Intrinsic parametrization for approximation
Computer Aided Geometric Design
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Multiresolution feature extraction for unstructured meshes
Proceedings of the conference on Visualization '01
Approximation with Active B-Spline Curves and Surfaces
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Analysis and application of subdivision surfaces
Analysis and application of subdivision surfaces
Fitting Subdivision Surfaces to Unorganized Point Data Using SDM
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Optimization methods for scattered data approximation with subdivision surfaces
Graphical Models - Solid modeling theory and applications
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Design and Analysis of Optimization Methods for Subdivision Surface Fitting
IEEE Transactions on Visualization and Computer Graphics
Technical Section: Ternary butterfly subdivision
Computers and Graphics
SMI 2012: Short A revisit to fitting parametric surfaces to point clouds
Computers and Graphics
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Various methods have been proposed for fitting subdivision surfaces to different forms of shape data (e.g., dense meshes or point clouds), but none of these methods effectively deals with shapes with sharp features, that is, creases, darts and corners. We present an effective method for fitting a Loop subdivision surface to a dense triangle mesh with sharp features. Our contribution is a new exact evaluation scheme for the Loop subdivision with all types of sharp features, which enables us to compute a fitting Loop subdivision surface for shapes with sharp features in an optimization framework. With an initial control mesh obtained from simplifying the input dense mesh using QEM, our fitting algorithm employs an iterative method to solve a nonlinear least squares problem based on the squared distances from the input mesh vertices to the fitting subdivision surface. This optimization framework depends critically on the ability to express these distances as quadratic functions of control mesh vertices using our exact evaluation scheme near sharp features. Experimental results are presented to demonstrate the effectiveness of the method.