<?xml version="1.0" encoding="UTF-8"?>
 <rdf:RDF xmlns="http://purl.org/rss/1.0/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:taxo="http://purl.org/rss/1.0/modules/taxonomy/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://web.resource.org/cc/" xmlns:syn="http://purl.org/rss/1.0/modules/syndication/" xmlns:admin="http://webns.net/mvcb/">
  <channel rdf:about="http://pinboard.in">
    <title>Pinboard (Vaguery)</title>
    <link>https://pinboard.in/u:Vaguery/public/</link>
    <description>recent bookmarks from Vaguery</description>
    <items>
      <rdf:Seq>	<rdf:li rdf:resource="http://arxiv.org/abs/1511.08264"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1006.4327"/>
      </rdf:Seq>
    </items>
  </channel><item rdf:about="http://arxiv.org/abs/1511.08264">
    <title>[1511.08264] A new property of dual bases and its application</title>
    <dc:date>2015-12-06T12:04:11+00:00</dc:date>
    <link>http://arxiv.org/abs/1511.08264</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this paper, we introduce a new property of dual bases. Let there be given a dual basis Dn+1 for a basis Bn+1:={b0,b1,…,bn+1} of the linear space n+1:=spanBn+1 with an inner product ⟨⋅,⋅⟩. A dual basis Dn for the basis Bn:=Bn+1∖{bn+1} of the linear space n:=spanBn with respect to the same inner product can be computed quickly using a new formula connecting the dual functions from Dn+1 and Dn. The presented algorithm, along with the methods given in (P. Wo\'zny, Journal of Computational and Applied Mathematics 260 (2014), 301--311), can be used to solve efficiently the problem of degree reduction of B\'ezier curves with box constraints, which has been proposed recently in (P. Gospodarczyk, Computer-Aided Design 62 (2015), 143--151).
]]></description>
<dc:subject>Bezier-curves approximation geometry computational-geometry computational-complexity rather-interesting nudge-targets algorithms consider:feature-discovery consider:stress-testing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1275456eb1bf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Bezier-curves"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:stress-testing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1006.4327">
    <title>[1006.4327] On computing B\'ezier curves by Pascal matrix methods</title>
    <dc:date>2010-06-28T23:31:21+00:00</dc:date>
    <link>http://arxiv.org/abs/1006.4327</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA["The main goal of the paper is to introduce methods which compute B\'ezier curves faster than Casteljau's method does. These methods are based on the spectral factorization of a $n\times n$ Bernstein matrix, $B^e_n(s)= P_nG_n(s)P_n^{-1}$, where $P_n$ is the $n\times n$ lower triangular Pascal matrix. So we first calculate the exact optimum positive value $t$ in order to transform $P_n$ in a scaled Toeplitz matrix, which is a problem that was partially solved by X. Wang and J. Zhou (2006). Then fast Pascal matrix-vector multiplications and strategies of polynomial evaluation are put together to compute B\'ezier curves. Nevertheless, when $n$ increases, more precise Pascal matrix-vector multiplications allied to affine transformations of the vectors of coordinates of the control points of the curve are then necessary to stabilize all the computation."
]]></description>
<dc:subject>nudge-targets algorithms numerical-methods computer-graphics Bezier-curves computational-complexity</dc:subject>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fa28a8906050/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:numerical-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computer-graphics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Bezier-curves"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-complexity"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>