Limit properties of rational Bézier curves with mixed weights(具有混合权函数的有理Bézier曲线的极限性质)
The weights of a rational Bézier curve play a crucial role in shape modification of the curve. As the weight of a rational Bézier curve approaches infinity, the curve tends towards the corresponding control point. Previous research has shown that when all weights of a rational Bézier curve tend to i...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | zho |
| Published: |
Zhejiang University Press
2025-01-01
|
| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2025.01.012 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841525570168422400 |
|---|---|
| author | 魏琦文(WEI Qiwen) 刘向云(LIU Xiangyun) 吴金明(WU Jinming) 朱春钢(ZHU Chungang) |
| author_facet | 魏琦文(WEI Qiwen) 刘向云(LIU Xiangyun) 吴金明(WU Jinming) 朱春钢(ZHU Chungang) |
| author_sort | 魏琦文(WEI Qiwen) |
| collection | DOAJ |
| description | The weights of a rational Bézier curve play a crucial role in shape modification of the curve. As the weight of a rational Bézier curve approaches infinity, the curve tends towards the corresponding control point. Previous research has shown that when all weights of a rational Bézier curve tend to infinity in the form of power or exponential functions, the curve approaches its regular control curve. In this paper, we propose a new model, combining the transformation relationship between power functions and exponential functions, and then define the regular control curve of a rational Bézier curve with mixed weight functions. Based the toric degeneration theory, we prove that the limit of a rational Bézier curve is exactly its regular control curve when all weights tend to infinity in the form of mixed functions.(权因子是调整有理Bézier曲线形状的重要手段。当单个权因子趋于无穷时，有理Bézier曲线趋向于相应的控制顶点。已有研究表明，当所有权因子都以幂函数或指数函数形式趋于无穷时，有理Bézier曲线的极限曲线为其正则控制曲线。基于此，提出了一个新模型，结合幂权函数与指数权函数的转换关系，定义了具有混合权函数的有理Bézier曲线的正则控制曲线；结合toric退化理论，证明了当所有权因子都以混合函数形式趋于无穷时，有理Bézier曲线的极限曲线恰为其正则控制曲线；最后通过实例验证了结论的正确性。) |
| format | Article |
| id | doaj-art-bc634b1ea089489d9fbdf473e0d7b080 |
| institution | Kabale University |
| issn | 1008-9497 |
| language | zho |
| publishDate | 2025-01-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj-art-bc634b1ea089489d9fbdf473e0d7b0802025-01-17T08:42:35ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972025-01-0152111012110.3785/j.issn.1008-9497.2025.01.012Limit properties of rational Bézier curves with mixed weights(具有混合权函数的有理Bézier曲线的极限性质)魏琦文(WEI Qiwen)0https://orcid.org/0009-0007-5505-8209刘向云(LIU Xiangyun)1吴金明(WU Jinming)2朱春钢(ZHU Chungang)3https://orcid.org/0000-0002-0769-08121School of Mathematical Sciences， Dalian University of Technology， Dalian 116024， Liaoning Province， China(1大连理工大学 数学科学学院,辽宁大连116024)2School of Statistics and Mathematics， Zhejiang Gongshang University， Hangzhou 310018， China(2浙江工商大学 统计与数学学院,浙江杭州310018)2School of Statistics and Mathematics， Zhejiang Gongshang University， Hangzhou 310018， China(2浙江工商大学 统计与数学学院,浙江杭州310018)1School of Mathematical Sciences， Dalian University of Technology， Dalian 116024， Liaoning Province， China(1大连理工大学 数学科学学院,辽宁大连116024)The weights of a rational Bézier curve play a crucial role in shape modification of the curve. As the weight of a rational Bézier curve approaches infinity, the curve tends towards the corresponding control point. Previous research has shown that when all weights of a rational Bézier curve tend to infinity in the form of power or exponential functions, the curve approaches its regular control curve. In this paper, we propose a new model, combining the transformation relationship between power functions and exponential functions, and then define the regular control curve of a rational Bézier curve with mixed weight functions. Based the toric degeneration theory, we prove that the limit of a rational Bézier curve is exactly its regular control curve when all weights tend to infinity in the form of mixed functions.(权因子是调整有理Bézier曲线形状的重要手段。当单个权因子趋于无穷时，有理Bézier曲线趋向于相应的控制顶点。已有研究表明，当所有权因子都以幂函数或指数函数形式趋于无穷时，有理Bézier曲线的极限曲线为其正则控制曲线。基于此，提出了一个新模型，结合幂权函数与指数权函数的转换关系，定义了具有混合权函数的有理Bézier曲线的正则控制曲线；结合toric退化理论，证明了当所有权因子都以混合函数形式趋于无穷时，有理Bézier曲线的极限曲线恰为其正则控制曲线；最后通过实例验证了结论的正确性。)https://doi.org/10.3785/j.issn.1008-9497.2025.01.012rational bézier curve(有理bézier曲线)weights(权因子)mixed weight functions(混合权函数)toric degeneration(toric退化) |
| spellingShingle | 魏琦文(WEI Qiwen) 刘向云(LIU Xiangyun) 吴金明(WU Jinming) 朱春钢(ZHU Chungang) Limit properties of rational Bézier curves with mixed weights(具有混合权函数的有理Bézier曲线的极限性质) Zhejiang Daxue xuebao. Lixue ban rational bézier curve(有理bézier曲线) weights(权因子) mixed weight functions(混合权函数) toric degeneration(toric退化) |
| title | Limit properties of rational Bézier curves with mixed weights(具有混合权函数的有理Bézier曲线的极限性质) |
| title_full | Limit properties of rational Bézier curves with mixed weights(具有混合权函数的有理Bézier曲线的极限性质) |
| title_fullStr | Limit properties of rational Bézier curves with mixed weights(具有混合权函数的有理Bézier曲线的极限性质) |
| title_full_unstemmed | Limit properties of rational Bézier curves with mixed weights(具有混合权函数的有理Bézier曲线的极限性质) |
| title_short | Limit properties of rational Bézier curves with mixed weights(具有混合权函数的有理Bézier曲线的极限性质) |
| title_sort | limit properties of rational bezier curves with mixed weights 具有混合权函数的有理bezier曲线的极限性质 |
| topic | rational bézier curve(有理bézier曲线) weights(权因子) mixed weight functions(混合权函数) toric degeneration(toric退化) |
| url | https://doi.org/10.3785/j.issn.1008-9497.2025.01.012 |
| work_keys_str_mv | AT wèiqíwénweiqiwen limitpropertiesofrationalbeziercurveswithmixedweightsjùyǒuhùnhéquánhánshùdeyǒulǐbezierqūxiàndejíxiànxìngzhì AT liúxiàngyúnliuxiangyun limitpropertiesofrationalbeziercurveswithmixedweightsjùyǒuhùnhéquánhánshùdeyǒulǐbezierqūxiàndejíxiànxìngzhì AT wújīnmíngwujinming limitpropertiesofrationalbeziercurveswithmixedweightsjùyǒuhùnhéquánhánshùdeyǒulǐbezierqūxiàndejíxiànxìngzhì AT zhūchūngāngzhuchungang limitpropertiesofrationalbeziercurveswithmixedweightsjùyǒuhùnhéquánhánshùdeyǒulǐbezierqūxiàndejíxiànxìngzhì |