A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Combining 4- and 3-direction subdivision
ACM Transactions on Graphics (TOG)
Artifact analysis on B-splines, box-splines and other surfaces defined by quadrilateral polyhedra
Computer Aided Geometric Design
Artifacts in box-spline surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Artifact analysis on B-splines, box-splines and other surfaces defined by quadrilateral polyhedra
Computer Aided Geometric Design
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Surface artifacts are features in a surface which cannot be avoided by movement of control points. They are present in B-splines, box splines and subdivision surfaces. We showed how the subdivision process can be used as a tool to analyse artifacts in surfaces defined by quadrilateral polyhedra (Sabin et al., 2005; Augsdorfer et al., 2011). In this paper we are utilising the subdivision process to develop a generic expression which can be employed to determine the magnitude of artifacts in surfaces defined by any regular triangular polyhedra. We demonstrate the method by analysing box-splines and regular regions of subdivision surfaces based on triangular meshes: Loop subdivision, Butterfly subdivision and a novel interpolating scheme with two smoothing stages. We compare our results for surfaces defined by triangular polyhedra to those for surfaces defined by quadrilateral polyhedra.