Abstract
A new quartic Bernstein-like basis possessing two exponential shape parameters is developed and the condition of C2 ∩ FC2l+3 continuity and the definition of such continuity-related curves are discussed. Based on this new basis, a new cubic B-spline-like basis possessing two global and three local shape parameters is presented and the related cubic B-spline-like curves have C2 ∩ FC2l+3 continuity at each point and include the classical cubic uniform curves as a special case. Representative properties regarding connecting, interpolation and local adjustment of the cubic Bspline-like curves are also discussed.
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