@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-LSC1HV6F-0
  skos:prefLabel "squircle"@fr, "squircle"@en ;
  a skos:Concept ;
  skos:broader psr:-B827BGSZ-S .

psr:-B827BGSZ-S
  dc:modified "2023-07-31"^^xsd:date ;
  dc:created "2023-07-31"^^xsd:date ;
  skos:definition """Les <b>courbes de Lamé</b> (ou superellipses) sont un groupe de courbes définies pour la première fois par le mathématicien français Gabriel Lamé en 1818. Elles sont définies par leur équation cartésienne&nbsp;:
<br/>
<br/><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\left|{\\rac {x}{a}}\\
ight|^{n}\\\\!+\\\\left|{\\rac {y}{b}}\\
ight|^{n}\\\\!=1.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow>
<br/>            <mo>|</mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mi>x</mi>
<br/>                <mi>a</mi>
<br/>              </mfrac>
<br/>            </mrow>
<br/>            <mo>|</mo>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mo>+</mo>
<br/>        <msup>
<br/>          <mrow>
<br/>            <mo>|</mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mi>y</mi>
<br/>                <mi>b</mi>
<br/>              </mfrac>
<br/>            </mrow>
<br/>            <mo>|</mo>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mo>=</mo>
<br/>        <mn>1.</mn>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\left|{\\rac {x}{a}}\\
ight|^{n}\\\\!+\\\\left|{\\rac {y}{b}}\\
ight|^{n}\\\\!=1.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/204cbefb228abe490c9d8e487e0b87a619683762" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.005ex; width:16.156ex; height:5.176ex;" alt="{\\\\displaystyle \\\\left|{\\rac {x}{a}}\\
ight|^{n}\\\\!+\\\\left|{\\rac {y}{b}}\\
ight|^{n}\\\\!=1.}"></span></dd></dl>
<br/>Similairement, elles sont définies par l'équation polaire (où les points <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle (r,\\	heta )}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>r</mi>
<br/>        <mo>,</mo>
<br/>        <mi>θ<!-- θ --></mi>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle (r,\\	heta )}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed8396fdc359fb06c93722137c959e7496e47ed6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:4.982ex; height:2.843ex;" alt="(r,\\	heta)"></span> qui respectent l'équation)&nbsp;:
<br/><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle r=\\\\left(\\\\left|{\\rac {cos(\\	heta )}{a}}\\
ight|^{n}\\\\!\\\\!+\\\\left|{\\rac {sin(\\	heta )}{b}}\\
ight|^{n}\\\\!\\
ight)^{-1/n}\\\\!,}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>r</mi>
<br/>        <mo>=</mo>
<br/>        <msup>
<br/>          <mrow>
<br/>            <mo>(</mo>
<br/>            <mrow>
<br/>              <msup>
<br/>                <mrow>
<br/>                  <mo>|</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mfrac>
<br/>                      <mrow>
<br/>                        <mi>c</mi>
<br/>                        <mi>o</mi>
<br/>                        <mi>s</mi>
<br/>                        <mo stretchy="false">(</mo>
<br/>                        <mi>θ<!-- θ --></mi>
<br/>                        <mo stretchy="false">)</mo>
<br/>                      </mrow>
<br/>                      <mi>a</mi>
<br/>                    </mfrac>
<br/>                  </mrow>
<br/>                  <mo>|</mo>
<br/>                </mrow>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mi>n</mi>
<br/>                </mrow>
<br/>              </msup>
<br/>              <mspace width="negativethinmathspace"></mspace>
<br/>              <mspace width="negativethinmathspace"></mspace>
<br/>              <mo>+</mo>
<br/>              <msup>
<br/>                <mrow>
<br/>                  <mo>|</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mfrac>
<br/>                      <mrow>
<br/>                        <mi>s</mi>
<br/>                        <mi>i</mi>
<br/>                        <mi>n</mi>
<br/>                        <mo stretchy="false">(</mo>
<br/>                        <mi>θ<!-- θ --></mi>
<br/>                        <mo stretchy="false">)</mo>
<br/>                      </mrow>
