Approximately developable surface design method of interpolation given boundary curve

Abstract

The present invention discloses an approximately developable surface design method of an interpolation given boundary curve. The approximately developable surface design method comprises the steps ofdefining a developability objective function on a ruled surface, minimizing the developability objective function, at the same time, restraining a boundary curve of a surface to approximate the giventarget curve data points to obtain an approximately developable surface of the boundary approximation given curve data points, and then parameterizing the target data points to obtain an approximatelydevelopable surface of the boundary curve interpolation given data points. According to the present invention, an overall B spline surface is constructed directly without needing to utilize the independent surface patches to splice to construct a smooth surface.

Description

technical field [0001] The invention relates to an approximate developable curved surface design method for interpolating a given boundary curve. Background technique [0002] A developable surface can be unfolded onto a plane without stretching, and its Gaussian curvature is zero everywhere, which is a one-way curved surface. Especially in hull manufacturing, thin plate materials (such as steel plates, wood boards, etc.) are easy to be bent in one direction, but if these materials are used to form a two-way bent shape, complex processing techniques such as water and fire forming must be used, and the manufacturing cost is high. [0003] It has been a long-sought goal to use developable curved surfaces to construct hull shapes in application fields such as ship shape surface design. In engineering practice, the shape of the hull is represented by the molded line that can reflect the change of the hull surface, and the hull shape surface is obtained by constructing the surfa...

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Problems solved by technology

[0004] There are a lot of research work on developable surface modeling. One type of method uses B-spline or Bézier surface as the representation of developable surface, but this method sometimes produces surface shapes that do not meet expectations. The other type of method is to study the A method for constructing a developable mesh surface that interpolates discrete curves or sampled data points on the curves, given two curves C 1 and C 2 After that, first in the curve C 1 and C 2 Sampling on , discretize the two curves, and then seek the sampling point C 1 (u i )(i=0,...,n) and C 2 (t j )(j=0,...,m), the goal is to find the surface with the best scalability among all possible grids. The disadvantages of this type of method are:

[0005] 1) Too few sampling points will affect the quality of the final surface, and too many sampling points will result in low algorithm efficiency;

[0006] 2) The overall smoothness of the generated surface is difficult to control;

[0007] 3) The position of the self-intersection curve (regression curve) on the developable surface is difficult to control;

[0008] 4) Strict boundary interpolation conditions limit the degree of freedom of modeling, and in some cases it is difficult to obtain an interpolation surface with satisfactory scalability

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