Surface interpolation on irregular networks with normal conditions
Computer Aided Geometric Design
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Fundamentals of computer aided geometric design
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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
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
Subdivision Surface Fitting to a Range of Points
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
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Fitting Subdivision Surfaces to Unorganized Point Data Using SDM
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Parameterization of triangle meshes over quadrilateral domains
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
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Graphical Models - Solid modeling theory and applications
Interpolation over Arbitrary Topology Meshes Using a Two-Phase Subdivision Scheme
IEEE Transactions on Visualization and Computer Graphics
Point-tangent/point-normal B-spline curve interpolation by geometric algorithms
Computer-Aided Design
Local progressive-iterative approximation format for blending curves and patches
Computer Aided Geometric Design
The convergence of the geometric interpolation algorithm
Computer-Aided Design
Locally adjustable interpolation for meshes of arbitrary topology
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part I
Technical Section: An extended iterative format for the progressive-iteration approximation
Computers and Graphics
Technical note: Progressive iteration approximation and the geometric algorithm
Computer-Aided Design
Weighted progressive interpolation of Loop subdivision surfaces
Computer-Aided Design
B-spline surface fitting by iterative geometric interpolation/approximation algorithms
Computer-Aided Design
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
Computer Graphics in China: Convergence analysis for B-spline geometric interpolation
Computers and Graphics
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We present a novel geometric algorithm to construct a smooth surface that interpolates a triangular or a quadrilateral mesh of arbitrary topological type formed by n vertices. Although our method can be applied to B-spline surfaces and subdivision surfaces of all kinds, we illustrate our algorithm focusing on Loop subdivision surfaces as most of the meshes are in triangular form. We start our algorithm by assuming that the given triangular mesh is a control net of a Loop subdivision surface. The control points are iteratively updated globally by a simple local point-surface distance computation and an offsetting procedure without solving a linear system. The complexity of our algorithm is O(mn) where n is the number of vertices and m is the number of iterations. The number of iterations m depends on the fineness of the mesh and accuracy required.