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14
Adaptive resolution of 1d mechanical Bspline
 In Graphite
, 2005
"... This article presents an adaptive approach to Bspline curve physical simulation. We combine geometric refinement and coarsening techniques with an appropriate continuous mechanical model. We thus deal with the (temporal and geometric) continuity issues implied when mechanical adaptive resolution is ..."
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Cited by 10 (5 self)
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This article presents an adaptive approach to Bspline curve physical simulation. We combine geometric refinement and coarsening techniques with an appropriate continuous mechanical model. We thus deal with the (temporal and geometric) continuity issues implied when mechanical adaptive resolution is used. To achieve realtime local adaptation of spline curves, some criteria and optimizations are shown. Among application examples, realtime knot tying is presented, and curve cutting is also pointed out as a nice sideeffect of the adaptive resolution animation framework. CR Categories: I.3.5 [Computing Methodologies]: COMPUTER GRAPHICS—Computational Geometry and Object
Compressed PiecewiseCircular Approximations of 3D Curves
 COMPUTER–AIDED DESIGN
, 2001
"... We propose a compact approximation scheme for 3D curves. Consider a polygonal curve P, whose n vertices have been generated through adaptive (and nearly minimal) sampling, so that P approximates some original 3D curve, O, within tolerance 0 . We present a practical and efficient algorithm for comp ..."
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Cited by 8 (0 self)
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We propose a compact approximation scheme for 3D curves. Consider a polygonal curve P, whose n vertices have been generated through adaptive (and nearly minimal) sampling, so that P approximates some original 3D curve, O, within tolerance 0 . We present a practical and efficient algorithm for computing a continuous 3D curve C that approximates P within tolerance 1 and is composed of a chain of m circular arcs, whose endpoints coincide with a subset of the vertices of P. We represent C using 5m+3 scalars, which we compress within a carefully selected quantization error 2 . Our approximation uses a total of less than 7.5n bits, when O is a typical surface/surface intersection and when the error bound 1 + 2 is less than 0.02% of the radius of a minimal sphere around O. For less accurate approximations, the storage size drops further, reaching for instance a total of n bits when 1 + 2 is increased to 3%. The storage cost per vertex is also reduced when 0 is decreased to force a tighter fit for smooth curves. As expected, the compression deteriorates for jagged curves with a tight error bound. In any case, our representation of C is always more compact than a polygonal curve that approximate O with the same accuracy. To guarantee a correct fit, we introduce a new error metric for 1 , which prevents discrepancies between P and C that are not detected by previously proposed Hausdorff or leastsquare error estimates. We provide the details of the algorithms and of the geometric constructions. We also introduce a conservative speedup for computing C more efficiently and demonstrate that it is suboptimal in only 2% of the cases. Finally, we report results on several types of curves and compare them to previously reported polygonal approximations, observing compr...
Local Energy Fairing of BSpline Curves
, 1995
"... An automatic algorithm for fairing Bspline curves of general order is presented. This work was motivated by a method of Farin and Sapidis about fairing planar cubic Bspline curves by subsequently removing and reinserting knots. Instead our new algorithm is based on the idea of subsequently changin ..."
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Cited by 6 (0 self)
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An automatic algorithm for fairing Bspline curves of general order is presented. This work was motivated by a method of Farin and Sapidis about fairing planar cubic Bspline curves by subsequently removing and reinserting knots. Instead our new algorithm is based on the idea of subsequently changing one control point of a given Bspline curve so that the new curve minimizes the integral of the squared lth derivative of the Bspline curve. How to proceed, if a tolerance is given and must be kept, is also discussed.
HAdaptive Multiscale Schemes for the Compressible NavierStokes Equations  Polyhedral Discretization, Data Compression and Mesh Generation
, 2001
"... In this paper we present the main conceptual ingredients and the current state of development of the new solver QUADFLOW for large scale simulations of compressible fluid flow and fluidstructure interaction. In order to keep the size of the discrete problems at every stage as small as possible for ..."
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Cited by 5 (4 self)
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In this paper we present the main conceptual ingredients and the current state of development of the new solver QUADFLOW for large scale simulations of compressible fluid flow and fluidstructure interaction. In order to keep the size of the discrete problems at every stage as small as possible for any given target accuracy, we employ a multiresolution adaptation strategy that will be described in the first part of the paper. In the second part we outline a new mesh generation concept that is to support the adaptive concepts as well as possible. A key idea is to understand meshes as parametric mappings determined by possibly few control points as opposed to store each mesh cell separately. Finally, we present a finite volume discretization along with suitable data structures which again is to support the adaptation concepts. We conclude with numerical examples of realistic applications demonstrating different features of the solver.
