https://f-rep.org/ 2026-04-28T03:55:23+00:00 https://f-rep.org/ https://f-rep.org/_media/wiki/dokuwiki.svg text/html 2023-12-19T08:08:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/anim_meta?rev=1702973318&do=diff Controlled Metamorphosis D. Kravtsov, O. Fryazinov, V. Adzhiev, A. Pasko & P. Comninos, Controlled Metamorphosis Between Skeleton-Driven Animated Polyhedral Meshes of Arbitrary Topologies, Computer Graphics Forum, Volume 33, Issue 1, February 2014, pages 64–72 text/html 2023-12-19T08:08:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/asum?rev=1702973318&do=diff Deformation with algebraic sums A new deformation technique for F-rep objects uses algebraic sums (differences) between an object's defining function F and a function interpolating F values in given control points. The use of a volume spline for the interpolation made possible smooth deflation (left image) and inflation (right image) of a rubber cat (center). text/html 2023-12-19T08:08:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/bblend?rev=1702973318&do=diff Bounded Blending Operations Blend localization (left), multiple blending (middle), and blend on blend (right). Pasko G., Pasko A., Kunii T.L., Bounded blending for function-based shape modeling, IEEE Computer Graphics and Applications, vol. 25, No. 2, 2005, pp. 36-45. text/html 2023-12-19T08:08:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/bezier?rev=1702973318&do=diff Bezier patches and volumes a b c A 3D object (a) is modelled using a parametric Bezier volume with functional and extended Bezier clipping operations. It makes the object a legal primitive for set-theoretic (b), hypertexturing (c) and other operations closed on F-rep. text/html 2023-12-19T08:08:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/bspfields?rev=1702973318&do=diff Exact mesh-to-function conversion using BSP fields Oleg Fryazinov, Alexander Pasko and Valery Adzhiev, “BSP-fields: An exact representation of polygonal objects by differentiable scalar fields based on binary space partitioning”, Computer-Aided Design, Volume 43, Issue 3, pages 265-277, March 2011 text/html 2023-12-19T08:08:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/carv?rev=1702973318&do=diff Synthetic relief carving a b c Relief carving is modelled with the “offsetting along the normal” operation where the offset value is defined by two-dimensional depth data. To generate depth data we use a polygon-to-function conversion algorithm. In the example shown above we illustrate the following steps: text/html 2023-12-19T08:08:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/colony?rev=1702973318&do=diff Mammalian cell colony growth A mammalian cell colony is modeled as a set of contacting deformable particles. A particle can be substituted by a pair of new particles that models the process of cell division. Specific features of this simulation are: text/html 2023-12-19T08:08:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/component?rev=1702973317&do=diff Component detection and separation for FRep O. Fryazinov and A. Pasko, Reliable detection and separation of components for solid objects defined with scalar fields, Computer-Aided Design, Volume 58, January 2015, pages 43-50 (Solid and Physical Modeling 2014) text/html 2023-12-19T08:08:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/crafts?rev=1702973317&do=diff Digitally interpreting traditional folk crafts T. Vilbrandt, C. Vilbrandt, G. Pasko, C. Stamm, A. Pasko, Digitally interpreting traditional folk crafts, IEEE Computer Graphics and Applications, vol. 31, No. 4, July/Aug. 2011, pp. 12-18. Electronic version: text/html 2023-12-19T08:08:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/csg?rev=1702973317&do=diff Set-theoretic operations with R-functions = & & We use R-functions to represent a CSG object by a single real function. Well-known min/max functions are only C0 continuous. This can cause unpredictable results in further operations on the object. Other R-functions can provide C1 and even Ck continuity of the resulting function. It helped to formulate analytical descriptions for such operations as blending, offsetting, sweeping and others. text/html 2023-12-19T08:08:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/discret?rev=1702973317&do=diff Surface and Volume Discretization of FRep Heterogeneous Objects E. Kartasheva, Adzhiev V., Pasko A., O. Fryazinov, V. Gasilov, “Surface and volume discretization of functionally based heterogeneous objects”, Journal of Computing and