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Text File | 1997-03-18 | 18KB | 345 lines

This file lists the set of papers and tech reports that were written with the aid of the IRIT solid modeling tool. ----------------------------------------------------------------------------- Orthogonal Decomposition of Non-Uniform Bspline Spaces using Wavelets Roman Kazinnik and Gershon Elber We take advantage of ideas of an orthogonal wavelet complement to produce multiresolution orthogonal decomposition of nonuniform \Bspline{} (NUB) spaces. The editing of NUB curves and surfaces can be handled at different levels of resolutions. Applying Multiresolution decomposition to, possibly $C^1$ discontinuous surfaces, one can preserve the general shape on one hand and local features on the other of the free-form models, including geometric discontinuities. The Multiresolution decomposition of the NUB tensor product surface is computed via the symbolic computation of inner products of \Bspline{} basis functions. To find a closed form representation for the inner product of the \Bspline{} basis functions, an equivalent interpolation problem is solved. As a one example for the strength of the Multiresolution decomposition, a tool demonstrating the Multiresolution editing capabilities of NUB surfaces was developed and is presented as part of this work, allowing interactive 3D editing of NUB free-form surfaces. * To appear in Eurographics 97, Budapest, Hungary, September 1997. ----------------------------------------------------------------------------- Physically Based Adaptive Triangulation of Freeform Surfaces. Patrick Chouraqui and Gershon Elber This paper studies an adaptive polygonization method for parametric surfaces that is physically based. A set of sampled points is distributed by this algorithm according to the curvature field of the surface. A triangulation is then superimposed over this sampled set. The locations of these sampled points are obtained by employing physically based models of interaction of particles. Two physical models are considered in this study: a spring-mass model and a model of electrostatically charged particles. The resulting algorithm equally distributes the approximation error of the triangulation throughout the surface, once the equilibrium state of the physical model is reached. * Presented in Computer Graphics International 1996 (CGI 96), Pohang, Korea, pp 144-153, June 1996. ----------------------------------------------------------------------------- Fast Iso-Surface Extraction using Marching Gradients Olga Tebeleva and Gershon Elber Given an explicit trivariate hyper-surface defined over a three dimensional image data set, ${\cal D}$, and an iso-surface $S_1$ of ${\cal D}$ at some iso-value $v_1$, we present an algorithm to extract a new iso-surface $S_2$ at iso-value $v_2$, with $v_2$ sufficiently close to $v_1$. Off-line continuous reconstruction of ${\cal D}$ as a high order Bspline trivariate is employed, yielding a linear time complexity for the extraction of $S_2$ in the size of the data of iso-surface $S_1$. The end result allows real-time incremental modification of the iso-value. Hence, users can potentially modify and refine an extracted iso-surface to a precise iso-value, in an interactive manner. * Presented in The fourth Pacific Graphics Conference on Computer Graphics and Applications, Taipei, Taiwan, pp 80-90, August 1996. ----------------------------------------------------------------------------- New Approximation Methods of Planar Offset and Convolution Curves In-Kwon Lee, Myung-Soo Kim, and Gershon Elber We present new methods to approximate the offset and convolution of planar curves. These methods can be used as fundamental tools in various geometric applications such as NC machining and collision detection of planar curved objects. Using quadratic curve approximation and tangent field matching, the offset and convolution curves can be approximated by polynomial or rational curves within the tolerance of approximation error $\epsilon > 0$. We suggest three methods of offset approximation, all of which allow simple error analysis and at the same time provide high-precision approximation. Two methods of convolution approximation are also suggested that approximate convolution curves with polynomial or rational curves. * Presented in Theory and Practice of Geometric Modeling, University of Tubingen, Germany, October 1996. ----------------------------------------------------------------------------- Qualitative and Quantitative Comparisons of Offset Curve Approximation Methods Gershon Elber, In-Kwon Lee, and Myung-Soo Kim * To appear in CG&A ----------------------------------------------------------------------------- Inferring 3D models from freehand sketches and constraints Lynn Eggli, Ching-yao Hsu, Beat D. Br\"{u}derlin, and Gershon Elber This paper describes `Quick-sketch', a 2d and 3d modeling tool for pen based computers. Users of this system define a model by simple pen strokes, drawn directly on the screen of a pen-based PC. Exact shapes and geometric relationships are interpreted from the sketch. The system can be used to also sketch three-dimensional solid objects and B-spline surfaces. These objects may be refined by defining two- and three-dimensional geometric constraints. A novel graph-based constraint solver is used to establish the geometric relationships, or to maintain them when manipulating the objects interactively. The approach presented here, is a first step towards a conceptual design system. Quick-sketch can be used as a hand sketching front-end to more sophisticated modeling-, rendering- or animation