Lecture 10: Meshes and Manifolds (CMU 15-462/662)

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Keenan Crane

Күн бұрын

Full playlist: • Computer Graphics (CMU...
Course information: 15462.courses.cs.cmu.edu/

Пікірлер: 20

@user-ef3ej4pq4f 3 жыл бұрын

This is pure gold, thanks for sharing

@familywu3869 5 ай бұрын

Thank you very much for sharing your wisdom and precious education opportunity, Professor Crane. This is excellent and very helpful.

@mrinalde 3 жыл бұрын

we are fortunate to learn from him. I have been waiting to watch his lectures from a long time...

@tylerbakeman 5 ай бұрын

11:00 Manifolds aren’t restricted to 2D, and all of the meshes can be represented as a Manifold (not necessarily a “Smooth manifold”). A Manifold is a Geometric space (a collection of points), where limits are defined- in Euclidean Space (a smooth space), those 2 shapes are both continuous, but the limit is not defined for one of them (the one in the top right): I think the one in the top-left is probably a smooth manifold, because the limit should exist. However, technically none of these are functions- so it makes it more difficult (which is math that I would consult from someone who’s better at algebraic topology)… but yeah, each of these are manifolds- not necessarily Smooth manifolds. The top-right is tricky though. Idk very much about non-smooth manifolds.

@cagatayyigit683 3 жыл бұрын

thank you so much for these excellent lessons!

@luyucheng 3 жыл бұрын

Thanks for sharing.

@khoavo5758 3 ай бұрын

3:29 profound question… But I guess it has something to do with being able to measure distance between grid cells. Using square grids, the distance falls out of the cell coordinates; I guess it wouldn’t be so with f.ex a hex grid. And the deeper meaning is just… math: square grids play nice with the Cartesian coordinate system.

@tharteon1866 9 ай бұрын

Hello professor Crane, i'd really like you to make a video about voxel rendering and to talk about how it resembles pixels but in 3d. And explain all the intricacies it involves.

@max.bittker 2 жыл бұрын

great lecture

@diribigal 2 жыл бұрын

I didn't fully understand the halfedge idea from the DDG series, but this was very clear and seems like a great fit for manifolds.

@abakir8259 8 ай бұрын

The Stanford Bunny model is not a manifold because it contains holes.

@seremetvlad 3 жыл бұрын

thank you

@ai-vg2gi 6 ай бұрын

Hello Prof. thank you for making such beautifully explained videos. I would request you to kindly share the slides of 2020 lectures, on course link there is slides of current Lectures 2023.

@GuillermoValleCosmos 3 жыл бұрын

at 35:00, for the incidence matrices. Why is finding neighbours O(1)? Doesn't it require iterating over all rows of the matrix, so it's linear like before? Is it just that matrix operations are more optimized?

@keenancrane 3 жыл бұрын

Keep watching! The next slide discusses sparse matrix data structures, which make this an O(1) operation.

@GuillermoValleCosmos 3 жыл бұрын

@@keenancrane ah i see, thanks!. Hmm, tho the compressed column format would make it easy to find incident edges to a vertex, but to then find the vertices that those edges are incident into, you'd need to traverse the list of all edges? Unless you also had a compressed row linked list one lying around. I guess having both is a good idea if you want to find neighbouring vertices then?

@keenancrane 3 жыл бұрын

@@GuillermoValleCosmos Correct. In practice it's often useful to store the incidence matrices and their transposes. The discussion in this paper has some more details that will eventually be relevant for our discussion of discrete exterior calculus: multires.caltech.edu/pubs/scomplex.pdf