5683427
Developability-preserved free-form deformation of assembled patches
A novel and practical approach is presented in this paper that solves a constrained free-form deformation (FFD) problem where the developability of the tessellated embedded surface patches is preserved during the lattice deformation. The formulated constrained FFD problem has direct application in areas of product design where the surface developability is required, such as clothing, ship hulls, automobile parts, etc. In the proposed approach, the developability-preserved FFD problem is formulated as a constrained optimization problem. Different from other contained FFD approaches, the positions of lattice control points are not modified in our algorithm -- as their control is insufficient in regards to the developability of all the nodes in the mesh. Moreover, the optimization is performed on the parameters of the mesh nodes rather than directly modifying their 3D coordinates, which avoids the time-consuming inverse calculation of the parameters of every node in a non-parallelepiped control lattice when further deformations are required.
125731656
Congruent partition and certain computational geometry problems.
17802180
Pattern computation for compression garment
This paper addresses the problem of computing planar patterns for compression garments. In the garment industry, the compression garment has been more and more widely used to retain a shape of human body, where certain strain (or normal pressure) is designed at some places on the compression garment. Variant values and distribution of strain can only be generated by sewing different 2D patterns and warping them onto the body. We present a physical/geometric approach to compute 2D meshes that, when folded onto the 3D body, can generate a user-defined strain distribution through proper distortion. This is opposite to the widely studied mesh parameterization problem, whose objective is to minimize the distortion between the 2D and 3D meshes in angle, area or length.
5214346
Efficient and stable numerical algorithms on equilibrium equations for geometric modeling
In this paper the applications of equilibrium equation to geometric modeling is exploited and efficient numerical algorithms are proposed for solving the equilibrium equation. First we show that from diverse geometric modeling applications the equilibrium system can be extracted as the central framework. Second, by exploiting in-depth the special structures inherent in the geometric applications, we present simplified analytic solutions to the resulting geometric equilibrium equations via system decomposition. Finally, given the observation that the geometric equilibrium systems are extremely sensitive to both perturbations in input data and round off errors, efficient, stable and accurate numerical algorithms are proposed.
166971
Modeling wrinkles on smooth surfaces for footwear design
We describe two new shape operators that superimpose wrinkles on top of a smooth NURBS surface. Previous research studying wrinkles focused mostly on cloth modeling or in animations, which are driven more by visual realism, but allow large elastic deformations. Our operators generate wrinkle-shaped deformations in a region of a smooth surface along a given boundary based on a few basic parametric inputs such as wrinkle magnitude and extent (these terms will be defined in the paper). The essential geometric transformation to map the smooth surface to a wrinkled one will be defined purely in terms of the geometry of the surface and the input parameters. Our model is based on two surface properties: geodesic offsets and surface energy. Practical implementation of the operators is discussed, and examples presented. Finally, the motivation for the operators will be given through their application in the computer-aided design and manufacture of footwear.
12350684
Computing planar sections of surfaces of revolution with revolute quadric decomposition
Computing the planar sections of objects is a fundamental operation in solid modeling. Subdivision method is commonly used for solving such intersection problems. In this paper, a revolute quadric decomposition is proposed for surfaces of revolution, which are subdivided into a set of coaxial revolute quadrics along the generatrix. This reduces the intersection problem of a plane and a surface of revolution to the intersection problem of a plane and a revolute quadric, which has robust, accurate and efficient geometric solution. Further, the intersection curves can be represented with a group of G (G. Baciu et al., 2001) conic arcs. A new concept, valid intersection interval (VII), is introduced and a new technique, cylindrical bounding shell clipping, is proposed for efficient intersection detection for a plane and a surface of revolution. Finally, a tracing algorithm is presented for recognizing singular points and closed loops of intersection curves. Implemented examples show the robustness and effectiveness of the proposed algorithm.
195710929
A Supply Chain Network Design Model for Deteriorating Items
We consider a supply chain network design problem for deteriorating items, involving a single supplier, some potential distribution centers and multiple retailers. This problem is to determine how many distribution centers to set up, where to locate them, how to serve the retailers using these distribution centers, and to determine the optimal inventory policies for the whole supply chain network. The goal is to minimize the total deterioration, inventory, transportation and facilities location cost. We formulate this problem as a nonlinear mix-integer programming model. This model is a NP-Hard problem, so we present a Lagrangian relaxation solution algorithm and a Genetic algorithm to solve our model respectively. Finally, numerical examples are given to illustrate the application of these two algorithms, and our computational results show that Lagrangian relaxation algorithm is more efficient for our problem.