I'm rendering equilateral triangles of different sizes and I'm having trouble making them symmetric along the vertical axis. Here I have rendered two triangles. The triangle on the left (rendered correctly) has the coordinates (0.0, 0.0), (-7.0, 14.0) and (7.0, 14.0). The triangle on the right, on the other hand, has the coordinates (0.0, 0.0), (-7.0, 15.0) and (7.0, 15.0) and is not symmetric along the vertical axis.


Here are the matrices I'm using:

glm::mat4 model_matrix = glm::translate(glm::mat4(1.0f), glm::vec3(90.0f, 90.0f, 0.0f));
glm::mat4 view_matrix = glm::mat4(1.0f);
glm::mat4 projection_matrix = glm::ortho(0.0f, w * 1.0f, h * 1.0f, 0.0f);
glm::mat4 mvp_matrix = projection_matrix * view_matrix * model_matrix;

I'm aware of the diamond exit rule but I don't think that's the cause of the problem. Seems like the diamond exit rule only applies to line segments? This problem also exists when I try to make triangles symmetric in the horizontal axis. Cheers!

  • \$\begingroup\$ Can you try adding half a pixel to their coordinates and let us know what that does? \$\endgroup\$ – mouseas Apr 25 '14 at 22:51
  • \$\begingroup\$ I have tried that and it sometimes fixes the issue but not always. \$\endgroup\$ – Izaan Apr 25 '14 at 23:12
  • \$\begingroup\$ Can you speak more to your application for this? Neither of the triangles you've sketched out here is equilateral. Do you perhaps mean isosceles (mathworld.wolfram.com/IsoscelesTriangle.html )? \$\endgroup\$ – Steven Stadnicki Apr 26 '14 at 1:06
  • \$\begingroup\$ Sorry, the triangles were meant to be equilateral but I ended up making them isosceles while trying to make them symmetrical. The application is just me experimenting with things, I should have clarified this. \$\endgroup\$ – Izaan Apr 26 '14 at 11:36

This is a notoriously hard problem - the short answer is that to have all the right properties when it comes to overlapping line segments, line drawing has to have some inherent asymmetries; for instance, a line that falls on a half-pixel boundary must be drawn on that pixel can only be drawn on that half-pixel if the line comes 'from the left' but not 'from the right', in a loose sense. If you need your triangles to be perfectly symmetric, you're best off explicitly mirroring the pixels yourself.

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  • \$\begingroup\$ Thank you, that makes sense. Is there somewhere I can learn more about this? I'm guessing I should look for rasterization rules. \$\endgroup\$ – Izaan Apr 26 '14 at 11:37
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    \$\begingroup\$ @IzaanSiddiqi That's a good starting point; you'll also want to learn about line-drawing algorithms, in particular Bresenham's. If you're only drawing isolated triangles then the mirroring will work well, but note that even something as simple as trying to draw a strip of alternating point-up and point-down triangles will yield triangles of different shapes unless you're very careful - your left triangle, for instance, is left-right symmetric but its edges aren't top-bottom symmetric. \$\endgroup\$ – Steven Stadnicki Apr 26 '14 at 14:27

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