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Item Artistic Surface Rendering Using Layout of Text(Blackwell Publishers Ltd and the Eurographics Association, 2002) Surazhsky, Tatiana; Elber, GershonAn artistic rendering method of free-form surfaces with the aid of half-toned text that is laid-out on the given surface is presented. The layout of the text is computed using symbolic composition of the free-form parametric surface S(u, v) with cubic or linear Bezier curve segments C(t) = cu (t), cv (t), comprising the outline of the text symbols. Once the layout is constructed on the surface, a shading process is applied to the text, affecting the width of the symbols as well as their color, according to some shader function. The shader function depends on the surface orientation and the view direction as well as the color and the direction or position of the light source.Item Orthogonal Decomposition of Non-Uniform Bspline Spaces using Wavelets(Blackwell Publishers Ltd and the Eurographics Association, 1997) Kazinnik, Roman; Elber, GershonWe 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 C1 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 an 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.Item Efficient Minimum Distance Computation for Solids of Revolution(The Eurographics Association and John Wiley & Sons Ltd., 2020) Son, Sang-Hyun; Yoon, Seung-Hyun; Kim, Myung-Soo; Elber, Gershon; Panozzo, Daniele and Assarsson, UlfWe present a highly efficient algorithm for computing the minimum distance between two solids of revolution, each of which is defined by a planar cross-section region and a rotation axis. The boundary profile curve for the cross-section is first approximated by a bounding volume hierarchy (BVH) of fat arcs. By rotating the fat arcs around the axis, we generate the BVH of fat tori that bounds the surface of revolution. The minimum distance between two solids of revolution is then computed very efficiently using the distance between fat tori, which can be boiled down to the minimum distance computation for circles in the three-dimensional space. Our circle-based approach to the solids of revolution has distinctive features of geometric simplification. The main advantage is in the effectiveness of our approach in handling the complex cases where the minimum distance is obtained in non-convex regions of the solids under consideration. Though we are dealing with a geometric problem for solids, the algorithm actually works in a computational style similar to that of handling planar curves. Compared with conventional BVH-based methods, our algorithm demonstrates outperformance in computing speed, often 10-100 times faster. Moreover, the minimum distance can be computed very efficiently for the solids of revolution under deformation, where the dynamic reconstruction of fat arcs dominates the overall computation time and takes a few milliseconds.Item Isometric Texture Mapping for Free-form Surfaces(Blackwell Publishers Ltd and the Eurographics Association, 1997) Arad, Nur; Elber, GershonTexture mapping is a frequently exploited technique in computer graphics aimed at the emulation of high-resolution details in surfaces. In this paper we present a distance-ratios preservation method for bivariate raster texture mapping to free-form surfaces in an arbitrarily precise manner. The proposed method reduces the original general problem of computing the inverse of a three-dimensional parametric surface mapping into a problem of two-dimensional image warping. Several examples that demonstrate the proposed approach are also provided.Item Variable Offsets and Processing of Implicit Forms Toward the Adaptive Synthesis and Analysis of Heterogeneous Conforming Microstructure(The Eurographics Association and John Wiley & Sons Ltd., 2024) Hong, Q. Youn; Antolin, Pablo; Elber, Gershon; Kim, Myung-Soo; Chen, Renjie; Ritschel, Tobias; Whiting, EmilyThe synthesis of porous, lattice, or microstructure geometries has captured the attention of many researchers in recent years. Implicit forms, such as triply periodic minimal surfaces (TPMS) has captured a significant attention, recently, as tiles in lattices, partially because implicit forms have the potential for synthesizing with ease more complex topologies of tiles, compared to parametric forms. In this work, we show how variable offsets of implicit forms could be used in lattice design as well as lattice analysis, while graded wall and edge thicknesses could be fully controlled in the lattice and even vary within a single tile. As a result, (geometrically) heterogeneous lattices could be created and adapted to follow analysis results while maintaining continuity between adjacent tiles. We demonstrate this ability on several 3D models, including TPMS.Item Erratum: Artistic Surface Rendering Using Layout of Text(Blackwell Publishers, Inc and the Eurographics Association, 2002) Surazhsky, Tatiana; Elber, GershonItem Interactive Line Art Rendering of Freeform Surfaces(Blackwell Publishers Ltd and the Eurographics Association, 1999) Elber, GershonIn recent years, synthetically created line art renderings have reached quality levels that are aesthetically pleasing. Moreover, the sketch based approach was found to be quite capable at conveying geometrical information in an intuitive manner. While a growing interest in this type of rendering method has yielded successful and appealing results, the developed techniques were, for the most part, too slow to be embedded in real time interactive display. This paper presents a line art rendering method for freeform polynomial and rational surfaces that is capable of achieving real time and interactive display. A careful preprocessing stage that combines an a-priori construction of line art strokes with proper classification of these strokes, allows one to significantly alleviate the computational cost, in real time, of the sketch based rendering, and enables interactive line art display.Item Image Morphing with Feature Preserving Texture(Blackwell Publishers Ltd and the Eurographics Association, 1999) Tal, Ayellet; Elber, GershonImage metamorphosis as an animation tool has mostly been employed in the context of the entire image. This work explores the use of isolated and focused image based metamorphosis between two-dimensional objects, while capturing the features, colors, and textures of the objects. This pinpointed approach allows one to independently overlay several such dynamic shapes, without any bleeding of one shape into another. Hence, shape blending and metamorphosis of two-dimensional objects can be exploited as animated sequences of clip arts.