Design of an n-sided surface patch from Hermite boundary data
Computer Aided Geometric Design
An arbitrary mesh network scheme using rational splines
Mathematical methods in computer aided geometric design II
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
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Blending, smoothing and interpolation of irregular meshes using N-sided Varady patches
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Triangular G1 interpolation by 4-splitting domain triangles
Computer Aided Geometric Design
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Rapid evaluation of Catmull-Clark subdivision surfaces
Proceedings of the seventh international conference on 3D Web technology
Polynomial Surfaces Interpolating Arbitrary Triangulations
IEEE Transactions on Visualization and Computer Graphics
The SPHERIGON: A Simple Polygon Patch for Smoothing Quickly Your Polygonal Meshes
CA '98 Proceedings of the Computer Animation
Design of solids with free-form surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Variational shape approximation
ACM SIGGRAPH 2004 Papers
A realtime GPU subdivision kernel
ACM SIGGRAPH 2005 Papers
Geometric Modeling
N-sided patches with B-spline boundaries
Computers and Graphics
GPU conversion of quad meshes to smooth surfaces
Proceedings of the 2008 ACM symposium on Solid and physical modeling
PNG1 triangles for tangent plane continuous surfaces on the GPU
GI '08 Proceedings of graphics interface 2008
ACM SIGGRAPH Asia 2008 papers
ACM SIGGRAPH Asia 2008 papers
Approximating subdivision surfaces with Gregory patches for hardware tessellation
ACM SIGGRAPH Asia 2009 papers
A geometric criterion for smooth interpolation of curve networks
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Smooth force rendering on coarse polygonal meshes
Computer Animation and Virtual Worlds - CASA' 2010 Special Issue
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We present a method for refining n-sided polygons on a given piecewise linear model by using local computation, where the curved polygons generated by our method interpolate the positions and normals of vertices on the input model. Firstly, we construct a Bezier curve for each silhouette edge. Secondly, we employ a new method to obtain C^1 continuous cross-tangent functions that are constructed on these silhouette curves. An important feature of our method is that the cross tangent functions are produced solely by their corresponding facet parameters. Gregory patches can therefore be locally constructed on every polygon while preserving G^1 continuity between neighboring patches. To provide a flexible shape control, several local schemes are provided to modify the cross-tangent functions so that the sharp features can be retained on the resultant models. Because of the localized construction, our method can be easily accelerated by graphics hardware and fully run on the Graphics Processing Unit (GPU).