10-09-2018, 02:09 PM
(This post was last modified: 10-09-2018, 06:47 PM by josemendez.)
(10-09-2018, 12:19 PM)Wassink Wrote: Hi Jose, why do people prefer the triangle areas weights? I feel like I'm missing an important piece of the puzzle, so to speak.
Hi!
The link I posted at the end of the previous response does a great job at explaining it:
http://www.bytehazard.com/articles/vertnorm.html
My pitiful attempt of an explanation:
Consider a vertex where three triangles meet: one of them is fairly large, the other two are very small and have a completely different orientation. If you assigned the same weight to all three triangles, the two smaller ones would influence the normal a lot: 66% of the resulting normal would be that of those two small triangles, skewing the surface normal towards them. However one would expect the bigger triangle to "win" as it covers a lot more surface area of the model, and is visually more important.
By using areas as weights, larger triangles contribute more to the normal (in proportion to their size), and this problem is solved.
PS: quick tip: generally, the cross product of two triangle edges is used to calculate the face normal and accumulate it to each vertex. Since the length of the cross product of two vectors is proportional to the area of the parallelogram spawned by them, we can exploit this to calculate area weighted normals even more efficiently than we could by simply averaging: by skipping the normalization of each face's contribution to the vertex and only normalizing once all contributions have been added, you're area weighting for free. It's much faster and looks much better than the naive method, so what else could you ask for?. See:
https://www.iquilezles.org/www/articles/...ormals.htm