Information Science and Engineering, ASME Transactions, vol. 3, No. 4, 2003, pp. 285-294. text/html 2023-12-19T08:08:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/extend?rev=1702973317&do=diff Extended space mapping We have introduced a general mathematical framework for transforming functionally defined shapes. The proposed model of extended space mappings considers transformations of a hypersurface in coordinate-function space with its projection onto geometric space. This model covers coordinate text/html 2023-12-19T08:08:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/fbv?rev=1702973317&do=diff Feature-based volumes for implicit intersections Oleg Fryazinov, Pierre-Alain Fayolle, Turlif Vilbrandt, Galina Pasko and Alexander Pasko, “Feature Based Volumes for Implicit Intersections”, Computers & Graphics, Volume 35, Issue 3, June 2011, pages 524-531 (Proceedings of SMI'2011) text/html 2023-12-19T08:08:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/fvolume?rev=1702973317&do=diff Volume modeling a b c In our approach to volume modeling, we combine volume representations by voxel data and by continuous real functions. The figures above illustarte: a) sweeping by a volumetric head; b) head cut by a moving cutter; c) hair growth and styling on the voxel head. text/html 2023-12-19T08:08:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/gallery?rev=1702973317&do=diff Gallery <http://hyperfun.org/marble_vase.gif> Marble vase <http://hyperfun.org/chmu5.gif> Chmutov-5 <http://hyperfun.org/chmu6.gif> Chmutov-6 <http://hyperfun.org/silicon_quake.gif> Silicon quake Functionally Based Shape Modeling and Computer Art geoment Go to project page See also Some interesting images can be found on Sweeping, Carving, and Hair pages. <http://www.ntu.edu.sg/home/assourin>Pictures at A. Sourin's page. text/html 2023-12-19T08:08:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/geoment?rev=1702973317&do=diff Functionally Based Shape Modeling and Computer Art Authors: A.Sourin, V.Savchenko, A.Pasko <http://hyperfun.org/geoment.gif> Geometric Mentality (Click on the image to get its 500×500 143K version.) Designing complex three-dimensional shapes is one of the challenging problems of computer art. This sketch aims to illustrate the application of our approach to complex shape modeling in computer art. Our model, that we have called the function representation , can incorporate very different ge… text/html 2023-12-19T08:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/gpustandins?rev=1702973316&do=diff Polygonal-Functional Hybrids for Computer Animation and Games Abstract: We present an approach utilising hybrid models, combining together both polygonal and Function Representation models. We perform model evaluation and rendering entirely on the GPU using NVidia CUDA SDK. Our approach allows us to produce animations involving dramatic changes of the shape (e.g. metamorphosis, mimicked viscoelastic behaviour, character modifications etc) and interactively create complex shapes with changing t… text/html 2023-12-19T08:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/hair?rev=1702973316&do=diff Modeling hair Hairstyles are modeled by procedurally defined real functions with the use of “solid noise”, sweep-like technique, offsetting and set-theoretic operations, and non-linear deformations. Hairy Cube (500K), more hairy pictures More details on hair modeling can be found in the paper: text/html 2023-12-19T08:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/haniwa?rev=1702973316&do=diff Haniwa: Reconstruction Case Study M. B. H. Shanat, P.-A. Fayolle, B. Schmitt, T. Vilbrandt Haniwa : A Case Study of Digital Visualization of Virtual Heritage Properties, 20th Eurographics UK Conference (De Montfort University, Leicester, UK), IEEE Computer Society, 2002, pp. 24-32. text/html 2023-12-19T08:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/heritage?rev=1702973316&do=diff Cultural Heritage Preservation Using Constructive Shape Modeling A CSG model of the Sazaedo pagoda in the Aizu area of Japan (left image) and the evolution of a parameterized FRep model of a Japanese lacquer ware (shikki) during the fitting process (right image). text/html 2023-12-19T08:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/homa?rev=1702973316&do=diff Heterogeneous Objects Modelling and Applications (2008) book * An Implicit Complexes Framework for Heterogeneous Objects Modelling Elena Kartasheva, Valery Adzhiev, Peter Comninos, Oleg Fryazinov and Alexander