We present a framework for geometric warps and deformations. The framework provides a conceptual and mathematical foundation for analyzing known warps and for developing new warps, and serves as a common base for many warps and deformations. Our framework is composed of two components: a generic modular algorithm for warps and deformations; and a concise, geometrically meaningful formula that describes how warps are evaluated. Together, these two elements comprise a complete framework useful for analyzing, evaluating, designing, and implementing deformation algorithms. While the framework is independent of user-interfaces and geometric model representations and is formally capable of describing any warping algorithm, its design is geared toward the most prevalent class of user-controlled deformations: those computed using geometric operations. To demonstrate the expressive power of the framework, we cast several well-known warps in terms of the framework. To illustrate the framework's usefulness for analyzing and modifying existing warps, we present variations of these warps that provide additional functionality or improved behavior. To show the utility of the framework for developing new warps, we design a novel 3-D warping algorithm: a mesh warp ---useful as a modeling and animation tool---that allows users to deform a detailed surface by manipulating a low-resolution mesh of similar shape. Finally, to demonstrate the mathematical utility of the framework, we use the framework to develop guarantees of several mathematical properties such as commutativity and continuity for large classes of deformations.

The ability to specify non planar 3D curves is of fundamental importance in 3D modelling and animation systems. Effective techniques for specifying such curves using 2D input devices are desirable, but existing methods typically require the user to edit the curve from several viewpoints. We present a novel method for specifying 3D curves with 2D input from a single viewpoint. The user rst draws the curve as it appears from the current viewpoint, and then draws its shadow on the oor plane. The system correlates the curve with its shadow to compute the curve's 3D shape. This method is more natural than existing methods in that it leverages skills that many artists and designers have developed from work with pencil and paper.

Artists and illustrators can evoke the complexity of fur or vegetation with relatively few well-placed strokes. We present an algorithm that uses strokes to render 3D computer graphics scenes in a stylized manner suggesting the complexity of the scene without representing it explicitly. The basic algorithm is customizable to produce a range of effects including fur, grass and trees, as we demonstrate in this paper and accompanying video. The algorithm is implemented within a broader framework that supports procedural stroke-based textures on polyhedral models. It renders moderately complex scenes at multiple frames per second on current graphics workstations, and provides some interframe coherence. CR Categories and Subject Descriptors: I.3.3: Computer Graphics: Picture/Image Generation; line and curve generation; bitmap and frambuffer operations; I.3.5 Computer Graphics: Computational Geometry and Object Modeling: curve, surface, solid, and object representations; I.3.7: Three-Dimens...

We present an interactive system for creating pen-and-ink illustrations. The system uses stroke textures—collections of strokes arranged in different patterns—to generate texture and tone. The user “paints” with a desired stroke texture to achieve a desired tone, and the computer draws all of the individual strokes.

To provide a simpler metaphor for representing, selecting, and adjusting collections of attributes for interactive operations.

We present "dynamic constraints," a physically-based technique for constraint-based control of computer graphics models. Using dynamic constraints, we build objects by specifying geometric constraints; the models assemble themselves as the elements move to satisfy the constraints. The individual elements are rigid bodies which act in accordance with the rules of physics, and can thus exhibit physically realistic behavior. To implement the constraints, a set of "constraint forces" is found, which causes the bodies to act in accordance with the constraints; finding these "constraint forces" is an inverse dynamics problem.