We present a novel proposal for modeling complex dynamic terrains that offers real-time rendering, dynamic updates and physical interaction of entities simultaneously. We can capture any feature from landscapes including tunnels, overhangs and caves, and we can conduct a total destruction of the terrain. Our approach is based on a Constructive Solid Geometry tree, where a set of spheres are subtracted from a base Digital Elevation Model. Erosions on terrain are easily and efficiently carried out with a spherical sculpting tool with pixel-perfect accuracy. Real-time rendering performance is achieved by applying a one-direction CPU–GPU communication strategy and using the standard depth and stencil buffer functionalities provided by any graphics processor.

The availability of a model to measure the performance of evolutionary algorithms is very important, especially when these algorithms are applied to solve problems with high computational requirements. That model would compute an index of the quality of the solution reached by the algorithm as a function of run-time. Conversely, if we fix an index of quality for the solution, the model would give the number of iterations to be expected. In this work, we develop a statistical model to describe the performance of PBIL and CHC evolutionary algorithms applied to solve the root identification problem. This problem is basic in constraint-based, geometric parametric modeling, as an instance of general constraint-satisfaction problems. The performance model is empirically validated over a benchmark with very large search spaces.

The graph-based geometric constraint solving technique works in two steps. First the geometric problem is translated into a graph whose vertices represent the set of geometric elements and whose edges are the constraints. Then the constraint problem is solved by decomposing the graph into a collection of subgraphs each representing a standard problem which is solved by a dedicated equational solver. In this work we report on an algorithm to decompose biconnected tree-decomposable graphs representing either underor wellconstrained 2D geometric constraint problems. The algorithm recursively first computes a set of fundamental circuits in the graph then splits the graph into a set of subgraphs each sharing exactly three vertices with the fundamental circuit. Practical experiments show that the reported algorithm clearly outperforms the treedecomposition approach based on identifying subgraphs by applying specific decomposition rules.

Dynamic geometry systems are tools for geometric visualization. They allow the user to define geometric elements, establish relationships between them and explore the dynamic behavior of the remaining geometric elements when one of them is moved. The main problem in dynamic geometry systems is the ambiguity that arises from operations which lead to more than one possible solution. Most dynamic geometry systems deal with this problem in such a way that the solution selection method leads to a fixed dynamic behavior of the system. This is specially annoying when the behavior observed is not the one the user intended.

We develop a framework to support geometric constraint-based design systems with multiple views for concurrent engineering. The framework is based on a conceptual architecture with a master view and several client views with a two-way flow information between the master and client views. The tools in the framework are used to open a new application's view or when one of the applications changes its view by editing it and the master view and the other views must be updated to maintain consistency. A case study illustrates how the tools in the framework work.

In the past few years, there has been a strong trend towards developing parametric, computer-aided design systems based on geometric constraint solving. An effective way to capture the design intent in these systems is to define relationships between geometric and technological variables. In general, geometric constraint solving including functional relationships requires a general approach and appropriate techniques to achieve the expected functional capabilities. This work reports on a hybrid method that combines two geometric constraint solving techniques: constructive and equational. The hybrid solver has the capability of managing functional relationships between dimension variables and variables representing conditions external to the geometric problem. The hybrid solver is described as a rewriting system and is shown to be correct.

Abstract The paper focuses on automatic simplification algorithms for the generation of a multiresolution family of solid models from an initial boundary representation of a polyhedral solid. An algorithm for general polyhedra based on an intermediate octree representation is proposed. Simplified elements of the multiresolution family approximate the initial solid within increasing tolerances. A discussion among different octree‐based simplification methods and the standard marching cubes algorithm is presented.