With the advent of sketch-based methods for shape construction, there is a new degree of power availablecreating several models. Eurographics 2002This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved.
We introduce SmoothSketch---a system for inferring plausible 3D free-form shapes from visible-contour sketches. In our system, a user's sketch need not be a simple closed curve as in Igarashi's Teddy [1999], but may have cusps and T-junctions, i.e., endpoints of hidden parts of the contour. We follow a process suggested by Williams [1994] for inferring a smooth solid shape from its visible contours: completion of hidden contours, topological shape reconstruction, and smoothly embedding the shape via relaxation. Our main contribution is a practical method to go from a contour drawing to a fairly smooth surface with that drawing as its visible contour. In doing so, we make several technical contributions: • extending Williams' and Mumford's work [Mumford 1994] on figural completion of hidden contours containing T-junctions to contours containing cusps as well, • characterizing a class of visible-contour drawings for which inflation can be proved possible, • finding a topological embedding of the combinatorial surface that Williams creates from the figural completion, and • creating a fairly smooth solid shape by smoothing the topological embedding using a mass-spring system.We handle many kinds of drawings (including objects with holes), and the generated shapes are plausible interpretations of the sketches. The method can be incorporated into any sketch-based free-form modeling interface like Teddy.
We present a technique for visualizing complicated mathematical surfaces that is inspired by hand-designed topological illustrations. Our approach generates exploded views that expose the internal structure of such a surface by partitioning it into parallel slices, which are separated from each other along a single linear explosion axis. Our contributions include a set of simple, prescriptive design rules for choosing an explosion axis and placing cutting planes, as well as automatic algorithms for applying these rules. First we analyze the input shape to select the explosion axis based on the detected rotational and reflective symmetries of the input model. We then partition the shape into slices that are designed to help viewers better understand how the shape of the surface and its cross-sections vary along the explosion axis. Our algorithms work directly on triangle meshes, and do not depend on any specific parameterization of the surface. We generate exploded views for a variety of mathematical surfaces using our system.
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