(a)
(b)
(c)
Figure 1 Set (a) is not a solid object since it is not regular (it contains dangling lowerdimensional parts); sets (b) and (c) are solid objects; but only set (c) has a two-manifold
boundary.
Figure 2 Possible situations for two neighboring cells p1 and p2 in a mesh (the exploded view
of the two cells with their intersection segment is shown on the right). Mesh (a) is conforming,
while (b) is not conforming because the intersection between the boundaries of p1 and p2 is not
an edge of either of them.
(a)
(b)
Figure 3 Terrain models based on a planar triangle mesh with linear interpolating functions.
The mesh in (b) is not conforming (note the vertical crack in the surface over the thick edge).
Figure 4 Possible types of modifications of a given mesh
Figure 5 Some modification operators: (a) quadtree; (b) quaternary triangulation; (c)
bisection of right triangles; (d) vertex insertion; (e) vertex deletion; (f) edge collapse to a
middle point; (g) edge collapse to one endpoint.
Figure 6 A sequence of three batches refining an initial mesh. Modifications within the same
batch are highlighted with different colors.
Figure 7 The DAG of the multiresolution mesh defined by the modifications of Figure 6.
Figure 8 (a) A closed subset of nodes in the multiresolution mesh of Figure 7, and (b) the
corresponding mesh. Note that the mesh in (b) is not conforming (the thick segments have one
cell on one side and two cells on the other side).
Figure 9 The DAG of the conforming multiresolution mesh for the modifications of Figure 6.
(a)
(b)
(c)
Figure 10 (a) A non-conforming mesh from a quadtree, (b) balancing the subdivision, (c)
triangulation giving a conforming mesh.
(a)
(b)
Figure 11 (a) A non-conforming mesh from a quaternary triangulation; (b) the same mesh
made conforming through subdivision.
(a)
(b)
Figure 12 (a) The multiresolution mesh and (b) the conforming multiresolution mesh for a
quadtree.
(a)
(b)
(c)
Figure 13 (a) The batches, (b) the multiresolution mesh and (c) the conforming
multiresolution mesh of a hierarchy of right triangles.
(a)
(b)
Figure 14 (a) The multiresolution mesh and (b) the conforming multiresolution mesh for an
irregular nested model.
Figure 15 Edge collapse with its reverse edge split, and the corresponding forest branch.