Sharp Edges

As mentioned before, one of the problems with Loop’s subdivision schemes is that the end surface is C1 and there are numerous cases where we would like to preserve some sharp features.

Hughes Hoppe refined the Loop subdivision rules to accommodate sharp edges.

Boundary Problems

What happens at the edges of a control mesh. Loop’ scheme “shrinks” the surface therefore pasting surfaces is hard (not even C0) .One of the alternatives is to preserve the corner vertices forcing a Bezier curve on the boundary. Therefore, joining boundary vertices achieves C0 continuity. Another alternative is to force the curve to “stick” to the boundary. The result is that we lose the C1 continuity at the boundary, but may help us to achieve other effects.

Infinitely Sharp

In real life, even the sharpest edges when looked very very closely they seem smooth. Sometimes we do not want to have infinitely sharp edge.