<br/>                      <mi>b</mi>
<br/>                    </mfrac>
<br/>                  </mrow>
<br/>                  <mo>|</mo>
<br/>                </mrow>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mi>n</mi>
<br/>                </mrow>
<br/>              </msup>
<br/>              <mspace width="negativethinmathspace"></mspace>
<br/>            </mrow>
<br/>            <mo>)</mo>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mo>/</mo>
<br/>            </mrow>
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mo>,</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle r=\\\\left(\\\\left|{\\rac {cos(\\	heta )}{a}}\\
ight|^{n}\\\\!\\\\!+\\\\left|{\\rac {sin(\\	heta )}{b}}\\
ight|^{n}\\\\!\\
ight)^{-1/n}\\\\!,}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3eb7ee7cf8e105ccd966b79e9e8f08ae8245139" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.671ex; width:32.657ex; height:7.176ex;" alt="{\\\\displaystyle r=\\\\left(\\\\left|{\\rac {cos(\\	heta )}{a}}\\
ight|^{n}\\\\!\\\\!+\\\\left|{\\rac {sin(\\	heta )}{b}}\\
ight|^{n}\\\\!\\
ight)^{-1/n}\\\\!,}"> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Courbe_de_Lam%C3%A9">https://fr.wikipedia.org/wiki/Courbe_de_Lam%C3%A9</a>)"""@fr, """A <b>superellipse</b>, also known as a <b>Lamé curve</b> after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but a different overall shape.
<br/>In the Cartesian coordinate system, the set of all points <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle (x,y)}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>x</mi>
<br/>        <mo>,</mo>
<br/>        <mi>y</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle (x,y)}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41cf50e4a314ca8e2c30964baa8d26e5be7a9386" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:5.328ex; height:2.843ex;" alt="(x,y)"></span> on the curve satisfy the equation
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\left|{\\rac {x}{a}}\\
ight|^{n}\\\\!\\\\!+\\\\left|{\\rac {y}{b}}\\
ight|^{n}\\\\!=1,}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow>
<br/>            <mo>|</mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mi>x</mi>
<br/>                <mi>a</mi>
<br/>              </mfrac>
<br/>            </mrow>
<br/>            <mo>|</mo>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mo>+</mo>
<br/>        <msup>
<br/>          <mrow>
<br/>            <mo>|</mo>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mfrac>
<br/>                <mi>y</mi>
<br/>                <mi>b</mi>
<br/>              </mfrac>
<br/>            </mrow>
<br/>            <mo>|</mo>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mo>=</mo>
<br/>        <mn>1</mn>
<br/>        <mo>,</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\left|{\\rac {x}{a}}\\
ight|^{n}\\\\!\\\\!+\\\\left|{\\rac {y}{b}}\\
ight|^{n}\\\\!=1,}</annotation>
<br/>  </semantics>
<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdfa5548109ddd7129693b7e97fdff814da3c6be" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -2.005ex; width:15.769ex; height:5.176ex;" alt="{\\\\displaystyle \\\\left|{\\rac {x}{a}}\\
ight|^{n}\\\\!\\\\!+\\\\left|{\\rac {y}{b}}\\
ight|^{n}\\\\!=1,}"></div>
<br/>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle n,a}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>n</mi>
<br/>        <mo>,</mo>
<br/>        <mi>a</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle n,a}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65f10f65fcba30f32673bd2ffe9f8e006f5a624b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:3.658ex; height:2.009ex;" alt="{\\\\displaystyle n,a}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle b}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>b</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle b}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="b"></span> are positive numbers, and the vertical bars around a number indicate the absolute value of the number. The 3-dimensional generalization is called superellipsoid (some literatures also name it superquadrics).
