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A set of bathymetry point clouds acquired by different measurement techniques at different times, having different accuracy and varying patterns of points, are approximated by an LR B-spline surface. The aim is to represent the sea bottom with good accuracy and at the same time reduce the data size considerably. In this process the point clouds must be cleaned by selecting the "best" points for surface generation. This cleaning process is called deconfliction, and we use a rough approximationarXiv:1610.09992v1 fatcat:lgrrjomvivdwnibjdwmm3lslc4
more »... the combined point clouds as a reference surface to select a consistent set of points. The reference surface is updated with the selected points to create an accurate approximation. LR B-splines is the selected surface format due to its suitability for adaptive refinement and approximation, and its ability to represent local detail without a global increase in the data size of the surface
Lecture Notes in Computer Science
A commodity-type graphics card with its graphics processing unit (GPU) is used to detect, compute and visualize the intersection of two spline surfaces, or the self-intersection of a single spline surface. The parallelism of the GPU facilitates fast and efficient subdivision and bounding box testing of smaller spline patches and their corresponding normal subpatches. This subdivision and testing is iterated until a prescribed level of accuracy is reached, after which results are returned to thedoi:10.1007/11758549_32 fatcat:eield7o55jbepommxupxiw76ve
more »... main computer. We observe speedups up to 17 times relative to a contemporary 64 bit CPU.
Mathematics and Visualization
We compare several methods for approximate implicitization by piecewise polynomials which have been developed by the authors, and a linear-algebrabased numerical method for implicitization which is provided as a part of MAPLE. We investigate both quantitative criteria (such as computing time, memory use, and the error of the approximation) and qualitative criteria. As demonstrated by the results, piecewise approximate implicitization is able to handle surfaces arising in industrialdoi:10.1007/978-3-540-33275-6_3 fatcat:ezbxdm3lgfe7ndxwc57gv2piai
more »... However, special care has to be taken to avoid additional branches and unwanted singularities.
Least squares approximation Introduced in [Dokken, 2001] , [Corless et al., 2001] : min b 2 =1 Ω q(p(s)) 2 w (s) ds. ... Applied Mathematics Approximate Implicitization Original method (singular value decomposition) Original method [Dokken, 1997] , gives general framework: Form matrix D = (d jk ) L,M jk=1 such that q( ...doi:10.1155/2012/293746 fatcat:6y2efj4f3rbgnciwlwnglhoqvy
The recently proposed locally refined B-splines, denoted LR B-splines, by Dokken et al.  may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided ... For this proof, see Dokken et al.  . ... We will here briefly describe three methods, but for full details we reference the work of Dokken et.al  . ...doi:10.1016/j.cma.2013.09.014 fatcat:j4jmes3p7vgw3ihaazhcya2ieu
Dokken showed that the numerical stability of the approximation process bene ts from choosing a bounding triangle as the reference triangle. ... Approximate implicitization method Dokken developed a general method to approximately implicitize g-manifolds represented by parametric equations 11 . Here, we outline his approach. ...doi:10.1006/gmip.1999.0497 fatcat:zyrvkpv4ine4nfqbgkt53y3n7y
With the introduction in 2003 of standard GPUs with 32 bit floating point numbers and programmable Vertex and Fragment processors, the processing power of the GPU was made available to non-graphics applications. As the GPU is aimed at computer graphics, the concepts in GPU-programming are based on computer graphics terminology, and the strategies for programming have to be based on the architecture of the graphics pipeline. At SINTEF in Norway a 4-year strategic institute projectdoi:10.1145/1090122.1090126 dblp:conf/sccg/DokkenHH05 fatcat:pjaqblow3vc23mzeafh6ara3ay
more »... 06)(2007) "Graphics hardware as a high-end computational resource", http://www.math.sintef.no/gpu/ aims at making GPUs available as a computational resource both to academia and industry. This paper addresses the challenges of GPUprogramming and results of the project's first year.
The implementation of it is described in Dokken et al. (2013) in terms of matrices. ... ., 2008) , PB-splines (Engleitner and Jüttler, 2017) and LR B-splines (Dokken et al., 2013) . ...doi:10.1016/j.cagd.2019.101803 fatcat:rnovrdcmi5d7xii763noe6xp2y
The theory behind this approach to approximate implicitization of rational parametric manifolds in R l has been thoroughly developed in [Dokken 1997; Dokken 2001] . ... This is possible using either the original or weak methods [Dokken 1997; Dokken and Thomassen 2006 ]. Suppose we have several parametric surfaces p 1 (s), . . . , p r (s). ...doi:10.1145/1925059.1925084 dblp:conf/sccg/BarrowcloughD10 fatcat:r5zo6qxqmzc2fngdhc6wxu42tm
. * Corresponding Author Email addresses: firstname.lastname@example.org (Francesco Patrizi), email@example.com (Tor Dokken) of the univariate B-spline spaces will cause the insertion of an entire new ...arXiv:1811.04919v2 fatcat:rwkgh5lrw5cnfb7cad6utse4aa
The novel Locally Refined B-spline (LR B-spline) surface format is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline surface has an overall smooth behaviour and allows the modelling of local details with only a limited growth in data volume. In regions where many data points belong to the same smooth area LR B-splines allow a very lean representation of the shape byarXiv:2010.01980v2 fatcat:eofxarmajrey3cxlcpatbetc3e
more »... adapting the resolution of the spline space to the size and local shape variations of the region. The surfaces generated approximate the smooth component of a cloud of data points within user specified tolerances. The method can be modified to improve the accuracy in particular domains and selected data points. The resulting surfaces are well suited for analysis and computing secondary information such as contour curves and minimum and maximum points. The surfaces can be translated into a raster or a tessellated surface of desired quality or exported as collections of tensor product spline surfaces. Data transfer can also be performed using Part 42 of ISO 10303 (the STEP standard) where LR B-splines were published in 2018.
Tor Dokken Main reference T. Dokken, T. Lyche, K. F. ... Dokken, Thomas A. ...fatcat:ueipavtqxfgsbd4l7qkcc5no4i
Several theories exist, explaining the depleted benthic d 18 O by 1) increased temperatures (Rasmussen and Thomsen, 2008) , 2) brine water formation (Dokken and Jansen, 1999; Meland et al., 2008) , or ... & Andersson b ; Risebrobakken et al., 2011 16 MD95-2010 66 41 0 N 4 33 0 E 10.9 1,2,3,4 Dokken & Andersson b 17 MD95-2011 66 58 0 N 7 38 0 E 11.0 3,4,5,6 Andersson et al., 2003, 2010; ...doi:10.1016/j.quascirev.2014.06.028 fatcat:lhnkz3ijebhgblcjoz2t6wuiia
Digital representations targeting design and simulation for Additive Manufacturing (AM) are addressed from the perspective of Computer Aided Geometric Design. We discuss the feasibility for multi-material AM for B-rep based CAD, STL, sculptured triangles as well as trimmed and block-structured trivariate locally refined spline representations. The trivariate spline representations support Isogeometric Analysis (IGA), and topology structures supporting these for CAD, IGA and AM are outlined. Thedoi:10.1016/j.camwa.2018.08.017 fatcat:wqw53vfajrg77pr4cftlpr6cam
more »... ideas of (Truncated) Hierarchical B-splines, T-splines and LR B-splines are outlined and the approaches are compared. An example from the EC H2020 Factories of the Future Research and Innovation Actions CAxMan illustrates both trimmed and block-structured spline representations for IGA and AM.
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