In this paper, we identify a minimal and complete set of fundamental operators, which is necessary and sufficient for performing all homeomorphic and topological operations on 2-manifold mesh structures. Efficient algorithms are developed for the implementation of these operators. We also developed a set of powerful, userfriendly, and effective operators at the level of user-interface. Using these operators, we have developed a prototype system for robust, interactive and user friendly modeling of orientable 2-manifold meshes. Users of our system can perform a large set of homeomorphic and topological changes with these user-interface level operators. Our system is topologically robust in the sense that users will never create invalid 2-manifold mesh structure with these operators. In our system, the homeomorphic and topological surgery operations can be applied alternatively on 2-manifold meshes. With our system,users can blend surfaces, construct rinds and open holes on these rind shapes. With our system, the shapes that look like solid, non-manifold, or 2-manifold with boundary can be manipulated. The system also provides automatic texture mapping during topology changes.

In this paper, we present a new paradigm that allows dynamically changing the topology of 2-manifold polygonal meshes. Our new paradigm always guarantees topological consistency of polygonal meshes. Based on our paradigm, by simply adding and deleting edges, handles can be created and deleted, holes can be opened or closed, polygonal meshes can be connected or disconnected. These edge insertion and edge deletion operations are highly consistent with subdivision algorithms. In particular, these operations can be easily included into a subdivision modeling system such that the topological changes and subdivision operations can be performed alternatively during model construction. We demonstrate practical examples of topology changes based on this new paradigm and show that the new paradigm is convenient, effective, efficient, and friendly to subdivision surfaces. 1

In this paper, we present a new paradigm that allows dynamically changing the topology of 2-manifold polygonal meshes. Our new paradigm always guarantees topological consistency of polygonal meshes. Based on our paradigm, by simply adding and deleting edges, handles can be created and deleted, holes can be opened or closed, polygonal meshes can be connected or disconnected.

We describe a newly established research project called SoftLab in the area of computational science and computational engineering. The SoftLab project attempts to link physical laboratory experimentation with computer control and simulation to provide a virtual laboratory for computational science. We describe the overall project objectives and then introduce the three focus projects of SoftLab: Two Chemical Engineering SoftLabs (bioseparation and computational electronics) and a Mechanical Engineering SoftLab (computational mechanics). Preliminary results of our efforts are also described.

In Architecture, it is essential to design functional and topologically compli-cated 3D shapes (i.e. shapes with many holes, columns and handles). In this paper, we present a robust and interactive system for the design of functional and topologically complicated 3D shapes. Users of our system can easily change topology (i.e. they can create and delete holes and handles, connect and dis-connect surfaces). Our system also provide smoothing operations (subdivision schemes) to create smooth surfaces. Moreover, the system provides automatic texture mapping during topology and smoothing operations. We also present new design approaches with the new modeling system. The new design approaches include blending surfaces, construction of crusts and opening holes on these crusts.

Solid models may be blended through filleting or rounding operations that typically replace the vicinity of concave or convex edges by blends that smoothly connect to the rest of the solid’s boundary. Circular blends, which are popular in manufacturing, are each the subset of a canal surface that bounds the region swept by a ball of constant or varying radius as it rolls on the solid while maintaining two tangential contacts. We propose to use a second solid to control the radius variation. This new formulation supports global blending (simultaneous rounding and filleting) operations and yields a simple set-theoretic formulation of the relative blending RB(A) of a solid A given a control solid B. We propose user-interface options, describe practical implementations, and show results in 2 and 3 dimensions.

The goal of this research is to develop new, interactive methods for creating very high-genus 2-manifold meshes. The various approaches investigated in this research can be categorized into two groups – interactive methods, where the user primarily controls the creation of the high-genus mesh, and automatic methods, where there is minimal user interaction and the program automatically creates the high-genus mesh. In the interactive

structure introduces a powerful modeling paradigm that allows users to alternatively apply topological change operations and subdivision operations on mesh structure. Moreover, the DLFL is topologically robust in the sense that it always guarantees valid 2-manifold surfaces. In this paper, we further study the relationship between DLFL structure and subdivision algorithms. The paper has three contributions. First, we develop a new corner cutting scheme, which provides a tension parameter to control the shape of subdivided surface. Second, we develop a careful and efficient algorithm for our corner cutting scheme on the DLFL structure that uses only the basic operations provided by the DLFL structure. This implementation ensures that our new corner cutting scheme preserves topological robustness. The comparative study shows that the corner cutting schemes create better handles and holes than Catmull-Clark scheme.

rist. i ces i i f tte,

Traditional t.echniques for computing offsets are local in nature and lack good criteria for eliminating possible self-intersections of the offset. Methods based on integrating differential equations or on image processing do not lack such criteria, but seem to require constructing the solution in the ambient space, i.e., in one dimension larger than the offset. We investigate such methods. 1.