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.
Developable surfaces are surfaces that can be unfolded into the plane with no distortion. Although ubiquitous in our everyday surroundings, modeling them using existing tools requires significant geometric expertise and time. Our paper simplifies the modeling process by introducing an intuitive sketch-based approach for modeling developables. We develop an algorithm that given an arbitrary, user specified 3D polyline boundary, constructed using a sketching interface, generates a smooth discrete developable surface that interpolates this boundary. Our method utilizes the connection between developable surfaces and the convex hulls of their boundaries. The method explores the space of possible interpolating surfaces searching for a developable surface with desirable shape characteristics such as fairness and predictability. The algorithm is not restricted to any particular subset of developable surfaces. We demonstrate the effectiveness of our method through a series of examples, from architectural design to garments. 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. Developable surfaces have many desired properties in manufacturing process. Since most existing CAD systems utilize parametric surfaces as the design primitive, there is a great demand in industry to convert a parametric surface within a prescribed global error bound into developable patches. In this work we propose a simple and efficient solution to approximate a general parametric surface with a minimum set of C0-joint developable strips. The key contribution of the proposed algorithm is that, several global 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. Design using free-form developable surfaces plays an important role in the manufacturing industry. Currently most commercial systems can only support converting free-form surfaces into approximate developable surfaces. Direct design using developable surfaces by interpolating descriptive curves is much desired in industry. In this paper, by enforcing a propagation scheme and observing its nesting and recursive nature, a dynamic programming method is proposed for the design task of interpolating 3D boundary curves with a discrete developable surface. By using dynamic programming, the interpolatory discrete developable surface is obtained by globally optimizing an objective that minimizes tangent plane variations over a boundary triangulation. The proposed method is simple and effective when used in industry. Experimental results are presented that demonstrate its practicality and efficiency in industrial design.