Pasko * Heterogeneous Object Design: An Integrated CAX Perspective text/html 2023-12-19T08:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/hybrid?rev=1702973316&do=diff Hybrid system architecture for volume modeling A hybrid volume modeling system architecture was proposed. The key architectural decision of the system design is based on the combination of volume representations by voxel data and by real continuous functions (F-rep). The concept of the volume model, hybrid voxel-function representation, system input in different forms, and possible applications are discussed. text/html 2023-12-19T08:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/hypervol?rev=1702973316&do=diff Constructive Hypervolume Modeling Pasko A., Adzhiev V., Schmitt B., Schlick C., Constructive Hypervolume Modeling, Graphical Models, special issue on Volume Modeling, vol. 63, No. 6, November 2001, pp. 413-442. Electronic version: PDF (1.69 Mb) See also: text/html 2023-12-19T08:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/isopol?rev=1702973316&do=diff Isosurface Polygonization using Hyperbolic Arcs to Resolve Topological Ambiguity Problems Pasko A. A., Pilyugin V. V., Pokrovskiy V. N., “Geometric modeling in the analysis of trivariate functions”, Computers and Graphics, vol.12, Nos.3/4, 1988, pp.457-465. text/html 2023-12-19T08:09:17+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/main?rev=1702973357&do=diff Shape Modeling and Computer Graphics with Real Functions Key words: implicit surfaces, real functions, R-functions, Function Representation FRep, solid modeling, sweeping, set-theoretic operations, CSG, blobby, soft objects, Radial Basis Functions RBF, deformation, metamorphosis, isosurfaces, volume modeling, heterogeneous objects, procedural modeling, visualization. text/html 2023-12-19T08:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/metamor?rev=1702973316&do=diff Metamorphosis Animation: * QuickTime (350K), * SGI movie (313K) Metamorphosis (shape transformation, morphing) between two functionally represented objects can be described by the interpolation between their defining functions. Such interpolation procedure defines a homotopy map in n+1-dimensional space. This makes possible metamorphosis between a blobby object and a constructive solid (frames shown above). text/html 2023-12-19T08:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/microstructures?rev=1702973316&do=diff Procedural volumetric microstructures O. Fryazinov, T. Vilbrandt, A. Pasko, Multi-scale space-variant FRep cellular structures, Computer-Aided Design, vol. 45, No. 1, 2013, pp. 26–34. Electronic version (preprint): PDF (1.1 Mb) A. Pasko, O. Fryazinov, T. Vilbrandt, P.-A. Fayolle and V. Adzhiev, Procedural function-based modelling of volumetric microstructures, Graphical Models, Volume 73, Issue 5, September 2011, pages 165-181 text/html 2023-12-19T08:08:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/mink?rev=1702973315&do=diff Minkowski Sums A constant-radius offset of a 2D, R-functions based set-theoretic solid, is generated by taking the Minkowski sum with a disk. Metamorphosis of a “silly boy” into a “wise pelican” using time-weighted Minkowski sums. text/html 2023-12-19T08:08:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/morphological?rev=1702973315&do=diff Morphological Shape Generation M. Sanchez, O. Fryazinov, T. Vilbrandt and A. Pasko, Morphological Shape Generation through User-Controlled Group Metamorphosis, Computers & Graphics, Volume 37, Issue 6, October 2013, pages 620-627 [PDF (preprint)] Abstract: Morphological shape design is interpreted in this paper as a search for new shapes from a particular application domain represented by a set of selected shape instances. This paper proposes a new foundation for morphological shape design a… text/html 2023-12-19T08:08:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/new?rev=1702973315&do=diff What's new on FRep Home Page * December 2012: Publications updated by the journal papers published in 2012 * April 2012: Students' projects added: FRep Kinect Modeller, FRep in Houdini, and "Lifetime" animation: Maya plug-in * October 2011: Another free FRep modelling system: Symvol for Rhino - Maker version developed by Uformia, Norway, in partnership with the text/html 2023-12-19T08:08:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/projection?rev=1702973315&do=diff Projection operation To project a surface or a solid in geometric modeling is a much more difficult problem than to project points