Swen Campagna

Interactive multi-resolution modeling on arbitrary meshes

During the last years the concept of multi-resolution modeling has gained special attention in many fields of computer graphics and geometric modeling. In this paper we generalize powerful multiresolution techniques to arbitrary triangle meshes without requiring subdivision connectivity. Our major observation is that the hierarchy of nested spaces which is the structural core element of most multi-resolution algorithms can be replaced by the sequence of intermediate meshes emerging from the application of incremental mesh decimation. Performing such schemes with local frame coding of the detail coefficients already provides effective and efficient algorithms to extract multi-resolution information from unstructured meshes. In combination with discrete fairing techniques, i.e., the constrained minimization of discrete energy functionals, we obtain very fast mesh smoothing algorithms which are able to reduce noise from a geometrically specified frequency band in a multiresolution decomposition. Putting mesh hierarchies, local frame coding and multi-level smoothing together allows us to propose a flexible and intuitive paradigm for interactive detail-preserving mesh modification. We show examples generated by our mesh modeling tool implementation to demonstrate its functionality.

Directed edges—A scalable representation for triangle meshes

Abstract In a broad range of computer graphics applications, the representation of geometric shape is based on triangle meshes. General purpose data structures for polygonal meshes typically provide fast access to geometric objects (e.g., points) and topological entities (e.g., neighborhood relationships) but the memory requirements are rather high due to the many special configurations. In this paper, we present a new data structure which is specifically designed for triangle meshes. The data structure enables the programmer to trade memory for access time by either storing internal references explicitly, or by reconstructing them locally on demand. The trade-off can be hidden from the programmer by an object-oriented API and can automatically adapt to the available hardware resources or the complexity of the mesh (scalability).

Ray tracing of spline surfaces: Bézier clipping, Chebyshev boxing, and bounding volume hierarchy – a critical comparison with new results

Ray tracing is a well-known rendering technique for producing high-quality and photorealistic pictures. Spline surfaces are also well known and widely used. Thus, there is the need for fast and robust methods for computing the intersections of rays with these surfaces. In this paper, we discuss and compare three recent geometric algorithms for solving the raypatch intersection problem and present new results that are helpful in dealing with this problem.

Enhancing digital documents by including 3D-models

Abstract Due to their simplicity, triangle meshes are used to represent geometric objects in many applications. Since the number of triangles often goes beyond the capabilities of computer graphics hardware and the transmission time of such data is often inappropriately high, a large variety of mesh simplification algorithms has been proposed in the last years. In this paper we identify major requirements for the practical usability of general purpose mesh reduction algorithms to enable the integration of triangle meshes into digital documents. The driving idea is to understand mesh reduction algorithms as a software extension to make more complex meshes accessible with limited hardware resources (regarding both transmission and display). We show how these requirements can be efficiently satisfied and discuss implementation aspects in detail. We present a mesh decimation scheme that fulfills these design goals and which has already been evaluated by several users from different application areas. We apply this algorithm to typical mesh data sets to demonstrate its performance.