systems. * To appear in CAD ----------------------------------------------------------------------------- Ruled Tracing Gershon Elber, Jung-Ju Choi, and Myung-Soo Kim The traditional ray tracing technique based on a ray--surface intersection is reduced to a ruled- or developable-surface surface intersection problem, enabling direct freeform surface rendering. By exploiting the spatial coherence gained in the ruled/developable surface tracing approach presented in this work, the emulation of shadows, specular reflections and/or refractions in a freeform surface environment can all be efficiently implemented. The approach proposed herein provides a direct freeform surface rendering alternative to ray tracing. An implementation of a direct freeform surface renderer that emulates shadows as well as specular reflections is discussed. This renderer processes isoparametric curves as its basic building block, eliminating the need for any polygonal approximation. * To appear in The Visual Computer. Also Center for Intelligent Systems Tech. Report, CIS 9501, Computer Science Department, Technion. ----------------------------------------------------------------------------- Matching of Freeform Curves Gershon Elber Freeform parametric curves are extensively employed in various fields such as computer graphics, computer vision, robotics, and geometric modeling. While many applications exploit and combine univariate freeform entities into more complex forms such as sculptured surfaces, the problem of a fair or even optimal {\em relative} parameterization of freeforms, under some norm, has been rarely considered. In this work, we present a scheme that closely approximates the optimal relative matching between two or even $n$ given freeform curves, under a user's prescribed norm that is based on differential properties of the curves. This matching is computed as a reparameterization of $n-1$ of the curves that can be applied explicitly using composition. The proposed matching algorithm is completely automatic and has been successfully employed in different applications with several demonstrated herein: metamorphosis of freeform curves with feature preservations, key frame interpolation for animation, self intersection free ruled surface construction, and automatic matching of rail curves of blending surfaces. * To appear in CAD. Also Center for Intelligent Systems Tech. Report, CIS 9527, Computer Science Department, Technion. ----------------------------------------------------------------------------- Planar Curve Offset Based on Circle Approximation In-Kwon Lee, Myung-Soo Kim, and Gershon Elber An algorithm is presented to approximate planar offset curves within an arbitrary tolerance $\epsilon>0$. Given a planar parametric curve $C(t)$ and an offset radius $r$, the circle of radius $r$ is first approximated by piecewise quadratic B\'ezier curve segments within the tolerance $\epsilon$. The exact offset curve $C_r(t)$ is then approximated by the convolution of $C(t)$ with the quadratic B\'ezier curve segments. For a polynomial curve $C(t)$ of degree $d$, the offset curve $C_r(t)$ is approximated by planar rational curves, $C^a_r(t)$'s, of degree $3d-2$. For a rational curve $C(t)$ of degree $d$, the offset curve is approximated by rational curves of degree $5d-4$. When they have no self-intersections, the approximated offset curves, $C^a_r(t)$'s, are guaranteed to be within $\epsilon$-distance from the exact offset curve $C_r(t)$. The effectiveness of this approximation technique is demonstrated in the offset computation of planar curved objects bounded by polynomial/rational parametric curves. * CAD, Vol 28, No 8, pp 617-630, August 1996. ----------------------------------------------------------------------------- Multiresolution Control for Nonuniform Bspline Curve Editing Gershon Elber and Craig Gotsman The piecewise polynomial \bspline{} representation is widely used throughout the CAGD community as the representation of choice. However, the locality of \bspline{} curves, while important in many respects, disables global control of the curve, preventing efficient and easy manipulation. Multiresolution representations for uniform \bspline{} curves have been recently proposed to alleviate this problem. Herein, we extend the use of multiresolution representations to non uniform \bspline{} (NUBS) curves, including periodic curves. Our method supports local non uniform refinement and (dis)continuity preservation. The multiresolution decomposition of the freeform NUBS curve is computed using least-squares approximation, based on existing data reduction techniques. The majority of contemporary modeling systems that employ the NUBS representation may now employ this multiresolution NUBS curve editing method. The least-squares decomposition allows us to support NUBS curves, but it also imposes some preprocessing penalties in both time and space compared to techniques for multiresolution uniform \bspline{} curves. Nonetheless, the entire process is fast enough to enable interactive editing of complex NUBS curves, as is demonstrated by an interactive editor implemented to test our methods. * The third Pacific Graphics Conference on Computer Graphics and Applications, Seoul, Korea, pp 267-278, August 1995. ----------------------------------------------------------------------------- Line Art Rendering via a Coverage of Isoparametric Curves Gershon Elber A line-art non-photorealistic rendering scheme of scenes composed of freeform surfaces is presented. A freeform surface coverage is constructed using a set of isoparametric curves. The density of the isoparametric curves is set to be a function of