A survey on shape preserving interpolation

Shape preserving interpolation is an essential technique in geometric design and of great significance in various areas such as curve/surface modeling, numerical approximation and reverse engineering. In this paper, we summarize roundly various shape preserving interpolation theories and algorithms in curve/surface modeling. Then, shape preserving offset approximation and shape preserving degree reduction approximation are investigated. Finally, we bring up some problems which are significant but have not been solved well up to now.