Fig. 1. Example of non-manifold face topology.

Fig. 2. Stages of arc contraction. (a) to (b) Steps 1–3. Joining the cluster nodes and reassigning the node arcs. (b) to (c) Step 5. Uniting duplicate arcs.

Fig. 3. Geometric indices: (a) boundary angle sharpness; (b) relative region size.

Fig. 4. Boundary shape measures: (a) shared boundary ratio; (b) contact angle.

Fig. 5. The effect of the region-curvature measure on the model and its mesh: (a) original model; (b) the model simplified with no region-curvature constraint; (c) tetrahedral mesh of the model (873 elements), a good hexahedral mesh cannot be built; (d) model simplified with a region-curvature constraint (after applying the face-collapse procedure); (e) hexahedral mesh of the model (125 elements).

Fig. 6. Region curvature measurements: (a) measuring ψ_a and ψ_b; (b) measure ψ" height="17" width="13">_a by taking into account the change in the face normal over the distance. For a cylindrical surface this gives (c) the difference between ψ_a and ψ" height="17" width="13">_a on a complex surface.

Fig. 7. The stages of a face collapse between all neighbors: (a) a brick with a cut corner; (b) splitting the corner face into three parts; (c) the final model after the merge of the parts with adjacent faces.

Fig. 8. The stages of a face collapse between a sub-set of the neighbors: (a) a brick with a chamfered face; (b) intermediate state after splitting the chamfer into halves; (c) the brick after the collapse of the chamfer between two neighbor faces.

Fig. 9. Simplification of a dreidel shape: (a) initial model with 47 faces; (b) simplified model with 23 faces; (c) quadrilateral surface mesh of the simplified model.

Fig. 10. Simplification of a pump housing model: (a) initial model with 127 faces; (b) simplified model with 46 faces; (c) tetrahedral mesh of the simplified model (7491 elements).

Fig. 11. A faceted model simplification: (a) original model (94 faces); (b) model simplified using a planarity-based measure (use S¹ in S computation) (8 faces); (c) model simplified using a curvature-based measure (use S² in S computation) (3 faces).

Table 1. Simplification examples data. (NA stands for unset constraint value). The only threshold value which depends on the model or mesh size is A_max. For the dreidel model (the only one where A_max is set), A_max is four times the mesh size used in Fig. 9(c)