We introduce the problem of clustering the set of vertices in a given 3D mesh. The problem is motivated by the need for value engineering in architectural projects. We first derive a max-norm based metric to estimate the geometric disparity between a given pair of vertices, and characterize the problem in terms of this measure. We show that this distance can be computed by using Sequential Quadratic Programming (SQP). Next we introduce two different algorithms for clustering the set of vertices on a given mesh, respectively based on two disparity measurements: max-norm and L2-norm based metric. An equivalence is established between mesh vertices and physical joints in an architectural mesh. By replacing individual joints by their equivalent cluster representative, the number of unique joints in the facade mesh, and therefore the fabrication cost, is dramatically reduced. Finally, we present an algorithm for remeshing a given surface in order to further reduce the number of joint clusters. The framework is tested for a set of real-world architectural surfaces to illustrate the effectiveness and utility of our approach. Overall, this approach tackles the important problem reducing fabrication cost of joints without modifying the underlying connectivity that was specified by the architect.

We introduce a method to design architectural buildings that are inspired by shapes of non-architectural forms. The user inputs a few binary images, each providing an indicative shape for the building from a different viewpoint. A discrete visual hull corresponding to each binary image is generated. A voxel model is then constructed by intersecting the hulls corresponding to the images. The shape of the voxel model depends on the parameters of the projections. Real buildings must also obey some topological and structural constraints. We develop a shape metric to evaluate a given design in terms of topological, functional and structural requirements of the building. This allows us to optimize the building shape as a function of the parameters of the projection. The optimization problem is solved by means of an improved cuckoo search metaheuristic. The resulting voxel model is converted into a mesh. Finally, we apply a novel smoothing algorithm that produces a smooth surface while preserving sharp creases and roof structures. Several examples are presented in the paper to illustrate the methodology and results.

This paper addresses the issue of placing a simple polygon (upon translation and rotation) on an isometric triangular grid such that the polygon contains the maximum number of triangles in its closure. This solves the problem left open in two recent papers titled “On the problem of the automated design of large-scale robot skin” and “An improved algorithm for the automated design of large scale robot skin” published in the IEEE Transactions on Automation Science and Engineering . Based on the properties of the grid, an improved algorithm is also presented. We also present some experimental results describing the use of this algorithm.

A recent paper titled “On the Problem of the Automated Design of Large-Scaled Robot Skin” (Anghinolfi et al., 2013) published in the IEEE Transactions on Automation Science and Engineering addressed the problem of covering the surface of a humanoid robot with the largest number of nonoverlapping equilateral triangular sensor modules. The problem is eventually approximated by a simpler one: how to find the placement of a given polygon P on an equilateral triangular grid G that contains the largest number of the grid triangles. In this paper, we show how to improve the efficiency of the algorithm presented in that paper. Further, we show that the general problem of filling P with the largest number of disjoint equilateral triangles (all entirely contained in P and all of the same size) is not equivalent to that of finding an optimal placement of P on G. Using this result, we propose an improved heuristic for the original problem of covering the skin of a robot with the largest number of triangular sensor modules.

3-D CAD models are an important digital resource in the manufacturing industry. 3-D CAD model retrieval has become a key technology in product lifecycle management enabling the reuse of existing design data. In this paper, we propose a new method to retrieve 3-D CAD models based on 2-D pen-based sketch inputs. Sketching is a common and convenient method for communicating design intent during early stages of product design, e.g., conceptual design. However, converting sketched information into precise 3-D engineering models is cumbersome, and much of this effort can be avoided by reuse of existing data. To achieve this purpose, we present a user-adaptive sketch-based retrieval method in this paper. The contributions of this work are twofold. First, we propose a statistical measure for CAD model retrieval: the measure is based on sketch similarity and accounts for users' drawing habits. Second, for 3-D CAD models in the database, we propose a sketch generation pipeline that represents each 3-D CAD model by a small yet sufficient set of sketches that are perceptually similar to human drawings. User studies and experiments that demonstrate the effectiveness of the proposed method in the design process are presented.

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.