66 lines
2.1 KiB
C++
66 lines
2.1 KiB
C++
#include <fstream>
|
|
#include <iostream>
|
|
#include <vector>
|
|
|
|
constexpr double sqrt3_2 = 0.86602540378444; // sqrt(3)/2
|
|
|
|
struct point {
|
|
double x;
|
|
double y;
|
|
};
|
|
|
|
std::vector<point> sierpinski_arrowhead_next(const std::vector<point>& points) {
|
|
size_t size = points.size();
|
|
std::vector<point> output(3*(size - 1) + 1);
|
|
double x0, y0, x1, y1;
|
|
size_t j = 0;
|
|
for (size_t i = 0; i + 1 < size; ++i, j += 3) {
|
|
x0 = points[i].x;
|
|
y0 = points[i].y;
|
|
x1 = points[i + 1].x;
|
|
y1 = points[i + 1].y;
|
|
double dx = x1 - x0;
|
|
output[j] = {x0, y0};
|
|
if (y0 == y1) {
|
|
double d = dx * sqrt3_2/2;
|
|
if (d < 0) d = -d;
|
|
output[j + 1] = {x0 + dx/4, y0 - d};
|
|
output[j + 2] = {x1 - dx/4, y0 - d};
|
|
} else if (y1 < y0) {
|
|
output[j + 1] = {x1, y0};
|
|
output[j + 2] = {x1 + dx/2, (y0 + y1)/2};
|
|
} else {
|
|
output[j + 1] = {x0 - dx/2, (y0 + y1)/2};
|
|
output[j + 2] = {x0, y1};
|
|
}
|
|
}
|
|
output[j] = {x1, y1};
|
|
return output;
|
|
}
|
|
|
|
void write_sierpinski_arrowhead(std::ostream& out, int size, int iterations) {
|
|
out << "<svg xmlns='http://www.w3.org/2000/svg' width='"
|
|
<< size << "' height='" << size << "'>\n";
|
|
out << "<rect width='100%' height='100%' fill='white'/>\n";
|
|
out << "<path stroke-width='1' stroke='black' fill='none' d='";
|
|
const double margin = 20.0;
|
|
const double side = size - 2.0 * margin;
|
|
const double x = margin;
|
|
const double y = 0.5 * size + 0.5 * sqrt3_2 * side;
|
|
std::vector<point> points{{x, y}, {x + side, y}};
|
|
for (int i = 0; i < iterations; ++i)
|
|
points = sierpinski_arrowhead_next(points);
|
|
for (size_t i = 0, n = points.size(); i < n; ++i)
|
|
out << (i == 0 ? "M" : "L") << points[i].x << ',' << points[i].y << '\n';
|
|
out << "'/>\n</svg>\n";
|
|
}
|
|
|
|
int main() {
|
|
std::ofstream out("sierpinski_arrowhead.svg");
|
|
if (!out) {
|
|
std::cerr << "Cannot open output file\n";
|
|
return EXIT_FAILURE;
|
|
}
|
|
write_sierpinski_arrowhead(out, 600, 8);
|
|
return EXIT_SUCCESS;
|
|
}
|