Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not adequate for generating smooth quasi-developable surfaces. We propose the first method which is capable of exploring the full solution space of continuous input curves to compute a smooth quasi-developable ruled surface with as large developability as possible. The resulting surface is exactly bounded by the input smooth curves and is guaranteed to have no self-intersections. The main contribution is a variational approach to compute a continuous mapping of parameters of input curves by minimizing a function evaluating surface developability. Moreover, we also present an algorithm to represent a resulting surface as a B-spline surface when input curves are B-spline curves.
use a composition of B-spline developable strips to approximate freeform architectural models @cite_16 , which essentially solve a constrained B-spline surface fitting problem @cite_17 . proposed an interactive developable surface design approach to create composite B-spline developable surfaces @cite_2 , in which a shape is designed through an incremental procedure of user modification and surface optimization. make use of the rectifying developable and propose an algorithm for modeling smooth developable surfaces from geodesic curves on surfaces @cite_22 . Complex developable surfaces are modeled by composing cone patches with smooth transitions @cite_7 . These design methods cannot be applied directly to compute a developable surface bounded by specified curves.
@cite_22 @cite_7 @cite_2 @cite_16 @cite_17
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Developable surfaces have many desired properties in the manufacturing process. Since most existing CAD systems utilize tensor-product parametric surfaces including B-splines as design primitives, there is a great demand in industry to convert a general free-form parametric surface within a prescribed global error bound into developable patches. In this paper, we propose a practical and efficient solution to approximate a rectangular parametric surface with a small set of C 0 -joint developable strips. The key contribution of the proposed algorithm is that, several optimization problems are elegantly solved in a sequence that offers a controllable global error bound on the developable surface approximation. Experimental results are presented to demonstrate the effectiveness and stability of the proposed algorithm. Abstract The use of developable surfaces in ship design is of engineering importance because they can be easily manufactured without stretching or tearing, or without the use of heat treatment. In some cases, a ship hull can be entirely designed with the use of developable surfaces. In this paper, a method to create a quasi-developable B -spline surface between two limit curves is presented. The centreline, chines and sheer lines of a vessel are modelled as B -spline curves. Between each pair of these boundary curves or directrix lines, the generator lines or rulings are created and a quasi-developable B -spline surface containing the rulings is defined. A procedure based on multiconic development is used to modify the directrix lines in case the rulings intersect inside the boundary curves, avoiding non-developable portions of the surface. B -spline curves and surfaces are widely used today in practically all the design and naval architecture computer programs. Some examples of ship hulls entirely created with developable surfaces are presented. Motivated by applications in architecture and manufacturing, we discuss the problem of covering a freeform surface by single curved panels. This leads to the new concept of semi-discrete surface representation, which constitutes a link between smooth and discrete surfaces. The basic entity we are working with is the developable strip model. It is the semi-discrete equivalent of a quad mesh with planar faces, or a conjugate parametrization of a smooth surface. We present a B-spline based optimization framework for efficient computing with D-strip models. In particular we study conical and circular models, which semi-discretize the network of principal curvature lines, and which enjoy elegant geometric properties. Together with geodesic models and cylindrical models they offer a rich source of solutions for surface panelization problems. AbstractSurface development is used in many manufacturing planning operations, e.g. for garments, ships and automobiles. However, most freeform surfaces used in design are not developable, and therefore the developed patterns are not isometric to the designed surface. In some domains, the CAD model is created by skinning operations that interpolate smooth strips between a specified set of skeleton curves. In this paper, we propose a method to approximate a strip with a developable surface between the two space curves bounding it. We allow one of the bounding curves to be perturbed within a controllable tolerance and meet some other special engineering requirements. We formulate the problem as a combination of a discrete combinatorial optimization problem and a constrained nonlinear optimization problem, and propose an efficient iterative approach to solve the problem.