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2D Circles and Triangles

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Wayfarer    122
Anyone like to recommend an optimum way of drawing a 2D circle with triangles (least most triangles and still looks good)? I have two ways I''m considering. The easiest and simplest way is slicing the circle into triangle pies from the center. This would probably require a lot of triangle slices to get the circle smooth. The other way is starting with two large triangles at the top and bottom poles of the circle (like a diamond) and continually dividing the space in the corners into triangles until it appears smooth. Any suggestions? Wayfarer

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40 Thieves    122
Maybe draw a triangle, rotate it x number of degrees about one of the vertices then redraw... repeat (360/x) times... of course you''ll need to make the edge farthest from the rotation vertex (circumference / (360/x)) in length....

40

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Serge K    154
quote:
Original post by Wayfarer

Anyone like to recommend an optimum way of drawing a 2D circle with triangles (least most triangles and still looks good)?

I have two ways I''m considering. The easiest and simplest way is slicing the circle into triangle pies from the center. This would probably require a lot of triangle slices to get the circle smooth. The other way is starting with two large triangles at the top and bottom poles of the circle (like a diamond) and continually dividing the space in the corners into triangles until it appears smooth.

Actually, number of triangles appears to be (almost) the same for both ways.
Anyway - if you want to subdivide the circle (I mean - circular curve) into N pieces, you need >=(N-2) triangles.

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Wayfarer    122
Serge K,

So, given any curved surface, if I draw a line from one endpoint to the
other endpoint, and then both endpoints to the center of the curve,
I have my triangle representation of that curved surface?

Wayfarer

Edited by - Wayfarer on July 23, 2000 5:07:01 PM

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Mezz    571
I think Serge''s formula comes from the fact that you have one piece of a three sided triangle describing the edge of the circle, and they will undoubtably share some sides, I''m not too sure though.

Anyway...

Have you considered implicit surfaces?

-Mezz

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Wayfarer    122
Mezz,

Nope I haven''t. I did a quick search for polygon triangulation and that topic
came up a few, but it seemed a bit out of my league. I didn''t find anything
that focused on 2D circles and triangles specifically, but I think I will go
with the simple method of triangle slices around a center point. Thanks.

Wayfarer