Curvature continuous triangular interpolants
Mathematical methods in computer aided geometric design
On the G1 continuity of piecewise Be´zier surfaces: a review with new results
Computer-Aided Design - Special Issue: Be´zier Techniques
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
An implicit surface polygonizer
Graphics gems IV
A G1 triangular spline surface of arbitrary topological type
Computer Aided Geometric Design
Degenerate polynomial patches of degree 4 and 5 used for geometrically smooth interpolation in R3
Computer Aided Geometric Design
SIAM Journal on Numerical Analysis
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Optimal geometric Hermite interpolation of curves
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Triangular G1 interpolation by 4-splitting domain triangles
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Quadric-based simplification in any dimension
ACM Transactions on Graphics (TOG)
Hierarchical triangular splines
ACM Transactions on Graphics (TOG)
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Parametric triangular Bézier surface interpolation with approximate continuity
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
High-order approximation of implicit surfaces by G1 triangular spline surfaces
Computer-Aided Design
Interpolating G1 Bézier surfaces over irregular curve networks for ship hull design
Computer-Aided Design
G1 Bézier surface generation from given boundary curve network with T-junction
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Constructing G1 Bézier surfaces over a boundary curve network with T-junctions
Computer-Aided Design
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We develop a scheme for constructing G 1 triangular spline surfaces of arbitrary topological type. To assure that the scheme is local and singularity-free, we analyze the selection of scalar weight functions and the construction of the boundary curve network in detail. With the further requirements of interpolating positions, normals, and surface curvatures, we show that the minimum degree of such a triangular spline surface is 6. And we present a method for constructing boundary curves network, which consists of cubic Bézier curves. To deal with certain singular cases, the base mesh must be locally subdivided and we proposed an adaptive subdivision strategy for it. An application of our G 1 triangular spline surfaces to the approximation of implicit surfaces is described. The visual quality of this scheme is demonstrated by some examples.