Will approximation always lead to the mesh becoming smaller?
x-fa19
I think so; if we're approximating, then this means that the mesh will "compress," but if we interpolate, then the size should remain relatively unchanged. Can someone correct/confirm?
DavidVakshlyak
Interpolation means that the original vertices of the control cage must be in the final smooth surface. This is also the case when interpolating two points in 1D given their values and derivatives. In approximation, the control cage may not include vertices of the final surface but it will influence where those final vertices are. It's kind like how in a beziér curve, the curve will never go through the middle two control points, but it will be influenced by them.
lhagaman
I think that the mesh becoming smaller is only guaranteed for convex meshes; if the mesh is concave, the vertices in the concave region will be pulled toward their neighbors, further from the center of the mesh.
Will approximation always lead to the mesh becoming smaller?
I think so; if we're approximating, then this means that the mesh will "compress," but if we interpolate, then the size should remain relatively unchanged. Can someone correct/confirm?
Interpolation means that the original vertices of the control cage must be in the final smooth surface. This is also the case when interpolating two points in 1D given their values and derivatives. In approximation, the control cage may not include vertices of the final surface but it will influence where those final vertices are. It's kind like how in a beziér curve, the curve will never go through the middle two control points, but it will be influenced by them.
I think that the mesh becoming smaller is only guaranteed for convex meshes; if the mesh is concave, the vertices in the concave region will be pulled toward their neighbors, further from the center of the mesh.