Development of vector-parametric fifth-degree B-spline with control points incident the surface
DOI:
https://doi.org/10.15587/2312-8372.2016.72032Keywords:
vector-parametric spline, B-spline, spline with control points incident the curve, smoothnessAbstract
Studies in the field of geometric modeling are aimed at the development of the already existing ways of describing spline surfaces, because to be a bit inconvenient to construct smooth contours of the existing methods. A method in which the control points belong to the curve is proposed.
Based on previous research the method of B-spline construction is proposed. B-spline is a vector-parametric surface with control points incident (belonging to) the curve based on the fifth-degree splines in compliance with the smoothness of the first to the second order. To do this, the resulting vector-parametric spline r = r(u) will «stretch» to v, in a direction different from the u, which gives an opportunity to build a relevant «portions» of the surface. Further, to obtain a B-spline with full smoothness order it is necessary to ensure the «gluing» of the respective portions of the surface providing the appropriate smoothness by «gluing» line, i. e. ensure equality of the corresponding (first and second) derivatives. However, to achieve full smoothness of second order (i. e., ensure continuity of the second fundamental form across the surface), it is necessary to provide equal mixed derivatives through «gluing» line. Test examples of bicubic splines are given.
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