Why the same mesh topology results are very different? Is that because mesh topology defines how the triangles are connected, but not constrains positions and distortion of triangles?
kevinliu64
@E-BAO I think that different geometry means that the points are located at different coordinates but the points for each triangle still remain the same. As a result, for the point that changes coordinates, all triangles using that point will also be affected. For same geometry but different mesh topology, I think that it means that each of the triangles have different points, which results in the mesh covering the same area, just in a different way/order.
gprechter
@E-BAO I think the use of topology is related to the graph representation of the shapes. In graph theory, IIRC, the topology of a graph has to do with its connectedness, like what vertices are connected by what edges. So, in the first example it seems like the geometry is the same, due to the layout of the vertices in space, but their connectedness (topology) is different. In the second example, their layout in 3D space is different, so the triangles are stretched, and the edges extended, but the connectedness of the vertices is the same. I could be wrong, but that is how I've interpreted it. I believe the professor mentioned thinking about it like a graph in lecture, and that definitely helped me understand what's happening here.
glee-
Linear transformations (e.g. scaling) of the mesh topology, as seen in the bottom example will preserve the mesh topology, but create a different geometry. One image that I found exemplifies this: https://www.scratchapixel.com/images/upload/transformations/cow-transform.png?
By scaling different parts of the mesh topology, we can simulate 'movement'.
ricli
My understanding of geometry vs topology is shapes that have the same geometry have the same coordinates for their points and shapes that have the same topology have edges that connect the same relative points. If you look at the same geometry different topology example on top, the vertices have the same relative locations, but the edges that connect the vertices are different (i.e. the right face). If you look at the same topology different geometry example on bottom, the edges are connecting the same points, but the relative positions of the vertices is different (i.e. the exaggerated top right corner).
eliot1019
Helped me understand what this meant from quora: "For example, for a topologist, a sphere and a bowl are the same, since you can deform one into the other. A coffee cup and a donut are also equivalent, they both have one hole. But a sphere and a donut are not the same since you can't deform continuously one into the other."
AronisGod
Different topology becomes relevant in our loop subdivision algorithm. The resultant shape will differ for the two different topological configurations of the cube presented on this page.
jchen12197
In project 4 part 5, we implemented bump mapping and displacement mapping. The only difference between the two was that displacement mapping changed the topology and position of vertices.
Why the same mesh topology results are very different? Is that because mesh topology defines how the triangles are connected, but not constrains positions and distortion of triangles?
@E-BAO I think that different geometry means that the points are located at different coordinates but the points for each triangle still remain the same. As a result, for the point that changes coordinates, all triangles using that point will also be affected. For same geometry but different mesh topology, I think that it means that each of the triangles have different points, which results in the mesh covering the same area, just in a different way/order.
@E-BAO I think the use of topology is related to the graph representation of the shapes. In graph theory, IIRC, the topology of a graph has to do with its connectedness, like what vertices are connected by what edges. So, in the first example it seems like the geometry is the same, due to the layout of the vertices in space, but their connectedness (topology) is different. In the second example, their layout in 3D space is different, so the triangles are stretched, and the edges extended, but the connectedness of the vertices is the same. I could be wrong, but that is how I've interpreted it. I believe the professor mentioned thinking about it like a graph in lecture, and that definitely helped me understand what's happening here.
Linear transformations (e.g. scaling) of the mesh topology, as seen in the bottom example will preserve the mesh topology, but create a different geometry. One image that I found exemplifies this: https://www.scratchapixel.com/images/upload/transformations/cow-transform.png?
By scaling different parts of the mesh topology, we can simulate 'movement'.
My understanding of geometry vs topology is shapes that have the same geometry have the same coordinates for their points and shapes that have the same topology have edges that connect the same relative points. If you look at the same geometry different topology example on top, the vertices have the same relative locations, but the edges that connect the vertices are different (i.e. the right face). If you look at the same topology different geometry example on bottom, the edges are connecting the same points, but the relative positions of the vertices is different (i.e. the exaggerated top right corner).
Helped me understand what this meant from quora: "For example, for a topologist, a sphere and a bowl are the same, since you can deform one into the other. A coffee cup and a donut are also equivalent, they both have one hole. But a sphere and a donut are not the same since you can't deform continuously one into the other."
Different topology becomes relevant in our loop subdivision algorithm. The resultant shape will differ for the two different topological configurations of the cube presented on this page.
In project 4 part 5, we implemented bump mapping and displacement mapping. The only difference between the two was that displacement mapping changed the topology and position of vertices.