Control point based exact description of trigonometric/hyperbolic curves, surfaces and volumes
Using the normalized B-bases of vector spaces of trigonometric and hyperbolic polynomials of finite order, we specify control point configurations for the exact description of the zeroth and higher order (mixed partial) derivatives of integral curves and (hybrid) multivariate surfaces determined by...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2015-12, Vol.290, p.74-91 |
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| container_title | Journal of computational and applied mathematics |
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| creator | Roth, Agoston |
| description | Using the normalized B-bases of vector spaces of trigonometric and hyperbolic polynomials of finite order, we specify control point configurations for the exact description of the zeroth and higher order (mixed partial) derivatives of integral curves and (hybrid) multivariate surfaces determined by coordinate functions that are exclusively given either by traditional trigonometric or hyperbolic polynomials in each of their variables. Based on homogeneous coordinates and central projection, we also propose algorithms for the control point and weight based exact description of the zeroth order (partial) derivative of the rational counterpart of these integral curves and surfaces. The core of the proposed modeling methods relies on basis transformation matrices with entries that can be efficiently obtained by order elevation. |
| doi_str_mv | 10.1016/j.cam.2015.05.003 |
| format | Article |
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Based on homogeneous coordinates and central projection, we also propose algorithms for the control point and weight based exact description of the zeroth order (partial) derivative of the rational counterpart of these integral curves and surfaces. 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Based on homogeneous coordinates and central projection, we also propose algorithms for the control point and weight based exact description of the zeroth order (partial) derivative of the rational counterpart of these integral curves and surfaces. The core of the proposed modeling methods relies on basis transformation matrices with entries that can be efficiently obtained by order elevation.</description><subject>Basis transformation</subject><subject>Control surfaces</subject><subject>Curves and multivariate surfaces</subject><subject>Derivatives</subject><subject>Elevation</subject><subject>Integrals</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Normalized B-basis functions</subject><subject>Order elevation</subject><subject>Polynomials</subject><subject>Subdivision</subject><subject>Transformations</subject><subject>Trigonometric and hyperbolic polynomials</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LxDAQxYMouK5-AG85erDdpE2bFk-y-A8WvOjVkCYTzdI2NUkX99ubZT0LD97AvDcwP4SuKckpofVqmys55AWhVU6SSHmCFrThbUY5b07RgpScZ4QV_BxdhLAlhNQtZQv0sXZj9K7Hk7NjxJ0MoDH8SBWxhqC8naJ1I3YGR28_3egGSINafe0n8J3rrcJq9jsItzjM3kgFActR453r5wHCJTozsg9w9edL9P748LZ-zjavTy_r-02mSl7GDFquNet43bSm0R2voKZpYRSTysiiltpUnCUjrKwrJVlFiK54WwMriqaCcolujncn775nCFEMNijoezmCm4M4UEg_t1WZovQYVd6F4MGIydtB-r2gRBxYiq1ILMWBpSBJ5NC5O3Yg_bCz4EVQFkYF2npQUWhn_2n_As2nfgc</recordid><startdate>20151215</startdate><enddate>20151215</enddate><creator>Roth, Agoston</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20151215</creationdate><title>Control point based exact description of trigonometric/hyperbolic curves, surfaces and volumes</title><author>Roth, Agoston</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c373t-e97dd4b7689f8db75e61373fc4acfa26adf5746ad04365ca4500d5796e42285e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Basis transformation</topic><topic>Control surfaces</topic><topic>Curves and multivariate surfaces</topic><topic>Derivatives</topic><topic>Elevation</topic><topic>Integrals</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Normalized B-basis functions</topic><topic>Order elevation</topic><topic>Polynomials</topic><topic>Subdivision</topic><topic>Transformations</topic><topic>Trigonometric and hyperbolic polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Roth, Agoston</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Roth, Agoston</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Control point based exact description of trigonometric/hyperbolic curves, surfaces and volumes</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2015-12-15</date><risdate>2015</risdate><volume>290</volume><spage>74</spage><epage>91</epage><pages>74-91</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><abstract>Using the normalized B-bases of vector spaces of trigonometric and hyperbolic polynomials of finite order, we specify control point configurations for the exact description of the zeroth and higher order (mixed partial) derivatives of integral curves and (hybrid) multivariate surfaces determined by coordinate functions that are exclusively given either by traditional trigonometric or hyperbolic polynomials in each of their variables. Based on homogeneous coordinates and central projection, we also propose algorithms for the control point and weight based exact description of the zeroth order (partial) derivative of the rational counterpart of these integral curves and surfaces. The core of the proposed modeling methods relies on basis transformation matrices with entries that can be efficiently obtained by order elevation.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2015.05.003</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0377-0427 |
| ispartof | Journal of computational and applied mathematics, 2015-12, Vol.290, p.74-91 |
| issn | 0377-0427 1879-1778 |
| language | eng |
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| source | Elsevier ScienceDirect Journals Complete; EZB-FREE-00999 freely available EZB journals |
| subjects | Basis transformation Control surfaces Curves and multivariate surfaces Derivatives Elevation Integrals Mathematical analysis Mathematical models Normalized B-basis functions Order elevation Polynomials Subdivision Transformations Trigonometric and hyperbolic polynomials |
| title | Control point based exact description of trigonometric/hyperbolic curves, surfaces and volumes |
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