We present a new approach for establishing correspondence between two homeomorphic 3D polyhedral models. The user can specify corresponding feature pairs on the polyhedra with a simple and intuitive interface. Based on these features, our algorithm decomposes the boundary of each polyhedron into the same number of morphing patches. A 2D mapping for each morphing patch is computed in order to merge the topologies of the polyhedra one patch at a time. We create a morph by defining morphing trajectories between the feature pairs and by interpolating them across the merged polyhedron. The user interface provides high-level control as well as local refinement to improve the morph. The implementation has been applied to several complex polyhedra composed of thousands of polygons. The system can also handle non-simple polyhedra that have holes.

We present a powerful morphing technique based on level set methods, that can be combined with a variety of scan conversion/model processing techniques. Bringing these techniques together creates a general morphing approach that allows a user to morph a number of geometric model types in a single animation. We have developed techniques for converting several types of geometric models (polygonal meshes, CSG models and MRI scans) into distance volumes, the volumetric representation required by our level set morphing approach. The combination of these two capabilities allows a user to create a morphing sequence regardless of the model type of the source and target objects, freeing him/her to use whatever model type is appropriate for a particular animation. 1.

A metamorphosis or a (3D) morphing is the process of continuously transforming one object into another. 2D and 3D morphing are popular in computer animation, industrial design or growth simulation. Since there is no intrinsic solution to the morphing problem, user interaction can be a key component of a morphing software. Many morphing techniques have been proposed in the recent years for 2D or 3D objects. We present a survey of the different approaches in 3D giving a special attention to the user interface. We show how the approaches are intimately related to the object representations. We conclude by sketching some morphing strategies for the future. Key Words: metamorphosis, shape transformation, interpolation, computer animation, geometric modeling. 1 Introduction Shape interpolation is the process of transforming one shape into another. A metamorphosis or a (3D) morphing of 3D graphical objects [GCDV96] includes the interpolation of their shapes as well as an interpolation of th...

Based on classical geometric concepts we discuss the computational geometry of envelopes. The main focus is on envelopes of planes and natural quadrics. There, it turns out that projective duality and sphere geometry are powerful tools for developing efficient algorithms. The general concepts are illustrated at hand of applications in geometric modeling. Those include the design and NURBS representation of developable surfaces, canal surfaces and offsets. Moreover, we present applications in NC machining, geometrical optics, geometric tolerancing and error analysis in CAD constructions. Keywords: envelope, duality, sphere geometry, NURBS surface, developable surface, canal surface, geometric tolerancing. 1

Recent work has on combining techniques from Constructive Solid Geometry and Implicit Surface Modeling based on soft objects has resulted in a powerful modelling technique the models are known as Boolean Compound Soft Objects, or BCSO for short) which consists of a boolean expression with union, intersection, and set difference operators. The geometric primitives that form the operands are soft objects bounded by the iso-surfaces resulting from suitable potential fields. These potential fields are parameterized by configurations of so called skeletal elements. The resulting system, unlike most CSG systems, combines blended and unblended primitives. These models have many of the advantages of both implicit surface and CSG models. One technique that has proved useful in animation of implicit surface models is metamorphosis, smoothly changing one model into another. Since CSG models are defined by boolean expressions it is not obvious how to apply such a smooth change to CSG models. In th...

Nowadays, there is a lack of existing practical modeling tools suitable for specification of free-form implicit shapes. In this paper, we propose a new interpolation technique supplemented by interactive tools aimed at shape modeling by feature preserving metamorphosis of two-dimensional implicit shapes. The metamorphosis is controlled by global parameters and a set of correspondence vectors that are drawn directly to the scene. The underlying environment is the XISL package for definition and manipulation of implicit objects, which offers additional modeling and rendering possibilities. CR Categories: I.3.5 [COMPUTER GRAPHICS]: Computational Geometry and Object Modeling—Curve, surface, solid and object