Subject:
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Re: Checking for bowtie quads?
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Newsgroups:
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lugnet.cad.dev
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Date:
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Thu, 30 Mar 2000 20:11:00 GMT
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Reply-To:
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RUI.MARTINS@LINKspamcake.PT
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Viewed:
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5634 times
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It's funny but two weeks ago, I developed exactly this method, the one
with the cross products, and all the findings you got, too.
> Here is the algorithm I came up with before I decided to use the L3
> code as is. I had kinda given up on it since I only had it figured
> out for 2D screen coords. The trick of using the dot product to
> determine if the cross product vectors pointed in the opposite
> direction eluded me until I saw Lars' code. (You don't need it in 2D
> since the normals have only a z component and it's sign determines the
> direction of the turn).
>
> I think this is pretty similar to the method in L3.
>
> Calculate the normal vector for each vertex in the quad using the
> cross product. (We can use these again later for lighting, cool!)
>
> Eliminate colinear points (i = j = k = 0 in the normal). Make a
> triangle if only one. Discard the quad if more than one. Either way
> you're done if you found any colinear points.
>
> For each vertex calculate the dot product of its normal with the
> normal of the first vertex. The sign determines whether the
> turn at that vertex is clockwise or counterclockwise.
>
> If you get 3 similar turns and 1 opposite turn then you have a concave
> point at the oddball turn. Split the quad into 2 triangles at that
> point and you're done.
>
> If you have 2 clockwise and 2 counterclockwise turns then you have
> a bowtie. Find the first two adjacent vertices with the same turn,
> swap them, and you're done.
>
> Otherwise you must have 4 similar turns and an nice simple convex
> quad.
>
> Pretty neat, eh? And it's not all that complicated after all...
Isn't 3D math a wonderfull thing
P.S.
Maybe if I would have look at someone elses code or book, my life could
have been a lot easyer.
See ya
Rui Martins
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Message is in Reply To:
 | | Re: Checking for bowtie quads?
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| (...) Wow, I'm glad I revisited this since I think I can save some rendering time by saving the vertex normals from the bowtie checks for the OpenGl lighting phase in LdGLite. Here is the algorithm I came up with before I decided to use the L3 code (...) (27 years ago, 30-Mar-00, to lugnet.cad.dev)
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