Computing Contour Generators of Evolving Implicit Surfaces

The contour generator is an important visibility feature of a smooth object seen under parallel projection. It is the curve on the surface which seperates front-facing from back-facing regions. The apparent contour is the projection of the contour generator onto a plane perpendicular to the view direction. Both curves play an important role in computer graphics. Our goal is to obtain fast and robust algorithms that compute the contour generator with a guarantee of topological correctness. To this end, we first study the singularities of the contour generator and apparent contour for both generic views and generic time-dependent projections, for example, when the surface is rotated or deformed. The singularities indicate when components of the contour generator merge or split as time evolves. We present an algorithm to compute an initial contour generator by using a dynamic step size. An interval test guarantees the topological correctness. This initial contour generator can thus be maintained under a time-dependent projection by examining its singularities

View-dependent Object Simplification and its Application in the case of Billboard Clouds

Slightly modified from the original versionNational audienceIn this Master thesis we will present a new approach to simplify a model representation based on a supplementary knowledge of a region in which the observer is allowed to move, the so-called view cell. The simplified representation should be faster to render, without loosing the similarity to the original objects. To assure this we will present our main contribution, a new error bounding method, which to our best knowledge, allows for the first time to restrain the error of a representation for a given view cell. In particular, a lot of common assumptions that were widely accepted are proven to be inexact. We will show several properties for the 3D case and solve a particular case, as well as a numerical solution for points in 3D. For the 2D case we were able to obtain an exact solution which allows our method to be applied on 2.5 dimensional scenes. Our error bounding method is then used in the context of Billboard Clouds [DDSD03]. Still, our result is more general and thus not at all restricted to this particular usage. The view-dependent Billboard Clouds that we will introduce in this master thesis have several advantages. The error of the representation can be bound and the simplification is very successful; to mention one example a 4480 triangle scene has been simplified to approximately 40 billboards (80 triangles) with a ¼ 5% representation error1, for a centered view cell inside of the scene with a size approximately 1/10 of the bounding diagonal. Most algorithms add ad-hoc criteria to preserve silhouettes, our algorithm preserves them automatically. Other advantages of our method are that it works for any kind of triangulated input and that it is easy to use; only two parameters are needed (simplification error and texture quality). It is completely independent of the view frustum that is used for the observer, which is not very common, as most image based view-dependent simplification methods need a fixed view frustum. Also our method does not share a common problem with most other view cell approaches, where the representation becomes worse when the observer approaches the border of the view cell. The construction of view-dependent Billboard Clouds is mostly based on the original Billboard Cloud approach [DDSD03], but some slight improvements were made with respect to the original algorithm