Limit curve of H-Bézier curves and rational Bézier curves in standard form with the same weight
The basis of H-Bézier curves of degree n is 1 , t , … , t n − 2 , sinh α t and cosh α t , for t ∈ [ 0 , 1 ] . We find the limit curve of H-Bézier curves of degree n as a parameter α goes to ∞ , which is the Bézier curve of degree n − 2 , and prove it using mathematical induction and special properti...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Lee, Ryeong [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Umfang: |
9 |
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| Übergeordnetes Werk: |
Enthalten in: Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics - Hu, Xing ELSEVIER, 2015transfer abstract, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:281 ; year:2015 ; pages:1-9 ; extent:9 |
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10.1016/j.cam.2014.12.007 |
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The basis of H-Bézier curves of degree n is 1 , t , … , t n − 2 , sinh α t and cosh α t , for t ∈ [ 0 , 1 ] . We find the limit curve of H-Bézier curves of degree n as a parameter α goes to ∞ , which is the Bézier curve of degree n − 2 , and prove it using mathematical induction and special properties of H-basis functions. We also compare it to the limit curve of rational Bézier curves of degree n in standard form with the same weight w as it goes to ∞ , which is the rational Bézier curve of degree n − 2 . |
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The basis of H-Bézier curves of degree n is 1 , t , … , t n − 2 , sinh α t and cosh α t , for t ∈ [ 0 , 1 ] . We find the limit curve of H-Bézier curves of degree n as a parameter α goes to ∞ , which is the Bézier curve of degree n − 2 , and prove it using mathematical induction and special properties of H-basis functions. We also compare it to the limit curve of rational Bézier curves of degree n in standard form with the same weight w as it goes to ∞ , which is the rational Bézier curve of degree n − 2 . |
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The basis of H-Bézier curves of degree n is 1 , t , … , t n − 2 , sinh α t and cosh α t , for t ∈ [ 0 , 1 ] . We find the limit curve of H-Bézier curves of degree n as a parameter α goes to ∞ , which is the Bézier curve of degree n − 2 , and prove it using mathematical induction and special properties of H-basis functions. We also compare it to the limit curve of rational Bézier curves of degree n in standard form with the same weight w as it goes to ∞ , which is the rational Bézier curve of degree n − 2 . |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV034588353</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230624014220.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">180603s2015 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.cam.2014.12.007</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">GBVA2015012000018.pica</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV034588353</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0377-0427(14)00549-4</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">670</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">540</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">630</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lee, Ryeong</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Limit curve of H-Bézier curves and rational Bézier curves in standard form with the same weight</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">9</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The basis of H-Bézier curves of degree n is 1 , t , … , t n − 2 , sinh α t and cosh α t , for t ∈ [ 0 , 1 ] . 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