I. IntroductionWe propose a unified method of generating a wide range of three dimensional objects from polyhedra to solids with free-form surfaces.Modeling systems for polyhedra and systems for free-form surfaces have been developed independently in the past because of the difference in their underlying theory and practices. However, this is not desirable for a designer.So in this paper, we have shown a method in which a wide range of shapes are generated in one system by using local modifications. Local modifications are procedures used to change the shape of solids locally. The construction and the modification of three dimensional shapes by these procedures are natural and easy for a designer in many cases. The implementation of these procedures in a computer is easy and their execution does not require much time~ Our method to construct a solid with free-form surfaces consists of following three phases, i) A solid which serves as a basis of free-form shape design is generated by local modifications. Edges of this solid are straight lines but its faces are not necessarily flat planes. 2) From this model, a curve model which adequately represents the characteristics of a free-form shape is generated.3) Surface equations interpolating over the curve model are generated.We have made a geometric modeling system MODIF. Using this system, a complicated solid with free-form surfaces can be designed easily. MODIF can generate color shaded pictures and cutter path data for making a real object model by NC machining tool.

In this paper, we propose a new multiresolution-based shape representation for 3 0 mesh morphing. Our approach does not use combination operations that caused some serious problems in the previous approaches for mesh morphing. Therefore, we can calculate a hierarchical interpolation mesh robustly using two types of subdivision jitting schemes. Our new representation has a hierarchical semiregular mesh structure based on subdivision connectivi9. This leads to various advantages including eficient data storage, and easy acquisition of an interpolation mesh with arbitrary subdivision level. We also demonstrate several new features for 3 0 morphing using multiresolution interpolation meshes.

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By using scanning 3D-CT image data of patients with cleft lips, 3D-CG models of the cleft lips were created. Several animations for surgical procedures such as incision designs, rotation of small skin flaps, and sutures were made. This system can recognize the details of an operation procedure clearly from any viewpoint, which cannot be acquired from the usual textbook illustrations. This animation system can be used for developing new skin-flap design, understanding the operational procedure, and using tools in case presentations. The 3D animations can also be uploaded to the World Wide Web for use in teleconferencing.

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This paper presents a method for Boolean operations on open and closed surface-based sets. An open set defines the partial boundary of a solid. A closed set corresponds to the complete boundary of a solid. In conventional boundary-oriented solid modeling systems, Boolean operations only apply to closed sets, but in the modeling process, it is convenient to be able to deal with open sets. We propose a systematic use of unbounded open sets at the user level for modeling solids. The Boolean operations algorithm on open sets is described and several applications are discussed. Self-intersecting solid correction, offset solid generation, and closed solid generation from surface data are examples.