Optimization methods for scattered data approximation with subdivision surfaces
Graphical Models - Solid modeling theory and applications
Interpolation by geometric algorithm
Computer-Aided Design
A fast algorithm for ICP-based 3D shape biometrics
Computer Vision and Image Understanding
Semantic fitting and reconstruction
Journal on Computing and Cultural Heritage (JOCCH)
Technical Section: Fourier method for large-scale surface modeling and registration
Computers and Graphics
Fitting sharp features with loop subdivision surfaces
SGP '08 Proceedings of the Symposium on Geometry Processing
Fitting subdivision surface models to noisy and incomplete 3-D data
MIRAGE'07 Proceedings of the 3rd international conference on Computer vision/computer graphics collaboration techniques
Use of sub-division surfaces in architectural form-finding and procedural modelling
Proceedings of the 2011 Symposium on Simulation for Architecture and Urban Design
Fitting polynomial volumes to surface meshes with Voronoï squared distance minimization
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We study the reconstruction of smooth surfaces from point clouds. We use a new squared distance error term in optimization to fit a subdivision surface to a set of unorganized points, which defines a closed target surface of arbitrary topology. The resulting method is based on the framework of squared distance minimization (SDM) proposed by Pottmann et al. Specifically, with an initial subdivision surface having a coarse control mesh as input, we adjust the control points by optimizing an objective function through iterative minimization of a quadratic approximant of the squared distance function of the target shape. Our experiments show that the new method (SDM) converges much faster than the commonly used optimization method using the point distance error function, which is known to have only linear convergence. This observation is further supported by our recent result that SDM can be derived from the Newton method with necessary modifications to make the Hessian positive definite and the fact that the Newton method has quadratic convergence.