<br/>In the Polar coordinate system, the superellipse equation is (the set of all points <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle (r,\\	heta )}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>r</mi>
<br/>        <mo>,</mo>
<br/>        <mi>θ<!-- θ --></mi>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle (r,\\	heta )}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed8396fdc359fb06c93722137c959e7496e47ed6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:4.982ex; height:2.843ex;" alt="(r,\\	heta )"></span> on the curve satisfy the equation)&nbsp;:
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle r=\\\\left(\\\\left|{\\rac {\\\\cos(\\	heta )}{a}}\\
ight|^{n}\\\\!\\\\!+\\\\left|{\\rac {\\\\sin(\\	heta )}{b}}\\
ight|^{n}\\\\!\\
ight)^{-1/n}\\\\!.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>r</mi>
<br/>        <mo>=</mo>
<br/>        <msup>
<br/>          <mrow>
<br/>            <mo>(</mo>
<br/>            <mrow>
<br/>              <msup>
<br/>                <mrow>
<br/>                  <mo>|</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mfrac>
<br/>                      <mrow>
<br/>                        <mi>cos</mi>
<br/>                        <mo>⁡<!-- ⁡ --></mo>
<br/>                        <mo stretchy="false">(</mo>
<br/>                        <mi>θ<!-- θ --></mi>
<br/>                        <mo stretchy="false">)</mo>
<br/>                      </mrow>
<br/>                      <mi>a</mi>
<br/>                    </mfrac>
<br/>                  </mrow>
<br/>                  <mo>|</mo>
<br/>                </mrow>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mi>n</mi>
<br/>                </mrow>
<br/>              </msup>
<br/>              <mspace width="negativethinmathspace"></mspace>
<br/>              <mspace width="negativethinmathspace"></mspace>
<br/>              <mo>+</mo>
<br/>              <msup>
<br/>                <mrow>
<br/>                  <mo>|</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mfrac>
<br/>                      <mrow>
<br/>                        <mi>sin</mi>
<br/>                        <mo>⁡<!-- ⁡ --></mo>
<br/>                        <mo stretchy="false">(</mo>
<br/>                        <mi>θ<!-- θ --></mi>
<br/>                        <mo stretchy="false">)</mo>
<br/>                      </mrow>
<br/>                      <mi>b</mi>
<br/>                    </mfrac>
<br/>                  </mrow>
<br/>                  <mo>|</mo>
<br/>                </mrow>
<br/>                <mrow class="MJX-TeXAtom-ORD">
<br/>                  <mi>n</mi>
<br/>                </mrow>
<br/>              </msup>
<br/>              <mspace width="negativethinmathspace"></mspace>
<br/>            </mrow>
<br/>            <mo>)</mo>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mo>−<!-- − --></mo>
<br/>            <mn>1</mn>
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mo>/</mo>
<br/>            </mrow>
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>        <mspace width="negativethinmathspace"></mspace>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle r=\\\\left(\\\\left|{\\rac {\\\\cos(\\	heta )}{a}}\\
ight|^{n}\\\\!\\\\!+\\\\left|{\\rac {\\\\sin(\\	heta )}{b}}\\
ight|^{n}\\\\!\\
ight)^{-1/n}\\\\!.}</annotation>
<br/>  </semantics>
<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23abaa22f09fd7e4e3427260598e66abc07c36ab" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -2.671ex; width:32.111ex; height:7.176ex;" alt="{\\\\displaystyle r=\\\\left(\\\\left|{\\rac {\\\\cos(\\	heta )}{a}}\\
ight|^{n}\\\\!\\\\!+\\\\left|{\\rac {\\\\sin(\\	heta )}{b}}\\
ight|^{n}\\\\!\\
ight)^{-1/n}\\\\!.}"></div>
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Superellipse">https://en.wikipedia.org/wiki/Superellipse</a>)"""@en ;
  a skos:Concept ;
  skos:altLabel "superellipse"@en, "superellipse"@fr ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Superellipse>, <https://fr.wikipedia.org/wiki/Courbe_de_Lam%C3%A9> ;
  skos:prefLabel "Lamé curve"@en, "courbe de Lamé"@fr ;
  skos:broader psr:-WFQQ48RG-8 ;
  skos:narrower psr:-LSC1HV6F-0 .

psr:-WFQQ48RG-8
  skos:prefLabel "plane curve"@en, "courbe plane"@fr ;
  a skos:Concept ;
  skos:narrower psr:-B827BGSZ-S .