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Determining an Aesthetic Inscribed Curve [article]

Brian Wyvill, P. G. Kry, R. Seidel, D. Mould
2012 Computational Aesthetics in Graphics  
In this work we propose both implicit and parametric curves to represent aesthetic curves inscribed within Voronoi cells in R2.  ...  A user survey was conducted to determine, which class of curves are generally accepted as the more aesthetic.  ...  Acknowledgements We wish to acknowledge the Natural Sciences and Engineering Research Council of Canada, and the GRAND Network of Centres of Excellence for partially supporting this work.  ... 
doi:10.2312/compaesth/compaesth12/063-070 fatcat:kzvzznjsunhkjdu6xrjxp6gauq

Optimizing the Geometrical Accuracy of 2D Curvilinear Meshes

Jean-François Remacle, Jonathan Lambrechts, Christophe Geuzaine, Thomas Toulorge
2014 Procedia Engineering  
This paper presents a method to generate valid 2D high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a straight sided mesh.  ...  An area based distance is proposed to compute the geometrical discrepancy between the mesh and its underlying geometry.  ...  To our knowledge, few robust implementations of Voronoi diagrams of line segments exist [8] and no extension to higher dimensions than two has been proposed to date.  ... 
doi:10.1016/j.proeng.2014.10.386 fatcat:2dhzzznytfculmtgh3edz4yis4

Mollified finite element approximants of arbitrary order and smoothness [article]

Eky Febrianto, Michael Ortiz, Fehmi Cirak
2019 arXiv   pre-print
The approximation properties of the obtained basis functions are governed by the local polynomial approximation order and mollifier smoothness.  ...  The approximation properties of the finite element method can often be substantially improved by choosing smooth high-order basis functions.  ...  Clipped Voronoi diagrams We briefly review the properties of Voronoi diagrams and sketch the generation of clipped Voronoi diagrams that approximately fill a given domain Ω.  ... 
arXiv:1910.04002v1 fatcat:dbeqwplkhbezzebvntxpy3k5iq

Real-time texture-mapped vector glyphs

Zheng Qin, Michael D. McCool, Craig S. Kaplan
2006 Proceedings of the 2006 symposium on Interactive 3D graphics and games - SI3D '06  
An optimized uniform grid accelerator is created using Voronoi analysis and redundancy elimination, so only the distances to a small constant number of features need be computed at every access.  ...  Variations in glyph complexity are handled by storing different glyphs at different grid resolutions.  ...  We adaptively approximate quadratics and cubics by line segments, subdividing the splines recursively until a given error bound is met.  ... 
doi:10.1145/1111411.1111433 dblp:conf/si3d/QinMK06 fatcat:v4h2p2fnxjhabjymzy6p7qcapy

Level set topology optimization with nodally integrated reproducing kernel particle method

Andreas Neofytou, Tsung-Hui Huang, Sandilya Kambampati, Renato Picelli, Jiun-Shyan Chen, H. Alicia Kim
2021 Computer Methods in Applied Mechanics and Engineering  
Moreover, useful characteristics of the RKPM such as the easily controlled order of continuity and the ability to freely place particles in a design domain wherever needed are illustrated through stress  ...  based and design-dependent surface loading examples.  ...  Acknowledgments We thank the support of the Engineering and Physical Sciences Research Council, fellowship grant EP/M002322/2.  ... 
doi:10.1016/j.cma.2021.114016 fatcat:rfffq5kue5f2bm6okwbkv6h3dy

Optimizing the geometrical accuracy of curvilinear meshes

Thomas Toulorge, Jonathan Lambrechts, Jean-François Remacle
2016 Journal of Computational Physics  
This paper presents a method to generate valid high order meshes with optimized geometrical accuracy.  ...  An unconstrained optimization procedure based on this estimate is shown to yield significant improvements in the geometrical accuracy of high order meshes, as measured by the standard Haudorff distance  ...  Acknowledgements This work has been partly funded by the European Commission under the FP7 grant "IDIHOM" (Industrialisation of High-Order Methods -A Top-Down Approach).  ... 
doi:10.1016/ fatcat:26hfxf3wevezhbhgbbucrml25a

Ardeco: Automatic Region DEtection and COnversion [article]

Gregory Lecot, Bruno Levy
2006 Symposium on Rendering  
In addition, more details can be generated in user-selected important regions, defined from eye-tracking data or from an importance map painted by the user.  ...  Our algorithm is based on a new two-level variational parametric segmentation algorithm, minimizing Mumford and Shah's energy and operating on an intermediate triangulation, well adapted to the features  ...  Those vector primitives are closed regions, bordered by cubic splines, and filled with a constant, linear or quadratic variation of color (all possible circular gradients and their linear transformations  ... 
doi:10.2312/egwr/egsr06/349-360 fatcat:qfszuz3m7bgibebshc57b5fyn4

