Shape preserving interpolation by curvature continuous parametric curves
Computer Aided Geometric Design
Local generalized Hermite interpolation by quartic C2 space curves
ACM Transactions on Graphics (TOG)
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
Local surface interpolation with Be´zier patches: errata and improvements
Computer Aided Geometric Design
An approximately G1 cubic surface interpolant
Mathematical methods in computer aided geometric design II
Surface approximation using geometric Hermite patches
Surface approximation using geometric Hermite patches
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
Geometric Hermite interpolation
Computer Aided Geometric Design
Geometric Hermite interpolation with maximal order and smoothness
Computer Aided Geometric Design
Matrix computations (3rd ed.)
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
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Implicit Objects in Computer Graphics
Implicit Objects in Computer Graphics
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Planar G2 Hermite interpolation with some fair, C-shaped curves
Journal of Computational and Applied Mathematics
Constrained interpolation with rational cubics
Computer Aided Geometric Design
Level of Detail for 3D Graphics
Level of Detail for 3D Graphics
Quadric-based simplification in any dimension
ACM Transactions on Graphics (TOG)
Hierarchical triangular splines
ACM Transactions on Graphics (TOG)
Geometric Hermite interpolation: in memoriam Josef Hoschek
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
G2 curve design with a pair of Pythagorean Hodograph quintic spiral segments
Computer Aided Geometric Design
Parametric triangular Bézier surface interpolation with approximate continuity
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Subdivision Surfaces
Interpolating G1 Bézier surfaces over irregular curve networks for ship hull design
Computer-Aided Design
Adaptive polygonization of implicit surfaces
Computers and Graphics
High accuracy geometric Hermite interpolation
Computer Aided Geometric Design
Local and singularity-free G 1 triangular spline surfaces using a minimum degree scheme
Computing - Geometric Modelling, Dagstuhl 2008
G2 B-spline interpolation to a closed mesh
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
Graphical Models
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In this paper, we present a method for the approximation of implicit surface by G^1 triangular spline surface. Compared with the polygonization technique, the presented method employs piecewise polynomials of high degree, achieves G^1 continuity and is capable of interpolating positions, normals, and normal curvatures at vertices of an underlying base mesh. To satisfy vertex enclosure constraints, we develop a scheme to construct a C^2 consistent boundary curves network which is based on the geometric Hermite interpolation of normal curvatures. By carefully choosing the degrees of scalar weight functions, boundary Bezier curves and triangular Bezier patches, we propose a local and singularity free algorithm for constructing a G^1 triangular spline surface of arbitrary topology. Our method achieves high precision at low computational cost, and only involves local and linear solvers which leads to a straightforward implementation. Analyses of freedom and solvability are provided, and numerical experiments demonstrate the high performance of algorithms and the visual quality of results.