Proceedings of the 2005 ACM symposium on Solid and physical modeling
Spherical manifolds for adaptive resolution surface modeling
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Graphical Models - Special issue on SPM 05
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Manifold splines with a single extraordinary point
Computer-Aided Design
Computer-Aided Design
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
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Traditional approaches for modeling a closed manifold surface with either regular tensor-product or triangular splines (defined over an open planar domain) require decomposing the acquired geometric data into a group of charts, mappingeach chart to a planar parametric domain, fitting an opensurface patch of certain degree to each chart, and finally,trimming the patches (if necessary) and stitching all of them together to form a closed manifold. In this paper, we develop a novel modeling method which does not need any cutting or patching operations for genus zero surfaces. Our new approach is founded upon the concept of spherical splines proposed by Pfeifle and Seidel. Our work is strongly inspired by the fact that, for genus zero surfaces, it is both intuitive and necessary to employ spheres as their natural domains. Using this framework, we can convert genus zero mesh to a single rational spherical spline whose maximal error deviated from the original data is less than a user-specified tolerance. With the rational spherical splines, we can model sharp features and edit both the global shape and the local details with ease. Furthermore, we can accurately compute the differential quantities without resorting to any numerical approximations. We conduct several experiments in order to demonstrate the efficacy of our approach for reverse engineering, shape modeling, and interactive graphics.