Subdivision surface fitting to a dense mesh using ridges and umbilics

Xinhui Ma, Simeon Keates, Yong Jiang, Jiri Kosinka

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
130 Downloads (Pure)


Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach.
Original languageEnglish
Pages (from-to)5-21
Number of pages17
JournalComputer Aided Geometric Design
Early online date20 Nov 2014
Publication statusPublished - Jan 2015


  • Hausdorff distance
  • Principal curvature vector
  • Subdivision surface fitting
  • Feature alignment
  • Ridges
  • Umbilics


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