Publication Detail

Piecewise continuous algebraic surfaces in terms of B-splines.

Nicholas M. Patrikalakis, George A. Kriezis
73 pp.
MITSG 88-5

Modeling with low-order algebraic B-spline patches bounded by rectangular boxes is investigated and reported in this work. Motivations behind the development of a method to represent sculptured shapes in the B-spline form are the degree reduction in the resulting representation, the capability for piecewise continuous shape representation, and the geometrical significance of the coefficients in this representation. Using Bernstein polynomials, a method of representing a finite portion of an algebraic surface within a rectangular box is extended to handle piecewise continuous algebraic surfaces within rectangular boxes defined in terms of triple products of B-spline basis functions. Various techniques for shape creation using the above formulation are developed, and several interrogation techniques used in the creation and analysis of the formulation are described. Results are summarized and possible applications given.

type: Technical reports

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