We propose the idea of simplification envelopes for generating a hierarchy of level-of-detail approximations for a given polygonal model.Our approach guarantees that all points of an approximation are within a user-specifiable distance from the original model and that all points of the original model are within a distance from the approximation.Simplification envelopes provide a general framework within which a large collection of existing simplification algorithms can run.We demonstrate this technique in conjunction with two algorithms, one local, the other global.The local algorithm provides a fast method for generating approximations to large input meshes (at least hundreds of thousands of triangles).The global algorithm provides the opportunity to avoid local "minima" and possibly achieve better simplifications as a result.Each approximation attempts to minimize the total number of polygons required to satisfy the above constraint.The key advantages of our approach are: General technique providing guaranteed error bounds for genus-preserving simplification Automation of both the simplification process and the selection of appropriate viewing distances Prevention of self-intersection Preservation of sharp features Allows variation of approximation distance across different portions of a model CR Categories and Subject Descriptors: I.3.

A parallel, analytic approach for defining and computing the inter and intra molecular interfaces in three dimensions is described. The molecular interface surfaces are derived from approximations to the power diagrams over the participating molecular units. For a given molecular interface our approach can generate a family of interface surfaces parametrized by /spl alpha/ and /spl beta/, where /spl alpha/ is the radius of the solvent molecule (also known as the probe radius) and /spl beta/ is the interface radius that defines the size of the molecular interface. Molecular interface surfaces provide biochemists with a powerful tool to study surface complementarity and to efficiently characterize the interactions during a protein substrate docking. The complexity of our algorithm for molecular environments is O(nk log/sup 2/ k), where n is the number of atoms in the participating molecular units and k is the average number of neighboring atoms-a constant, given /spl alpha/ and /spl beta/.

We present algorithms for 3-D manipulation and conformational analysis of molecular chains, when bond lengths, bond angles and related dihedral angles remain fixed. These algorithms are useful for local deformations of linear molecules, exact ring closure in cyclic molecules and molecular embedding for short chains. Other possible applications include structure prediction, protein folding, conformation energy analysis and 3D molecular matching and docking. The algorithms are applicable to all serial molecular chains and make no assumptions about their geometry. We make use of results on direct and inverse kinematics from robotics and mechanics literature and show the correspondence between kinematics and conformational analysis of molecules. In particular, we pose these problems algebraically and compute all the solutions making use of the structure of these equations and matrix computations. The algorithms have been implemented and perform well in practice. In particular, they take tens of milliseconds on current workstations for local deformations and chain closures on molecular chains consisting of six or fewer rotatable dihedral angles.

An interactive visualization of weighted three-dimensional alpha-hulls is presented for static and dynamic spheres. The alpha-hull is analytically computed and represented by a triangulated mesh. The entire surface is computed and displayed in real-time at interactive rates. The weighted three-dimensional alpha-hulls are equivalent to smooth molecular surfaces of biochemistry. Biochemistry applications of interactive computation and display of alpha-hulls or smooth molecular surfaces are outlined.

We present an atomic-scale teleoperation system that uses a head-mounted display and force-feedback manipulator arm for a user interface and a Scanning Tunneling Microscope (STM) as a sensor and effector.The system approximates presence at the atomic scale, placing the scientist on the surface, in control, w h i l e the experiment is happening.A scientist using the Nanomanipulator can view incoming STM data, feel the surface, and modify the surface (using voltage pulses) in real time.The Nanomanipulator has been used to study the effects of bias pulse duration on the creation of gold mounds.We intend to use the system to make controlled modifications to silicon surfaces.

The high-order probabilities of element sequences can be determined from a sample of linear structures and can be used for synthesis of new structures. From theoretical considerations one can identify the qualitative conditions for satisfactory output. The theoretical concepts can be tested and quantitative parameters determined by experiment. Such an experiment has been performed by analyzing written music and by testing the analysis through the synthesis of new musical compositions, using a digital computer. A sample of 37 melodies was analyzed for the probabilities of the elements, element pairs (digrams), trigrams, and so on to the eighth order. The tables derived were used for the synthesis of original melodies by a random process. The theory and the experimental verification are considered in detail. The experimental results presented include comparative statistics of the successful syntheses using each of the eight orders of analysis, examples of melodies generated by low, medium, and high-order synthesis, and confirmation of degeneracy and other effects predicted by the theory.