- 作者：Julien Colvin1 ; jcolvin@towson.edu" class="auth_mail" title="E-mail the corresponding author ; Devan DiMatteo1 ; ddimat2@students.towson.edu" class="auth_mail" title="E-mail the corresponding author ; Tatyana Sorokina ; 2 ; tsorokina@towson.edu" class="auth_mail" title="E-mail the corresponding author
- 关键词：Bipyramid ; Dimension ; Trivariate spline ; Cell ; Supersmoothness
- 刊名：Computer Aided Geometric Design
- 出版年：2016
- 出版时间：July 2016
- 年：2016
- 卷：45
- 期：Complete
- 页码：140-150
- 全文大小：360 K
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We introduce bipyramid cells in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167839615001405&_mathId=si3.gif&_user=111111111&_pii=S0167839615001405&_rdoc=1&_issn=01678396&md5=0fe28f43023c71f63ab35d5165232056" title="Click to view the MathML source">R3class="mathContainer hidden">class="mathCode">.
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We improve the lower bound on the dimension of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167839615001405&_mathId=si1.gif&_user=111111111&_pii=S0167839615001405&_rdoc=1&_issn=01678396&md5=c7817664a1a75f1f1ffd572361fea7f9" title="Click to view the MathML source">C1class="mathContainer hidden">class="mathCode"> splines for bipyramids.
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We derive a new upper bound that is equal to the known lower bound in most cases.
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We use tools from algebraic geometry and Bernstein–Bézier analysis.