Cutting and pasting to combine different elements into a common structure are widely used operations that have been successfully adapted to many media types. Surface design could also benefit from the availability of a general, robust, and efficient cut-andpaste tool, especially during the initial stages of design when a large space of alternatives needs to be explored. Techniques to support cut-and-paste operations for surfaces have been proposed in the past, but have been of limited usefulness due to constraints on the type of shapes supported and the lack of real-time interaction. In this paper, we describe a set of algorithms based on multiresolution subdivision surfaces that perform at interactive rates and enable intuitive cut-and-paste operations.

A piecewise smooth surface, possibly with boundaries, sharp edges, corners, or other features is defined by a set of samples. The basic idea is to model surface patches, curve segments and points explicitly, and then to glue them together based on explicit connectivity information. The geometry is defined as the set of stationary points of a projection operator, which is generalized to allow modeling curves with samples, and extended to account for the connectivity information. Additional tangent constraints can be used to model shapes with continuous tangents across edges and corners.

Figure 1: Volume subdivision, manipulation, and fitting. A lattice (top left) is recursively subdivided and re-shaped at the fourth subdivision level. This shape is low-pass filtered by removing fine-resolution wavelet coefficients (bottom right). We present a biorthogonal wavelet construction based on Catmull-Clark-style subdivision volumes, like multi-linear cell averaging (MLCA). Our wavelet transform is the three-dimensional extension of a previously developed construction of subdivision-surface wavelets that was used for multiresolution modeling of large-scale isosurfaces. Subdivision surfaces provide a flexible modeling tool for geometries of arbitrary topology and for functions defined thereon. Wavelet representations add the ability to compactly represent large-scale geometries at multiple levels of detail. Our wavelet construction based on subdivision volumes extends these concepts to trivariate geometries, such as time-varying surfaces, free-form deformations, and solid models with non-uniform material properties.

We present a flexible GPU kernel for adaptive on-the-fly refinement of meshes with arbitrary topology. By simply reserving a small amount of GPU memory to store a set of adaptive refinement patterns, on-the-fly refinement is performed by the GPU, without any preprocessing nor additional topology data structure. The level of adaptive refinement can be controlled by specifying a per-vertex depth-tag, in addition to usual position, normal, color and texture coordinates. This depth-tag is used by the kernel to instanciate the correct refinement pattern, which will map a refined connectivity on the input coarse polygon. Finally, the refined patch produced for each triangle can be displaced by the vertex shader, using any kind of geometric refinement, such as Bezier patch smoothing, scalar valued displacement, procedural geometry synthesis or subdivision surfaces. This refinement engine does neither require multi-pass rendering nor any use of fragment processing nor special preprocess of the input mesh structure. It can be implemented on any GPU with vertex shading capabilities.

Figure 1: Creating a surface with spherical topology. a) Sketch mesh (22 faces) and first subdivision level mesh embedded in the spherical domain. b) Initial geometry of sketch mesh and resulting surface (129 overlapping surface patches). c) Geometry specifying the next hierarchical level (average patch overlap, 3.4) This geometry is created by drawing on the surface in b). d) The resulting surface, colored by hierarchical level. e) Editing the first hierarchical level to produce arms and legs. f) Adding and editing a second hierarchical level. We present a surface modeling technique that supports adaptive resolution and hierarchical editing for surfaces of spherical topology. The resulting surface is analytic, Ck, and has a continuous local parameterization defined at every point. To manipulate these surfaces we describe a user-interface based on multiple, overlapping subdivision-style meshes.

Subdivision surfaces refer to a class of modelling schemes that define an object through recursive subdivision starting from an initial control mesh. Similar to B-splines, the final surface is defined by the vertices of the initial control mesh. These surfaces were initially conceived as an extension of splines in modelling objects with a control mesh of arbitrary topology. They exhibit a number of advantages over traditional splines. Today one can find a variety of subdivision schemes for geometric design and graphics applications. This paper provides an overview of subdivision surfaces with a particular emphasis on schemes generalizing splines. Some common issues on subdivision surface modelling are addressed. Several key topics, such as scheme construction, property analysis, parametric evaluation and subdivision surface fitting, are discussed. Some other important topics are also summarized for potential future research and development. Several examples are provided to highlight the modelling capability of subdivision surfaces for CAD applications.

triangle meshes produced by feature-insensitive sampling

We present methods for synthesizing 3D shape features on subdivision surfaces using multiscale procedural techniques. Multiscale synthesis is a powerful approach for creating surfaces with different levels of detail. Our methods can also blend multiple example multiresolution surfaces, including procedurally defined surfaces as well as captured models.

Introduction Subdivision surfaces are emerging as a powerful representation for shape design. Their simplicity and potential to overcome difficulties associated with traditional spline-based modeling has made them a popular choice for several applications. Among these, the modeling of animated characters for movie production has, by far, received the most attention in the literature. In contrast, we focus our attention on the use of subdivision surfaces for the automotive, aerospace, and consumer product industrial sectors. Over the past few years we have developed a suite of modeling tools to facilitate a more efficient and smooth transition from the initial stages of design to class-A surfaces. These tools considerably improve the efficiency of certain design operations and, in some cases, enable tasks that are difficult or even impossible to perform using NURBS-based approaches. Our presentation includes a brief review of multiresolution subdivision surfaces, followed by several i

Abstract. We present a construction of a piecewise rational free-form surface of arbitrary topological genus which may contain sharp features: creases, corners or cusps. The surface is automatically generated from a given closed triangular mesh. Some of the edges are tagged as sharp ones, defining the features on the surface. The surface is C s smooth, for an arbitrary value of s, except for the sharp features defined by the user. Our method is based on the manifold construction and follows the blending approach.