and line segments in computer graphics. The result of this operation in FRep is an object of the lower dimension with its own defining function. We have compared the following approaches: analytical methods, approximate projections and global maximum searches. There are several applications: text/html 2023-12-19T08:08:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/publications?rev=1702973315&do=diff Selected publications Books and book chapters * D. Kravtsov, O. Fryazinov, V. Adzhiev, A. Pasko, P. Comninos, Polygonal-functional hybrids for computer animation and games, chapter in GPU Pro: Advanced Rendering Techniques, Ed. W. Engel, A K Peters Publisher, USA, 2010, pp. 87-114. text/html 2023-12-19T08:08:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/rbfmpu?rev=1702973315&do=diff Shape Reconstruction Using Radial-Basis Functions and Partition of Unity Radial basis functions Ohtake Y., Belyaev A., Seidel H.-P., “3D scattered data approximation with adaptive compactly supported radial basis functions”, Shape Modeling International 2004, Genova, Italy, IEEE Computer Society, 2004, pp. 31-39. text/html 2023-12-19T08:08:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/reconstruction?rev=1702973315&do=diff Reconstruction from surface points and contours A femur reconstructed from cross-sections (left image) and the Mars sattelite Phobos reconstructed from scatterred surface points (right image). Our general approach to the reconstruction using Radial Basis Functions (RBF) is described in the paper: text/html 2023-12-19T08:08:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/revaa?rev=1702973315&do=diff Reliable Ray-Tracing and Enumeration Oleg Fryazinov, Alexander Pasko and Peter Comninos, “Fast Reliable Interrogation of Procedurally Defined Implicit Surfaces Using Extended Revised Affine Arithmetic”, Computers & Graphics, Volume 34, Issue 6, pages 708–718, December 2010 text/html 2023-12-19T08:08:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/sculpt?rev=1702973314&do=diff Feature-based sculpting Simulation of facial expressions. A volumetric head is converted to F-rep using trilinear interpolation (left image). The head is sculpted with space mapping defined by displacements of control points linked to the features of the object (right image). The displacements define scalar values in scattered points. These scalar values are interpolated by a volume spline based on the Green's function. text/html 2023-12-19T08:08:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/sharp_em?rev=1702973314&do=diff Polygonization with Embedded Sharp Features Extraction The surface reconstructed for the Fandisk dataset with embedded sharp features approximation. The image on the right shows additional interior points corresponding to vertex sharp features depicted with red colors, while additional basic polygon edge points corresponding to edge sharp features are depicted with green color. text/html 2023-12-19T08:08:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/sharp?rev=1702973314&do=diff Sharp Features of Polygonized Implicit Surfaces Ohtake Y., Belyaev A., Pasko A., Dynamic Mesh Optimization for Polygonized Implicit Surfaces with Sharp Features, The Visual Computer, vol. 19, No. 2-3, 2003, pp. 115-126. Electronic version: zipped PDF (1.24 Mb) , text/html 2023-12-19T08:08:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/sidebar?rev=1702973314&do=diff FRep FRep main page What is FRep? Selected topics Gallery Publications Relative sites text/html 2023-12-19T08:08:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/sig96?rev=1702973314&do=diff F-rep in the SIGGRAPH'96 Course on Implicit Surfaces Quotes from the SIGGRAPH'96 Course No.11 Implicit Surfaces for Geometric Modeling and Computer Graphics co-chaired by Jai Menon and Brian Wyvill “Three major lines of work in implicit models: text/html 2023-12-19T08:08:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/sites?rev=1702973314&do=diff FRep: Relative sites Geometric Modeling and Computer Graphics - Information Resources List of journals and bibliographies Research, Algorithms, Software * SVLIS Set-theoretic kernel modeller * GAS Computer algebra system for solving geometrical problems * DPGraph Mathematical visualization software by D. Parker text/html 2023-12-19T08:08:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/splitting?rev=1702973314&do=diff Splitting operation a b c d A femur (a) is split in two parts (c) by the deformed halfspace (b). Incorrect knitting (d) is modeled