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WindingPolygon

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WindingPolygon[{p1,p2,…,pn}]

给出一个多边形，表示所有被闭合环线 p1,p2,…,pn,p1 至少环绕一次的点.

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WindingPolygon[{{p11,p12,…},{p21,p22,…},…}]

根据闭合环线 p11,p12,… 和 p21,p22,… 给出一个多边形.

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WindingPolygon[…,"wrule"]

用指定的环绕规则 "wrule" 定义多边形.

更多信息和选项

  • WindingPolygon 亦称为环绕填充规则(winding filling rule).
  • WindingPolygon 通常用于根据自相交闭合曲线定义多边形.
  • 如果点 p 周围的闭合环线的环绕数不为零，则点 p 属于多边形. 环绕数由 WindingCount 给出.
  • 下面给出了每个区域的环绕数：
  • 不同的环绕规则 "wrule" 给出不同的多边形. 可能的环绕规则包括：
  • WindingPolygon[{p1,p2,…}] 等价于 WindingPolygon[{p1,p2,…},"NonzeroRule"].
  • 点 pi 可以有嵌入维度，但必须全部位于一个平面内并具有相同的嵌入维度.
  • WindingPolygon 和 Polygon 的选项相同.

    • 所有选项的列表

范例

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基本范例  (2)常见实例总结

定义一个多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-p3b1a8
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Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-it4riy
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Out[2]=2

根据自相交环线构建多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-ihjkg4
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Out[1]=1

面积：

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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-qdev09
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Out[2]=2

范围  (14)标准用法实例范围调查

基本用法  (5)

定义一个二维多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-6wznbi
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Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-k7h2jz
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Out[2]=2

三维多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-d5b3jx
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Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-zl0rxy
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Out[2]=2

n 维多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-tto0a3
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Out[1]=1

根据自相交环线构建多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-tgsruf
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Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-5pmab3
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Out[2]=2

多个环线：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-z2w99s
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Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-pageqd
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Out[2]=2

Nonzero 规则  (3)

多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-hbo7ye
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-5izmw
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Out[2]=2

三维多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-435l
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-bzv5ji
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Out[2]=2

n 维多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-cymmx9
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Out[1]=1

EvenOdd 规则  (3)

多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-iq6flg
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-u2y9kk
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Out[2]=2

三维多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-emp4sz
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-mj7qx7
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Out[2]=2

n 维多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-53u2au
Direct link to example
Out[1]=1

Two 规则  (3)

多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-9p0fmk
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Copy to clipboard.
In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-up92z
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Out[2]=2

三维多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-h7cau
Direct link to example
Copy to clipboard.
In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-ddzc0m
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Out[2]=2

n 维多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-ikf7sy
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Out[1]=1

选项  (6)各选项的常用值和功能

VertexColors  (2)

顶点被着色的多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-emgyge
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Out[1]=1

指定三维多边形顶点的颜色：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-2k04y9
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Out[1]=1

VertexNormals  (1)

用边向量的叉积计算法向量：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-lx25c
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-bpd9f0
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Out[2]=2

法线方向为 {1,-1,1} 的三角形：

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In[3]:=3
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https://wolfram.com/xid/0b0l38rewmi-cvwg32
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Out[3]=3

使用不同的法线将影响颜色的色度：

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In[4]:=4
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https://wolfram.com/xid/0b0l38rewmi-dxgk6r
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Out[4]=4

VertexTextureCoordinates  (3)

用二维多边形进行纹理映射：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-1jlxp
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Out[1]=1

用三维多边形进行纹理映射：

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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-eg1zja
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Out[2]=2

通过非统一纹理坐标值重复使用纹理：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-drfwj5
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纹理映射指令的作用出现在 VertexColors 之后：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-lazig8
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应用  (3)用该函数可以解决的问题范例

基本应用  (1)

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-f0eecn
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Out[1]=1

几何  (1)

生成正星形多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-32sy0l
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Copy to clipboard.
In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-lbxtsa
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Out[2]=2
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In[3]:=3
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https://wolfram.com/xid/0b0l38rewmi-lvckt4
Direct link to example
Out[3]=3

计算几何  (1)

生成任意多边形：

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In[3]:=3
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https://wolfram.com/xid/0b0l38rewmi-x3b685
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Out[3]=3
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In[4]:=4
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https://wolfram.com/xid/0b0l38rewmi-hz73c1
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Out[4]=4

属性和关系  (2)函数的属性及与其他函数的关联

一般情况下，WindingPolygon 不同于 Polygon：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-hf6fz3
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-c82bc3
Direct link to example
Out[2]=2

CrossingPolygon 是另一个多边形构造函数：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-0h89de
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-14smh2
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Out[2]=2

可能存在的问题  (2)常见隐患和异常行为

WindingPolygon 总是给出 full-dimensional 多边形：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-gs2kxl
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Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0b0l38rewmi-xtcaug
Direct link to example
Out[2]=2

WindingPolygon 中的点必须位于同一平面内：

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In[1]:=1
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https://wolfram.com/xid/0b0l38rewmi-4o4cqe
Direct link to example
Out[1]=1
Wolfram Research (2019)，WindingPolygon，Wolfram 语言函数，https://reference.wolfram.com/language/ref/WindingPolygon.html.
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Wolfram Research (2019)，WindingPolygon，Wolfram 语言函数，https://reference.wolfram.com/language/ref/WindingPolygon.html.

文本

Wolfram Research (2019)，WindingPolygon，Wolfram 语言函数，https://reference.wolfram.com/language/ref/WindingPolygon.html.

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Wolfram Research (2019)，WindingPolygon，Wolfram 语言函数，https://reference.wolfram.com/language/ref/WindingPolygon.html.

CMS

Wolfram 语言. 2019. "WindingPolygon." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/WindingPolygon.html.

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Wolfram 语言. 2019. "WindingPolygon." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/WindingPolygon.html.

APA

Wolfram 语言. (2019). WindingPolygon. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/WindingPolygon.html 年

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Wolfram 语言. (2019). WindingPolygon. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/WindingPolygon.html 年

BibTeX

@misc{reference.wolfram_2025_windingpolygon, author="Wolfram Research", title="{WindingPolygon}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/WindingPolygon.html}", note=[Accessed: 04-April-2025 ]}

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@misc{reference.wolfram_2025_windingpolygon, author="Wolfram Research", title="{WindingPolygon}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/WindingPolygon.html}", note=[Accessed: 04-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_windingpolygon, organization={Wolfram Research}, title={WindingPolygon}, year={2019}, url={https://reference.wolfram.com/language/ref/WindingPolygon.html}, note=[Accessed: 04-April-2025 ]}

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@online{reference.wolfram_2025_windingpolygon, organization={Wolfram Research}, title={WindingPolygon}, year={2019}, url={https://reference.wolfram.com/language/ref/WindingPolygon.html}, note=[Accessed: 04-April-2025 ]}