blocks|key|3560096|text|Marcelo|type|unstyled|depth|inlineStyleRanges|offset|length|style|BOLD|entityRanges|data|3560097|最常用的测地线镶嵌可以是Class-I或Class-II。您引用的图像是III类细分，更具体地说，是4v{3,1}。这些类可以用图表表示，因此：|3560098|​|3560099|📷|atomic|3560100|3560101|III类细分是手性的，可以有左手扭曲或右手扭曲。以下是您引用的样本的镜像：|3560102|3560103|3560104|3560105|你可以在谷歌的3D仓库中找到一些三级球体的3D模型：http://sketchup.google.com/3dwarehouse/cldetails?mid=b926c2713e303860a99d92cd8fe533cd|3560106|被正确地识别应该会让你有一个好的开始。|3560107|欢迎访问测地线帮助组；http://groups.google.com/group/GeodesicHelp?hl=en|3560108|TaffGoch|3560109|entityMap|0|IMAGE|mutability|IMMUTABLE|imageUrl|https://ask.qcloudimg.com/http-save/yehe-900000/47e105fa03d76a4980ebca84c88404de.png|imageAlt|1|https://i.stack.imgur.com/6SwvP.png|2|LINK|MUTABLE|url|http://sketchup.google.com/3dwarehouse/cldetails?mid=b926c2713e303860a99d92cd8fe533cd|3|http://groups.google.com/group/GeodesicHelp?hl=en^0|0|7|0|0|0|0|1|0|0|0|0|0|0|1|1|0|0|Q|2D|2|0|0|B|1D|3|0|0|8|0^^$0|@$1|2|3|4|5|6|7|1I|8|@$9|1J|A|1K|B|C]]|D|@]|E|$]]|$1|F|3|G|5|6|7|1L|8|@]|D|@]|E|$]]|$1|H|3|I|5|6|7|1M|8|@]|D|@]|E|$]]|$1|J|3|K|5|L|7|1N|8|@]|D|@$9|1O|A|1P|1|1Q]]|E|$]]|$1|M|3|I|5|6|7|1R|8|@]|D|@]|E|$]]|$1|N|3|O|5|6|7|1S|8|@]|D|@]|E|$]]|$1|P|3|I|5|6|7|1T|8|@]|D|@]|E|$]]|$1|Q|3|K|5|L|7|1U|8|@]|D|@$9|1V|A|1W|1|1X]]|E|$]]|$1|R|3|I|5|6|7|1Y|8|@]|D|@]|E|$]]|$1|S|3|T|5|6|7|1Z|8|@]|D|@$9|20|A|21|1|22]]|E|$]]|$1|U|3|V|5|6|7|23|8|@]|D|@]|E|$]]|$1|W|3|X|5|6|7|24|8|@]|D|@$9|25|A|26|1|27]]|E|$]]|$1|Y|3|Z|5|6|7|28|8|@$9|29|A|2A|B|C]]|D|@]|E|$]]|$1|10|3|-4|5|6|7|2B|8|@]|D|@]|E|$]]]|11|$12|$5|13|14|15|E|$16|17|18|-4]]|19|$5|13|14|15|E|$16|1A|18|-4]]|1B|$5|1C|14|1D|E|$1E|1F]]|1G|$5|1C|14|1D|E|$1E|1H]]]]

Marcelo,

The most-commonly employed geodesic tessellations are either Class-I or Class-II. The image you reference is of a Class-III tessellation, more-specifically, 4v{3,1}. The classes can be diagrammed, so:

<img src="https://i.stack.imgur.com/4qi1M.png" alt="Geodesic Division">

Class-III tessellations are chiral, and can have left-handed or right-handed twist. Here's the mirror-image of the sample you referenced:

<img src="https://i.stack.imgur.com/6SwvP.png" alt="Class III, 4v{1,3}">

You can find some 3D models of Class-III spheres, at Google's 3D Warehouse:
<a href="http://sketchup.google.com/3dwarehouse/cldetails?mid=b926c2713e303860a99d92cd8fe533cd" rel="nofollow noreferrer">http://sketchup.google.com/3dwarehouse/cldetails?mid=b926c2713e303860a99d92cd8fe533cd</a>

Being properly identified should get you off to a good start.

