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We present a genetic algorithm for approximating densely sampled curves with uniform cubic B-Splines suitable for Combined B-reps. A feature of this representation is altering the continuity property of the B-Spline at any knot, allowing to combine freeform curves and polygonal parts within one representation. Naturally there is a trade-off between different approximation properties like accuracy and the number of control points needed. Our algorithm creates very accurate B-Splines with few control points, as shown in Fig. 1. Since the approximation problem is highly nonlinear, we approach it with genetic methods, leading to better results compared to classical gradient based methods. Parallelization and adapted evolution strategies are used to create results very fast. [ABSTRACT FROM AUTHOR]

An extended subdivision surface (ESub) is a generalization of Catmull Clark and NURBS surfaces. Depending on the knot intervals and valences of the vertices and faces, Catmull Clark as well as NURBS patches can be generated using the extended subdivision rules. Moreover, an arbitrary choice of the knot intervals and the topology is possible. Special features like sharp edges and corners are consistently supported by setting selected knot intervals to zero or by applying special rules. Compared to the prior nonuniform rational subdivision surfaces (NURSS), the ESubs offer limit-point rules which are indispensable in many applications, for example, for computer-aided design or in adaptive visualization. The refinement and limit-point rules for our nonuniform, nonstationary scheme are obtained via a new method using local Bézier control points, With our new surface, it is possible to start with existing Catmull Clark as well as NURBS models and to continue the modeling process using the extended subdivision options. [ABSTRACT FROM AUTHOR]

The article focuses on a fast collision detection technique for all types of rigid bodies, using spherical distance fields. A spherical sampling requires a spherical parameterization. The spherical distance field approach consists of two parts, a preprocessing step and a testing routine that represents the intrinsic collision test. In the preprocessing step, an algorithm takes an initial model and determines a model center. The model is transformed into spherical coordinates with respect to its center, an arbitrary chosen point. After transformation, a simple and fast collision test is performed. The test must report an intersection, if one exists. The test might report an intersection by mistake. If the test is positive, the algorithm will increase the level of details. So, it is essential to maintain accuracy and efficiency. The implementation of the collision-detection algorithm is simple. There is a need for future research for the implementation of this technique to deformable models.

A typical industrial design modelling scenario involves defining the overall shape of a product followed by adding detail features. Procedural features are well-established in computer aided design (CAD) involving regular forms, but are less applicable to free-form modelling involving subdivision surfaces. Current approaches do not generate sparse subdivision control meshes as output, which is why free-form features are manually modelled into subdivision control meshes by domain experts. Domain experts change the local topology of the subdivision control mesh to incorporate features into the surface, without increasing the mesh density unnecessarily and carefully avoiding the appearance of artefacts. In this paper we show how to translate this expert knowledge to grammar rules. The rules may then be invoked in an interactive system to automatically apply features to subdivision surfaces. [ABSTRACT FROM AUTHOR]

Abstract: The creation of building and facility models is a tedious and complicated task. Existing CAD models are typically not well suited since they contain too much or not enough detail; the manual modeling approach does not scale; different views on the same model are needed, and different levels of detail and abstraction; and finally, conventional modeling tools are inappropriate for models with many internal parameter dependencies. As a solution to this problem we propose a combination of a procedural approach with shape grammars. The model is created in a top-down manner; high-level changeability and re-usability are much less of a problem; and it can be interactively evaluated to provide different views at runtime. We present some insights on the relation between imperative and declarative grammar descriptions, and show a detailed case study with facility surveillance as a practical application. [ABSTRACT FROM AUTHOR]