Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
An explicit basis for C1 quartic by various bivariate splines
SIAM Journal on Numerical Analysis
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
A sharp upper bound on the approximation order of smooth bivariate PP functions
Journal of Approximation Theory
An Introduction to Polar Forms
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Box splines
ROAMing terrain: real-time optimally adapting meshes
VIS '97 Proceedings of the 8th conference on Visualization '97
Quadratic Bezier triangles as drawing primitives
HWWS '98 Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware
Developments in bivariate spline interpolation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Smooth approximation and rendering of large scattered data sets
Proceedings of the conference on Visualization '01
Terrain Simplification Simplified: A General Framework for View-Dependent Out-of-Core Visualization
IEEE Transactions on Visualization and Computer Graphics
Adaptive smooth scattered-data approximation for large-scale terrain visualization
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Geometry clipmaps: terrain rendering using nested regular grids
ACM SIGGRAPH 2004 Papers
Adaptive 4-8 Texture Hierarchies
VIS '04 Proceedings of the conference on Visualization '04
Planet-Sized Batched Dynamic Adaptive Meshes (P-BDAM)
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Real-time GPU rendering of piecewise algebraic surfaces
ACM SIGGRAPH 2006 Papers
An explicit quasi-interpolation scheme based on C 1 quartic splines on type-1 triangulations
Computer Aided Geometric Design
Optimal Lagrange interpolation by quartic C1 splines on triangulations
Journal of Computational and Applied Mathematics
A bivariate rational interpolation based on scattered data on parallel lines
Journal of Visual Communication and Image Representation
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We present an adaptive quasi-interpolating quartic spline construction for regularly sampled surface data. The method is based on a uniform quasi-interpolating scheme, employing quartic triangular patches with C 1-continuity and optimal approximation order within this class. Our contribution is the adaption of this scheme to surfaces of varying geometric complexity, where the tiling resolution can be locally defined, for example driven by approximation errors. This way, the construction of high-quality spline surfaces is enhanced by the flexibility of adaptive pseudo-regular triangle meshes. Numerical examples illustrate the use of this method for adaptive terrain modeling, where uniform schemes produce huge numbers of patches.