the illumination of the surface determined using a simple shading model, or of regions of special importance such as silhouettes. The outcome is one way at achieving an aesthetic and attractive line-art rendering that employs isoparametric curve based drawings that is suitable for printing publication. * IEEE Transactions on Visualization and Computer Graphics, Vol 1, No 3, pp 231-239, September 1995. ----------------------------------------------------------------------------- Line Illustrations $\in$ Computer Graphics Gershon Elber The revolution of the computer graphics field during the last two decades made it possible to create high quality synthetic images that even experts find it difficult to differentiate from real imagery. In this paper, we explore a partially overlooked theme of computer graphics that aims at conveying simple information using simple line drawings and illustrations of polygonal as well as freeform objects. * The Visual Computer, Vol 11, No 6, 1995. ----------------------------------------------------------------------------- Error Bounded Piecewise Linear Approximation of Freeform Surfaces. Gershon Elber We present two models for piecewise linear approximation of freeform surfaces. One model exploits global curvature bounds and the other employs an intermediate bilinear approximation. In both models, a norm that minimizes the maximal deviation of the piecewise linear approximation from the freeform surface is used. * CAD, Vol 28, No 1, pp 51-57, January 1996. Also tech report CIS #9413, Computer Science Department, Technion, October 1994. ----------------------------------------------------------------------------- Symbolic and Numeric Computation in Curve Interrogation. Gershon Elber The control of shape of curves is of great importance in computer aided geometric design. Determination of planar curves' convexity, the detection of inflection points, coincident regions, and self intersection points, the enclosed area of a closed curve, and the locations of extreme curvature are important features of curves that can affect the design, in modeling environments. In this paper, we investigate the ability to robustly answer the above queries and related questions using an approach which exploits both symbolic computation and numeric analysis. * Computer Graphics {\it forum}, Vol 14, No 1, pp 25-34, March 1995. ----------------------------------------------------------------------------- Adaptive Isocurves Based Rendering: the Hardware Way. Gershon Elber In a recent work~\cite{Gershon-adap-iso-rend}, an almost optimal algorithm to provide a coverage based on the isoparametric curves of a surface was presented. This approach was combined successfully with curve rendering techniques and used to directly render surfaces using isoparametric curves instead of polygons. In this paper, we describes an adaptation of the rendering algorithm that uses adaptive isoparametric curves as the surface coverage, to a generic hardware. We also discuss the feasibility of implementing the adaptive isocurve extraction algorithm itself in hardware. The presented results make the surface coverage using adaptive extraction of isoparametric curves a tool for competitive freeform surface rendering in both software and hardware. Several results, including a videotape recording of a real time display, are demonstrated. * Presented in Computer Graphics International 1994 (CGI 94), Melbourne, Australia, June 1994. ----------------------------------------------------------------------------- Metamorphosis of Freeform Curves and Surfaces. Gershon Elber Metamorphosis between two freeform \bspline{} curves is considered and several approaches to control the process are discussed. Starting with simple convex combination, we examine two other approaches, one based on multiresolution decomposition of freeform curves and the other based on edge cutting of the control polygon of curves. The later is improved by introducing a correspondence test for simple metamorphosis relation. Finally, we consider the possibility of extending these algorithms to surfaces. * Presented in Computer Graphics International 1995 (CGI 95), Leeds, UK, June 1995. ----------------------------------------------------------------------------- Sketching as a Solid Modeling Tool Lynn Eggli, Beat Bruderlin, and Gershon Elber. This paper describes 'Quick-sketch', a 2d and 3d modeling tool for pen based computers. Users of this system define a model by simple pen strokes drawn directly on the screen of a pen-based PC. Lines, circles, arcs, or B-spline curves are automatically distinguished, and interpreted from these strokes. The system also automatically determines relations, such as right angles, tangencies, symmetry, and parallelism, from the sketch input. These relationships are then used to clean up the drawing by making the approximate relationships exact. Constraints are established to maintain the relationships in further editing. A constraint maintenance system, which is based on gestural manipulation and soft constraints, is employed in this system. Several techniques for sketch based definitions of 3d objects are provided as well, including extrusion, surface of revolution, ruled surfaces and sweep. Features can be sketched on the surfaces of 3d objects, using the same 2d- and 3d techniques. This way objects of medium complexity can be sketched in seconds. The system can be viewed as a front-end to more sophisticated modeling, rendering or animation environments, serving as a hand sketching tool in the preliminary design phase. * Presented in Solid Modeling 95, Salt Lake City, Utah, May 1995. Also to appear in CAD.