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The modeling of developable surfaces is considered a very important application in plat-metal-based industries. Relating to the purpose, this discussion aims to obtain some formulas for constructing the regular developable Bézier patches, in which each boundary curve must be laid in two parallel planes. The results as follows: We find some formulas of the equation systems that are described by the constant, linear, and quadratic control parameters of the regular developable Bézier patches criteria. The new approach is numerically tested for constructing the regular developable Bézier patches, in which their boundary curves are defined, respectively, by the combination of four, five, and six degrees.
- regular
- developable Bézier patches
- control parameter
The paper is organized in the following sections:In the first section, we discuss condition and regularity of the developable Bézier patches, which are supported by two parallel planes. In the second, we talk about the construction of the regular developable Bézier patches models that are defined by two curves planes from the combination of four, five, and sixdegrees. Finally, the results will be summarized in the conclusion section.
