TY - JOUR
T1 - Estimating Error Bounds for Ternary Subdivision Curves/Surfaces
JO - Journal of Computational Mathematics
VL - 4
SP - 473
EP - 484
PY - 2007
DA - 2007/08
SN - 25
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8705.html
KW - Subdivision curve, Subdivision surface, Subdivision depth, Error bound.
AB - <p style="text-align: justify;">We estimate error bounds between ternary subdivision curves/surfaces and their control polygons after $k$-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend on the subdivision mask. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Our technique is independent of parametrization therefore it can be easily and efficiently implemented. This is useful and important for pre-computing the error bounds of subdivision curves/surfaces in advance in many engineering applications such as surface/surface intersection, mesh generation, NC machining, surface rendering and so on.</p>