Abstract
This research studies a new method for discrete surface blending. This method is based on combination of morphing and extension. Deriving from continuity conditions, extension of discrete surface is discussed. Fairness functional is also studied in thesis. Both MES (minimum energy surface) and MVS (minimum variation surface) are extended into discrete case. For MES, discrete curvature is introduced; For MVS, two approximations are presented. One is to minimize curvature change rate along principal direction; the other is to minimize maximum curvature change rate. Multidirectional searching method is applied in optimization. Plenty of examples are discussed in the end. The method presented in thesis can be applied in surface modeling.