Bresenham's Line Algorithm
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Here's a C++ version; as in the previous article plot() draws a "dot" at (x, y):
#include <cmath> //////////////////////////////////////////////////////////////////////////////// void Bresenham(int x1, int y1, int x2, int y2) { int delta_x = std::abs(x2 - x1) << 1; int delta_y = std::abs(y2 - y1) << 1; // if x1 == x2 or y1 == y2, then it does not matter what we set here signed char ix = x2 > x1?1:-1; signed char iy = y2 > y1?1:-1; plot(x1, y1); if (delta_x >= delta_y) { // error may go below zero int error = delta_y - (delta_x >> 1); while (x1 != x2) { if (error >= 0) { if (error || (ix > 0)) { y1 += iy; error -= delta_x; } // else do nothing } // else do nothing x1 += ix; error += delta_y; plot(x1, y1); } } else { // error may go below zero int error = delta_x - (delta_y >> 1); while (y1 != y2) { if (error >= 0) { if (error || (iy > 0)) { x1 += ix; error -= delta_y; } // else do nothing } // else do nothing y1 += iy; error += delta_x; plot(x1, y1); } } }
And here 's a Ruby version, it returns an array of points, each being an hash with 2 elements (x and y)
def get_line(x0,x1,y0,y1)
points = [] steep = ((y1-y0).abs) > ((x1-x0).abs) if steep x0,y0 = y0,x0 x1,y1 = y1,x1 end if x0 > x1 x0,x1 = x1,x0 y0,y1 = y1,y0 end deltax = x1-x0 deltay = (y1-y0).abs error = (deltax / 2).to_i y = y0 ystep = nil if y0 < y1 ystep = 1 else ystep = -1 end for x in x0..x1 if steep points << {:x => y, :y => x} else points << {:x => x, :y => y} end error -= deltay if error < 0 y += ystep error += deltax end end return points end