rotate(src, 90);
|
|
|
|
for (unsigned int y = 0; y < rotated.height; ++y)
|
|
{
|
|
for (unsigned int x = 0; x < rotated.width; ++x)
|
|
{
|
|
unsigned rot_index = (y * rotated.width + x) * 3;
|
|
unsigned src_index = (x * src.width + (src.width - 1 - y)) * 3;
|
|
if (memcmp(&rotated.buffer[rot_index], &src.buffer[src_index], 3 * sizeof (uint8_t)) != 0)
|
|
{
|
|
Point r(x, y);
|
|
Point s((src.width - 1 - y), x);
|
|
cerr << __LINE__ << " | R: " << r << " != S:" << s << endl;
|
|
cerr << "R dim: " << rotated.width << " x " << rotated.height << endl;
|
|
cerr << "S dim: " << src.width << " x " << src.height << endl;
|
|
return false;
|
|
}
|
|
}
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
|
|
|
|
//
|
|
//
|
|
// Main
|
|
//
|
|
|
|
int main(int argc, char* argv[])
|
|
{
|
|
if (argc < 2)
|
|
{
|
|
cout << "Usage: " << argv[0] << " image.ppm" << endl;
|
|
return 1;
|
|
}
|
|
|
|
bool perform_check = true;
|
|
|
|
if (perform_check)
|
|
{
|
|
if (!check_points())
|
|
return 1;
|
|
|
|
if (!check_trigo())
|
|
return 1;
|
|
|
|
if (!check_90(argv[1]))
|
|
{
|
|
cerr << __LINE__ << " | 90 degrees check failed" << endl;
|
|
// return 1;
|
|
}
|
|
}
|
|
|
|
Image img(argv[1]);
|
|
|
|
for (double rotation = 0; rotation < 360; rotation += 5)
|
|
{
|
|
// double rotation = 45;
|
|
auto const before = chrono::high_resolution_clock::now();
|
|
|
|
Image rotated = rotate(img, rotation);
|
|
|
|
auto const after = chrono::high_resolution_clock::now();
|
|
auto const duration_ms = std::chrono::duration_cast<std::chrono::milliseconds>(after - before);
|
|
cout << "rotate(" << rotation << "): " << duration_ms.count() << " ms" << endl;
|
|
|
|
stringstream filename;
|
|
// filename << "/tmp/";
|
|
filename << "rotated_";
|
|
if (rotation < 100)
|
|
filename << "0";
|
|
if (rotation < 10)
|
|
filename << "0";
|
|
filename << rotation << ".ppm";
|
|
rotated.save(filename.str());
|
|
}
|
|
|
|
return 0;
|
|
}
|