TY - JOUR
T1 - Shape differentiation of freeform surfaces using a similarity measure based on an integral of Gaussian curvature
AU - Fu, Jing
AU - Joshi, Sanjay B.
AU - Simpson, Timothy W.
N1 - Funding Information:
Professor Simpson would like to acknowledge the support by NSF under grant# IIS 0325402. Any opinions, findings and conclusions or recommendations presented in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors thank Dr. Fabrice Alizon for providing the scanned models.
PY - 2008/3
Y1 - 2008/3
N2 - Freeform surfaces are popularly used to design and model complex 3D objects. These 3D models are stored as computerized models in databases. To facilitate data retrieval and shape matching, a major challenge lies in defining and computing the level of similarity between two or more freeform surfaces. In order to explore the useful 3D information associated with the surfaces, an integrated approach based on the integral of Gaussian curvature is proposed to develop the measures of similarity of freeform surfaces. Specifically, the integral of Gaussian curvature is mapped into the 2D space, and a shape-based measure is developed using statistical methods to compute the level of similarity. For smooth surfaces, a fast approximation algorithm is developed to calculate the curvature of individual subregions. In cases where the target surface has a complex topological structure or a smooth surface is not available, the integral of Gaussian curvature for the discrete surface is first calculated at each vertex, followed by mapping onto a 2D spherical coordinate. The distance measure focuses on the local geometry, which is critical to investigate models with a certain level of resemblance such as products in a family. This proposed approach can be applied to surfaces under various transformations, as well as 3D data from various sources.
AB - Freeform surfaces are popularly used to design and model complex 3D objects. These 3D models are stored as computerized models in databases. To facilitate data retrieval and shape matching, a major challenge lies in defining and computing the level of similarity between two or more freeform surfaces. In order to explore the useful 3D information associated with the surfaces, an integrated approach based on the integral of Gaussian curvature is proposed to develop the measures of similarity of freeform surfaces. Specifically, the integral of Gaussian curvature is mapped into the 2D space, and a shape-based measure is developed using statistical methods to compute the level of similarity. For smooth surfaces, a fast approximation algorithm is developed to calculate the curvature of individual subregions. In cases where the target surface has a complex topological structure or a smooth surface is not available, the integral of Gaussian curvature for the discrete surface is first calculated at each vertex, followed by mapping onto a 2D spherical coordinate. The distance measure focuses on the local geometry, which is critical to investigate models with a certain level of resemblance such as products in a family. This proposed approach can be applied to surfaces under various transformations, as well as 3D data from various sources.
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U2 - 10.1016/j.cad.2007.11.006
DO - 10.1016/j.cad.2007.11.006
M3 - Article
AN - SCOPUS:39949085783
SN - 0010-4485
VL - 40
SP - 311
EP - 323
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
IS - 3
ER -