with the blending union operation. The splitting halfspace is deformed by a non-linear transformation with arbitrary control points. text/html 2023-12-19T08:08:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/standins?rev=1702973314&do=diff Embedded Implicit Stand-ins for Animated Meshes D. Kravtsov, O. Fryazinov, V. Adzhiev, A. Pasko, P. Comninos, “Embedded Implicit Stand-Ins for Animated Meshes: A Case of Hybrid Modelling”, Computer Graphics Forum Volume 29, Issue 1, pages 128–140, March 2010 text/html 2023-12-19T08:08:34+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/stblend?rev=1702973314&do=diff Space-time Blending “Space-time blending” by Pasko G., Pasko A., Kunii T., Computer Animation and Virtual Worlds, vol. 15, No. 2, 2004, pp. 109-121. Electronic version: PDF (835K) We present a new approach to shape transformation for animation based on the text/html 2023-12-19T08:08:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/sweeping?rev=1702973313&do=diff Sweeping by a moving solid We have reduced the problem of a swept solid description to a global extremum search by a parameter of movement. It allows the user to apply arbitrary variable-shape and CSG solids as generators, arbitrary parametrized movement and self-intersections. An example of sweeping by falling cup and spoon is shown below. text/html 2023-12-19T08:08:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/synthcarv?rev=1702973313&do=diff Synthetic Carving a b c d Pasko A., Savchenko V., Sourin A., Synthetic carving using implicit surface primitives, Computer-Aided Design, Elsevier, vol. 33, No. 5, April 2001, pp. 379-388. Electronic version: PDF (1,034K) Abstract Several techniques of computer-aided synthetic carving are presented. We describe both procedural methods for relief carvings (Figs. a, d) and patterned lattices (Fig. b), as well as interactive carving (Fig. c). Different techniques of depth data generatio… text/html 2023-12-19T08:09:17+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/topics?rev=1702973357&do=diff Selected topics crafts Crafts microstructures Microstructures revaa Reliable Interrogation Ray-tracing and Enumeration fbv Feature-Based Volumes bspfields Exact Mesh-to-Function Conversion gpustandins Implicit stand-ins on GPU standins Implicit stand-ins <http://www.intellectbooks.co.uk/journals/view-Article,id=8781/> Fabricating Nature <http://portal.acm.org/citation.cfm?id=1562195&dl=GUIDE&coll=GUIDE&CFID=83485506&CFTOKEN=22051810> Multilevel Education <… text/html 2023-12-19T08:08:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/trimming?rev=1702973313&do=diff Trimming implicit surfaces A B C A = B \ C A is a trimmed implicit surface (2-manifold with boundary) - set difference of B and C, B is a spherical surface, C is a solid constructed by sweeping and set-theoretic operations. D E D = E \ C D is a trimmed blobby surface - set difference of E and C, text/html 2023-12-19T08:08:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/volsculpt?rev=1702973313&do=diff Constructive Volumetric Sculpting Using Trivariate B-splines a b c (a) A teapot-like object is modeled using a single cubic B-spline primitive. (b) Heterogeneous object modeling. Several primitives and operations, including the proposed B-spline primitive, are used to build the constructive trees for the geometry and the attributes. text/html 2023-12-19T08:08:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/webmod?rev=1702973313&do=diff Web-based Shape Modeling HyperFun Applet Cartwright R., Adzhiev V., Pasko A., Goto Y., Kunii T. L., Web-based shape modeling with HyperFun, IEEE Computer Graphics and Applications, vol. 25, No. 2, 2005, pp. 60-69. Electronic pre-final version: PDF (730K) Abstract We present a project on research and development of the high level language text/html 2023-12-19T08:08:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/what?rev=1702973313&do=diff What is FRep? The Function Representation (or FRep) defines a geometric object by a single real continuous function of point coordinates as <m>F(X) >= 0</m> It combines many different models like * algebraic surfaces * skeleton based “implicit text/html 2023-12-19T08:08:33+00:00 Anonymous (anonymous@undisclosed.example.com) https://f-rep.org/frep/why?rev=1702973313&do=diff Why not just implicit? What is the difference between traditional “implicits” and FRep ? Why is “implicit surface” not a very good term? It sounds well ... Should we keep it? There are several reasons why the terms “implicit surfaces