Progressive curve representation based on reverse subdivision
 IN THE 2003 INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE AND ITS APPLICATIONS
, 2003
"... A progressive curve representation based on reverse subdivision is introduced. Multiresolution structures for common subdivision rules that have both banded reconstruction and decomposition filters are produced. Multiresolution filters are usually applied to the whole curve uniformly, while progress ..."
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Cited by 1 (0 self)
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A progressive curve representation based on reverse subdivision is introduced. Multiresolution structures for common subdivision rules that have both banded reconstruction and decomposition filters are produced. Multiresolution filters are usually applied to the whole curve uniformly, while progressive curves are based on collapse and split operations that can be applied locally on any portion of a curve. In this work, firstly, small width multiresolution filters are constructed based on the reverse of the cubic Bspline subdivision. The collapse and split operations are replaced by a local decomposition and reconstruction process. Second, an efficient algorithm and data structures are presented to allow for the resulting progressive curve. Third, both a usercontrolled and an automatic method to select a portion of the curve for reconstruction or decomposition are described. The technique introduced has various applications such as viewdependent rendering, flexible editing and progressive transmission.
Fairing Spatial Bspline Curves
, 2013
"... Threedimensional curves are playing an increasing role in shiphull modeling and many other areas of computeraided design (CAD). The problem of evaluating and improving the fairness of such a curve is considered and three solutions (algorithms) are proposed representing all major methodologies cur ..."
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Threedimensional curves are playing an increasing role in shiphull modeling and many other areas of computeraided design (CAD). The problem of evaluating and improving the fairness of such a curve is considered and three solutions (algorithms) are proposed representing all major methodologies currently pursued by CAD researchers: local fairing by knot removal, and local/global fairing based on “energy ” minimization. The performance of the algorithms is studied for both cubic and quintic Bsplines using realistic testcases. Finally, a comparison with existing techniques is presented and some visualization tools for spatialcurve fairing are briefly discussed. i
Adaptive resolution of 1D mechanical Bspline
, 2008
"... This article presents an adaptive approach to Bspline curve physical simulation. We combine geometric refinement and coarsening techniques with an appropriate continuous mechanical model. We thus deal with the (temporal and geometric) continuity issues implied when mechanical adaptive resolution is ..."
Abstract
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This article presents an adaptive approach to Bspline curve physical simulation. We combine geometric refinement and coarsening techniques with an appropriate continuous mechanical model. We thus deal with the (temporal and geometric) continuity issues implied when mechanical adaptive resolution is used. To achieve realtime local adaptation of spline curves, some criteria and optimizations are shown. Among application examples, realtime knot tying is presented, and curve cutting is also pointed out as a nice sideeffect of the adaptive resolution animation framework.
A local fitting algorithm for converting planar curves to Bsplines
, 2007
"... In this paper we present a local fitting algorithm for converting smooth planar curves to Bsplines. For a smooth planar curve a set of points together with their tangent vectors are first sampled from the curve such that the connected polygon approximates the curve with high accuracy and inflexions ..."
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In this paper we present a local fitting algorithm for converting smooth planar curves to Bsplines. For a smooth planar curve a set of points together with their tangent vectors are first sampled from the curve such that the connected polygon approximates the curve with high accuracy and inflexions are detected by the sampled data efficiently. Then, a G¹ continuous Bézier spline curve is obtained by fitting the sampled data with shape preservation as well as within a prescribed accuracy. Finally, the Bézier spline is merged into a C² continuous Bspline curve by subdivision and control points adjustment. The merging is guaranteed to be within another error bound and with no more inflexions than the Bézier spline. In addition to shape preserving and error control, this conversion algorithm also benefits that the knots are selected automatically and adaptively according to local shape and error bound. A few experimental results are included to demonstrate the validity and efficiency of the algorithm.
Abstract Adaptive resolution of 1D mechanical Bspline
"... This article presents an adaptive approach to Bspline curve physical simulation. We combine geometric refinement and coarsening techniques with an appropriate continuous mechanical model. We thus deal with the (temporal and geometric) continuity issues implied when mechanical adaptive resolution is ..."
Abstract
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This article presents an adaptive approach to Bspline curve physical simulation. We combine geometric refinement and coarsening techniques with an appropriate continuous mechanical model. We thus deal with the (temporal and geometric) continuity issues implied when mechanical adaptive resolution is used. To achieve realtime local adaptation of spline curves, some criteria and optimizations are shown. Among application examples, realtime knot tying is presented, and curve cutting is also pointed out as a nice sideeffect of the adaptive resolution animation framework. CR Categories: I.3.5 [Computing Methodologies]: COMPUTER GRAPHICS—Computational Geometry and Object
To cite this version:
, 2008
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Adaptive resolution of 1D mechanical Bspline