On optimal interpolation triangle incidences
SIAM Journal on Scientific and Statistical Computing
Long and thin triangles can be good for linear interpolation
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific and Statistical Computing
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A Developer's Survey of Polygonal Simplification Algorithms
IEEE Computer Graphics and Applications
Quadric-based polygonal surface simplification
Quadric-based polygonal surface simplification
Robust statistical estimation of curvature on discretized surfaces
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Lepp terminal centroid method for quality triangulation
Computer-Aided Design
Lepp terminal centroid method for quality triangulation: a study on a new algorithm
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
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We propose and discuss a new Lepp-surface method able to produce a small triangular approximation of huge sets of terrain grid data by using a two-goal strategy that assures both small approximation error and well-shaped 3D triangles. This is a refinement method which starts with a coarse initial triangulation of the input data, and incrementally selects and adds data points into the mesh as follows: for the edge e having the highest error in the mesh, one or two points close to (one or two) terminal edges associated with e are inserted in the mesh. The edge error is computed by adding the triangle approximation errors of the two triangles that share e, while each L"2-norm triangle error is computed by using a curvature tensor (a good approximation of the surface) at a representative point associated with both triangles. The method produces triangular approximations that capture well the relevant features of the terrain surface by naturally producing well-shaped triangles. We compare our method with a pure L"2-norm optimization method.