Lecture 8: Mesh Representations and Geometry Processing (36)
yinxudeng
Since the calculation of new vertices depend on old vertices, do we update old vertices before updating new vertices or vice versa?
phoebeli23
Are new weights generated each time a triangle is split?
JefferyYC
On the bottom left image there are 5 new vertices. How do we update the other 4 besides the one drawn in white? Do we use other triangles not drawn in the image?
@yinxudeng I have the same question. I am guessing we calculate new values for both new and old vertices using the original values of the old vertices.
CarneAsadaFry
I'm also pretty confused by this slide. In addition to all the questions above, how are weights initialized in this algorithm? And how exactly are weights used to assign positions? Is it correct to say that the new vertex is a linear combination of the old vertices' positions, scaled by their weights?
atsu-kotani
The way I understand this slide is that the bottom two figures only talk about the new locations of two white vertices, and if we only focus on vertices on the center horizontal axis (i.e. marked as 83, white dot, 83, and also u, black dot, white dot, etc.) to make the argument simple, the white vertex on the bottom left figure is the midpoint of two original vertices and this is shown as two small black neighboring vertices of the white vertex in the right figure (i.e. the dot between u and 1-n*u and also between 1-n*u and u). If we imagine the white vertex on the right sticking out towards us on a surface of a bumpy sphere, the weighted average (i.e. a new vertex location for an old vertex) will pull the point towards the center of a sphere. Further, in the next iteration the black u vertices on the right will be the white new vertices from a previous iteration, which would further contribute to smooth the surface.
Since the calculation of new vertices depend on old vertices, do we update old vertices before updating new vertices or vice versa?
Are new weights generated each time a triangle is split?
On the bottom left image there are 5 new vertices. How do we update the other 4 besides the one drawn in white? Do we use other triangles not drawn in the image?
@yinxudeng I have the same question. I am guessing we calculate new values for both new and old vertices using the original values of the old vertices.
I'm also pretty confused by this slide. In addition to all the questions above, how are weights initialized in this algorithm? And how exactly are weights used to assign positions? Is it correct to say that the new vertex is a linear combination of the old vertices' positions, scaled by their weights?
The way I understand this slide is that the bottom two figures only talk about the new locations of two white vertices, and if we only focus on vertices on the center horizontal axis (i.e. marked as 83, white dot, 83, and also u, black dot, white dot, etc.) to make the argument simple, the white vertex on the bottom left figure is the midpoint of two original vertices and this is shown as two small black neighboring vertices of the white vertex in the right figure (i.e. the dot between u and 1-n*u and also between 1-n*u and u). If we imagine the white vertex on the right sticking out towards us on a surface of a bumpy sphere, the weighted average (i.e. a new vertex location for an old vertex) will pull the point towards the center of a sphere. Further, in the next iteration the black u vertices on the right will be the white new vertices from a previous iteration, which would further contribute to smooth the surface.