## List of Figures

1. Orientation of boundary data in two dimensions.
2. Orientation of cells and vertices for a three-dimensional face.
3. Framework used for the implementation of generic boundaries
4. Arbitrary original discretization of a spline. No vertex should be inserted in the shaded areas.
5. Procedure to follow to recover boundary edges
6. Face swapping in three dimensions
7. Edge swapping example
8. Canonical configurations for edge swapping, including repeat count.
9. Cross-section of the objective function in an optimization-based mesh-smoothing problem
10. Examples of apexes and folds.
11. Vertex removal by edge contraction in two dimensions