We present a framework to extract mesh features from unstructured two-manifold surfaces. Our method computes a collection of piecewise linear curves describing the salient features of surfaces, such as edges and ridge lines. We extend these basic techniques to a multiresolution setting which improves the quality of the results and accelerates the extraction process. The extraction process is semi-automatic, that is, the user is required to input a few control parameters and to select the operators to be applied to the input surface. Our mesh feature extraction algorithm can be used as a preprocessor for a variety of applications in geometric modeling including mesh fairing, subdivision and simplification.

The concept of fairing applied to triangular meshes with irregular connectivity has become more and more important. Previous contributions proposed a variety of fairing operators for manifolds and applied them to the design of multi-resolution representations and editing tools for meshes. In this paper, we generalize these powerful techniques to handle non-manifold models. We propose a method to construct fairing operators for non-manifolds which is based on standard operators for the manifold setting. Furthermore, we describe novel approaches to guarantee volume preservation. We introduce various multi-resolution techniques that allow us to represent, smooth and edit non-manifold models efficiently. Finally, we discuss a semi-automatic feature preservation strategy to retain important model information during the fairing process.

The concept of fairing applied to irregular triangular meshes has become more and more important. Previous contributions constructed better fairing operators, and applied them both to multiresolution editing tools and to multiresolution representations of meshes. The authors generalize these powerful techniques to handle non-manifold models. Our framework computes a multilevel fairing of models by fairing both the two-manifold surfaces that define the model, the so-called two-features, and all the boundary and intersection curves of the model, the so-called one-features. In addition we introduce two extensions that can be used in our framework as well as in manifold fairing concepts: an exact local volume preservation strategy and a method for feature preservation. Our framework works with any of the manifold fairing operators for meshes.