Blending using ODE swept surfaces with shape control and C1 continuity

Surface blending with tangential continuity is most widely applied in computer aided design, manufacturing systems, and geometric modeling. In this paper, we propose a new blending method to effectively control the shape of blending surfaces, which can also satisfy the blending constraints of tangent continuity exactly. This new blending method is based on the concept of swept surfaces controlled by a vector-valued fourth order ordinary differential equation (ODE). It creates blending surfaces by sweeping a generator along two trimlines and making the generator exactly satisfy the tangential constraints at the trimlines. The shape of blending surfaces is controlled by manipulating the generator with the solution to a vector-valued fourth order ODE. This new blending methods have the following advantages: 1). exact satisfaction of 1C continuous blending boundary constraints, 2). effective shape control of blending surfaces, 3). high computing efficiency due to explicit mathematical representation of blending surfaces, and 4). ability to blend multiple (more than two) primary surfaces

Generating Multiple Levels of Detail from Polygonal Geometry Models

This paper presents a new method for solving the following problem: Given a polygonal model of some geometric object generate several more and more approximative representations of this object containing less and less polygons. The idea behind the method is that small detail in the model is represented by many spatially close points. A hierarchical clustering algorithm is used to generate a hierarchy of clusters from the vertices of the object's polygons. The coarser the approximation the more points are found to lie within one cluster of points. Each cluster is replaced by one representative point and polygons are reconstructed from these points. A static detail elision algorithm was implemented to prove the practicability of the method. This paper shows examples of approximations generated from different geometry models, pictures of scenes rendered by a detail elision algorithm and timings of the method at work. 1 Introduction In several papers on recent developments in computer gr..