Feel free to stop by the Geodesic Help Group; <a href="http://groups.google.com/group/GeodesicHelp?hl=en" rel="nofollow noreferrer">http://groups.google.com/group/GeodesicHelp?hl=en</a>

TaffGoch

blocks|key|595018|text|这是一张来自乔·克林顿的NASA出版物的图片：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|595019|​|595020|📷|atomic|offset|length|595021|entityMap|0|IMAGE|mutability|IMMUTABLE|imageUrl|https://ask.qcloudimg.com/http-save/yehe-900000/fc57f7f8fab1ba982575841813aff405.png|imageAlt^0|0|0|0|1|0|0^^$0|@$1|2|3|4|5|6|7|R|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|S|8|@]|9|@]|A|$]]|$1|D|3|E|5|F|7|T|8|@]|9|@$G|U|H|V|1|W]]|A|$]]|$1|I|3|-4|5|6|7|X|8|@]|9|@]|A|$]]]|J|$K|$5|L|M|N|A|$O|P|Q|-4]]]]

Here's an image from one of Joe Clinton's NASA publications:

<a href="https://i.stack.imgur.com/okeFb.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/okeFb.png" alt="Geodesic Tessellation Classes"></a>

blocks|key|3559951|text|我相信这其实只是一个解决的问题(即细分的数量)。您显示的镶嵌看起来确实来自于一个二十面体方案:+cf+p.7+here，页面中间的示例。查看文档的其余部分，了解一些计算细节--还有它引用的参考资料，以及一些更多的代码示例here。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|3559952|entityMap|0|LINK|mutability|MUTABLE|url|http://www.fho-emden.de/~hoffmann/ikos27042002.pdf|1|http://www.geometrictools.com/Documentation/TessellateSphere.pdf^0|1J|4|0|32|4|1|0^^$0|@$1|2|3|4|5|6|7|N|8|@]|9|@$A|O|B|P|1|Q]|$A|R|B|S|1|T]]|C|$]]|$1|D|3|-4|5|6|7|U|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]|L|$5|G|H|I|C|$J|M]]]]

I believe it is actually just a matter of resolution (i.e., number of sub-divisions). The tessellation you show does seem to emanate from an icosahedron scheme: cf p.7 <a href="http://www.fho-emden.de/~hoffmann/ikos27042002.pdf" rel="nofollow noreferrer">here</a>, mid-page example. Check out the rest of the document for some calculation details - also its cited references, and some further code samples <a href="http://www.geometrictools.com/Documentation/TessellateSphere.pdf" rel="nofollow noreferrer">here</a>.

blocks|key|2152865|text|，Marcelo|type|unstyled|depth|inlineStyleRanges|offset|length|style|BOLD|entityRanges|data|2152866|如果你想设计算法来生成任何一类测地球体，你可以在这里完成：|2152867|http://thomson.phy.syr.edu/thomsonapplet.htm|2152868|首先使用"custom(m，n)“选项，选择所需的参数，然后点击"pause”按钮。切换到“晶格能量”并点击“自动”按钮。|2152869|2152870|如果你非常熟悉java，你可以为这个app保存"jar“文件，并检查它的内容，以便对算法进行反向工程。|2152871|2152872|顺便说一句，这个java应用程序还有一个“文件”菜单选项，它可以激活一个新窗口，列出“点集”(顶点坐标。)我将它们复制并粘贴到Excel电子表格中，从中我可以生成一个"csv“文件，随后可以将该文件导入到3D图形程序中。|2152873|Taff|2152874|entityMap|0|LINK|mutability|MUTABLE|url^0|1|7|0|0|T|0|0|18|0|18|0|0|0|1P|0|0|0|1F|0|0|0|32|0|0|4|0^^$0|@$1|2|3|4|5|6|7|10|8|@$9|11|A|12|B|C]]|D|@]|E|$]]|$1|F|3|G|5|6|7|13|8|@$9|14|A|15|B|C]]|D|@]|E|$]]|$1|H|3|I|5|6|7|16|8|@$9|17|A|18|B|C]]|D|@$9|19|A|1A|1|1B]]|E|$]]|$1|J|3|K|5|6|7|1C|8|@$9|1D|A|1E|B|C]]|D|@]|E|$]]|$1|L|3|-4|5|6|7|1F|8|@]|D|@]|E|$]]|$1|M|3|N|5|6|7|1G|8|@$9|1H|A|1I|B|C]]|D|@]|E|$]]|$1|O|3|-4|5|6|7|1J|8|@]|D|@]|E|$]]|$1|P|3|Q|5|6|7|1K|8|@$9|1L|A|1M|B|C]]|D|@]|E|$]]|$1|R|3|S|5|6|7|1N|8|@$9|1O|A|1P|B|C]]|D|@]|E|$]]|$1|T|3|-4|5|6|7|1Q|8|@]|D|@]|E|$]]]|U|$V|$5|W|X|Y|E|$Z|I]]]]

