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- This file lists the set of papers and tech reports that were written with
- the aid of the IRIT solid modeling tool.
-
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- 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.
-
- * To appear in CAD.
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- 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.
- -----------------------------------------------------------------------------
- Proper 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.
-
- * To appear in CAD. 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.
-