| Summary: | In order to make curves and surfaces have adjustable shape and simple G3 conditions,a kind of EI functions is defined recursively. Based on them, we construct EI curves and surfaces,which have the most properties of Bézier curves and surfaces. Owe to the particularity of EI functions EI curves and surfaces possess two distinct advantages. (1)They have shape control parameter; (2)Their G3 conditions are just the G1 conditions for usual Bézier curves and surfaces. For a given set of points,in order to generate automatically smooth composite curves and surfaces, another kind of MI functions is defined based on EI functions. The MI curves and surfaces defined by MI functions also enjoy adjustable shape, simple continuity conditions. According to the continuity conditions, we have defined the composite MI curves and surfaces by a special way. With no need for any constraints, they can naturally achieve smooth connection.
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