Marcelo,

If you want to devise algorithms to generate any class of geodesic spheres, you can do it here:

<a href="http://thomson.phy.syr.edu/thomsonapplet.htm" rel="nofollow noreferrer">http://thomson.phy.syr.edu/thomsonapplet.htm</a>

Start by using the "custom(m,n)" option, select your desired parameters, then hit the "pause" button. Switch to "lattice energy" and hit the "Auto" button.

<hr>

If you're intimately familiar with java, you can save the "jar" file(s) for this app, and examine the contents, to back-engineer the algorithms.

<hr>

BTW, this java app also has a "File" menu option, which can activate a new window, listing the "Point set" (vertex coordinates.) I copy &amp; paste them into an Excel spreadsheet, from which I can generate a "csv" file that can be, subsequently, imported into 3D-graphic programs.

Taff

I'm trying to create a very specific geodesic tessellation, but I can't find anything online about it.

It is normal to subdivide the triangles of an icosahedron into triangle patches and project them onto the sphere. However, I noticed an <a href="http://en.wikipedia.org/wiki/Geodesic_dome#Chord_factors" rel="nofollow noreferrer">animated GIF</a> on the Wikipedia entry for Geodesic Domes that appears not to follow this scheme. Geodesic spheres generally comprise a mixture of mostly hexagonal triangle patches, with pentagonal patches forming at the vertices of the original icosahedron; in most cases, these pentagons are linked together; that is, following a straight edge from the center of one pentagon leads to the center of another pentagon. In the Wikipedia animation, however, the edge from the center of one pentagon doesn't appear to intersect the center of an adjacent pentagons; instead it intersects the side of the other pentagon.

Where can I go to learn about the math behind this particular geometry? Ideally, I'd like to know of an algorithm for generating such tessellations.

Math for a geodesic sphere

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

文章

问答

视频

学习中心

腾讯云实验室

直播

竞赛

腾讯云代码分析专区

腾讯iOA零信任安全管理系统专区

腾讯云架构师技术同盟交流圈

腾讯云数据库专区

腾讯云顾问专区

腾讯云原生专区

腾讯混元专区

腾讯云TCE专区

腾讯云Lighthouse专区

腾讯云HAI专区

腾讯云Edgeone专区

腾讯云存储专区

腾讯云智能专区

腾讯轻联专区 

腾讯云开发专区

TAPD专区

腾讯轻量云游戏服专区

腾讯云最具价值专家

腾讯云架构师技术同盟

腾讯云创作之星

腾讯云开发者先锋

腾讯云代码助手

云原生构建

TAPD 敏捷项目管理

Cloud Studio

SDK中心

API中心

命令行工具

涵盖代码开发、场景应用、自动测试全流程，助你从零构建专属AI助手

一站式MCP教程库，解锁AI应用新玩法

我正在尝试创建一个非常具体的测地线镶嵌，但我在网上找不到任何关于它的东西。将二十面体的三角形细分为三角形面片并将其投影到球体上是正常的。然而，我注意到维基百科上关于测地圆顶的似乎不遵循这种方案。测地球体通常包含大多数六边形三角形面片的混合，其中五边形面片在原始二十面体的顶点形成；在大多数情况下，这些五边形连接在一起；也就是说，从一个五边形的中心沿着一条直边通向另一个五边形的中心。然而，在维基百科的

问测地球体的数学
EN

回答 4

Stack Overflow用户

Stack Overflow用户

Stack Overflow用户

社区

活动

圈层

关于

腾讯云开发者

热门产品

热门推荐

更多推荐

问测地球体的数学EN

回答 4

Stack Overflow用户

Stack Overflow用户

Stack Overflow用户

社区

活动

圈层

关于

腾讯云开发者

热门产品

热门推荐

更多推荐

问测地球体的数学
EN