Spherical DCB-Spline Surfaces with Hierarchical and Adaptive Knot Insertion

Juan Cao, Xin Li, Zhonggui Chen, Hong Qin
2012 IEEE Transactions on Visualization and Computer Graphics  
A key contribution for making such a fitting method both practical and accurate is our spherical generalization of the Delaunay configuration B-spline (DCB-spline), a new non-tensor-product spline.  ...  Also, we develop a hierarchical and adaptive method that progressively improves the fitting quality by new knot-insertion strategies guided by surface geometry and fitting error.  ...  ., computing 3D Voronoi diagrams needs quadratic complexity even for the first-order case [33] , [34] , [35] .  ... 
doi:10.1109/tvcg.2011.156 pmid:21931175 fatcat:epbze77pv5gp5m4whdiygg4dy4

A Review on Approaches for Handling Bezier Curves in CAD for Manufacturing

Hetal N. Fitter, Akash B. Pandey, Divyang D. Patel, Jitendra M. Mistry
2014 Procedia Engineering  
Various techniques and methodologies like curve fitting, curve manipulation, blending and merging of curves have been proposed over the years for better handling and enhancing Bezier curve use with every  ...  possible application in CAD domain such as image extraction, modelization, profile approximation, fairing and smoothing, etc.  ...  A Voronoi diagram of a polygon has various applications like pocketing tool path, automated mesh generation, computer vision and font generation.  ... 
doi:10.1016/j.proeng.2014.12.394 fatcat:dqa53x5ijnaq5nczua5vybi7su

Spline-based medial axis transform representation of binary images

Jieying Wang, Jiří Kosinka, Alexandru Telea
2021 Computers & graphics  
In this paper, we present a full pipeline for computing a stable and accurate piece-wise B-spline representation of Medial Axis Transforms (MATs) of binary images.  ...  We illustrate our approach on a multi-scale SMAT representation, generating super-resolution images, and free-form binary image deformation.  ...  or higher-order curves.  ... 
doi:10.1016/j.cag.2021.05.012 fatcat:ulme3ajrz5gp3eeuhl4rgs2iui

Negative Knowledge and a Novel Approach to Support MCAD Education

Ferruccio Mandorli, Harald E. Otto
2013 Computer-Aided Design and Applications  
The objective is to obtain an editable CAD model that is manufacturable and describes accurately the structure and topology of the point cloud. The point cloud is sliced into cross sections.  ...  So we compute a cubic B-Spline that interpolates the points of the feature polyline. The use of a cubic B-Spline ensures that we have G 1 continuity (instead of G 0 with the polyline).  ...  The process of interpolating the feature polyline with B-Splines is performed in all cross sections, and at the end, the point cloud is described by a sequence of B-Spline contours.  ... 
doi:10.3722/cadaps.2013.1007-1020 fatcat:renpjne4z5cpncu32qb4nyxu34

Hybrid PSO-cubic spline for autonomous robots optimal trajectory planning

Paulo Salgado, Getulio Igrejas, Paulo Afonso
2017 2017 IEEE 21st International Conference on Intelligent Engineering Systems (INES)  
The spline based trajectory generation gives us continuous, smooth and optimized path trajectories. Simulation and experimental results demonstrate the effectiveness of the proposed method. I.  ...  This paper presents a new version of the Particle Swarm Optimization algorithm where the particles are replaced by spline functions.  ...  The cubic or higher order polynomials such as B-splines have been widely used as single curves to generate two times continuously differentiable curvature (trajectories), C 2 [22] [23] [24] .  ... 
doi:10.1109/ines.2017.8118542 fatcat:lvhtyrbmobdmhgqeoz3wgitude


2009 Advances in Adaptive Data Analysis  
Simulations are made to focus mainly on the effect of interpolation methods by providing less or negligible control on the other parameters or factors of the BEMD process.  ...  In the decomposition process, local maxima and minima of the image are extracted at each iteration and then interpolated to form the upper and the lower envelopes, respectively.  ...  generating point than to any other. 27 A Voronoi diagram is sometimes also known as a Dirichlet tessellation.  ... 
doi:10.1142/s1793536909000084 fatcat:oc4aab2ahbel3fsneel46oqj34

Teaching meshes, subdivision and multiresolution techniques

Stephan Bischoff, Leif Kobbelt
2004 Computer-Aided Design  
modeling and is often the subject of seminars and presentations.  ...  These teaching blocks can be assembled so as to fit different occasions like lectures, courses, seminars and talks and different audiences like students and industrial practitioners.  ...  , uniform B-splines to higher dimensions and can also be defined using a convolution formula.  ... 
doi:10.1016/j.cad.2003.11.007 fatcat:24mdvy6dzzdexedu3zrts7kh6y

A History of Curves and Surfaces in CAGD [chapter]

Gerald Farin
2002 Handbook of Computer Aided Geometric Design  
We adopt the definition that CAGD deals with the construction and representation of free-form curves, surfaces, or volumes.  ...  This article provides a historical account of the major developments in the area of curves and surfaces as they entered the area of CAGD -Computer Aided Geometric Designuntil the middle 1980s.  ...  Higher order elements use C 1 quintic elements [92] or C 1 split triangle cubic elements.  ... 
doi:10.1016/b978-044451104-1/50002-2 fatcat:thb7qb27ebdwdbcshgnbzxvxq4
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