![我们可以画 Spikey 吗?](https://linux22.com/image/404808/%E6%88%91%E4%BB%AC%E5%8F%AF%E4%BB%A5%E7%94%BB%20Spikey%20%E5%90%97%EF%BC%9F.png)
“Spikey” 是 Wolfram Research 的标志,该公司是 Mathematica 和 Wolfram 语言的创造者。
我认为这将是一个有趣的实验,用 Tex 绘制各种版本的“Spikey”。
答案1
这只是为了好玩。确实可以画出一些朝那个方向的东西。如果你想运行这个,请tikz-3dtools
从下载库这里,并将其放在 TeX 可以找到的地方。
\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3dtools}
\begin{document}
\tikzset{closed polygon/.style={insert path={foreach \Coord [count=\nCoord] in {#1}
{\ifnum\nCoord=1
\Coord
\else
-- \Coord
\fi} -- cycle}},polygon/.style={insert path={foreach \Coord [count=\nCoord] in {#1}
{\ifnum\nCoord=1
\Coord
\else
-- \Coord
\fi}}}}
\makeatletter
% main code
\foreach \X in {5,15,...,355}
{\tdplotsetmaincoords{90+30*sin(\X)}{\X}
\begin{tikzpicture}[tdplot_main_coords,font=\sffamily,fill opacity=1,line
join=round,scale=pi]
\path[tdplot_screen_coords,use as bounding box] (-2,-2) rectangle (2,2);
% define the vertices (there are certainly superior naming conventions)
\path (0., 0., 1.63925) coordinate (p1)
(0.262866, -0.809017, 1.11352) coordinate (p2)
(0.262866, 0.809017, 1.11352) coordinate (p3)
(0.850651, 0., 1.11352) coordinate (p4)
(0., 0., -1.63925) coordinate (p5)
(-0.262866, -0.809017, -1.11352) coordinate (p6)
(-0.262866, 0.809017, -1.11352) coordinate (p7)
(0.688191, -0.5, -1.11352) coordinate (p8)
(0.688191, 0.5, -1.11352) coordinate (p9)
(-0.850651, 0., -1.11352) coordinate (p10)
(-0.688191, -0.5, 1.11352) coordinate (p11)
(-0.688191, 0.5, 1.11352) coordinate (p12)
(-1.37638, 0., -0.262866) coordinate (p13)
(1.11352, -0.809017, -0.262866) coordinate (p14)
(1.11352, 0.809017, -0.262866) coordinate (p15)
(-0.425325, -1.30902, -0.262866) coordinate (p16)
(-0.425325, 1.30902, -0.262866) coordinate (p17)
(1.37638, 0., 0.262866) coordinate (p18)
(0.425325, -1.30902, 0.262866) coordinate (p19)
(0.425325, 1.30902, 0.262866) coordinate (p20)
(-1.11352, -0.809017, 0.262866) coordinate (p21)
(-1.11352, 0.809017, 0.262866) coordinate (p22)
(1.18617, -0.861803, 0.733094) coordinate (p23)
(1.18617, 0.861803, 0.733094) coordinate (p24)
(-1.46619, 0., 0.733094) coordinate (p25)
(-0.453077, -1.39443, 0.733094) coordinate (p26)
(-0.453077, 1.39443, 0.733094) coordinate (p27)
(1.46619, 0., -0.733094) coordinate (p28)
(-1.18617, -0.861803, -0.733094) coordinate (p29)
(-1.18617, 0.861803, -0.733094) coordinate (p30)
(0.453077, -1.39443, -0.733094) coordinate (p31)
(0.453077, 1.39443, -0.733094) coordinate (p32);
% define the plane data as a list of <drawing options>/<shape>/<vertices>
\def\PlaneData{%
{draw,fill=randomcolor}/closed polygon/{(p1),(p26),(p2)},%
{draw,fill=randomcolor}/closed polygon/{(p5),(p31),(p6)},%
{draw,fill=randomcolor}/closed polygon/{(p3),(p27),(p1)},%
{draw,fill=randomcolor}/closed polygon/{(p7),(p32),(p5)},%
{draw,fill=randomcolor}/closed polygon/{(p19),(p26),(p31)},%
{draw,fill=randomcolor}/closed polygon/{(p32),(p27),(p20)},%
{draw,fill=randomcolor}/closed polygon/{(p26),(p23),(p2)},%
{draw,fill=randomcolor}/closed polygon/{(p3),(p24),(p27)},%
{draw,fill=randomcolor}/closed polygon/{(p30),(p29),(p13)},%
{draw,fill=randomcolor}/closed polygon/{(p29),(p26),(p21)},%
{draw,fill=randomcolor}/closed polygon/{(p22),(p27),(p30)},%
{draw,fill=randomcolor}/closed polygon/{(p16),(p26),(p29)},%
{draw,fill=randomcolor}/closed polygon/{(p30),(p27),(p17)},%
{draw,fill=randomcolor}/closed polygon/{(p31),(p29),(p6)},%
{draw,fill=randomcolor}/closed polygon/{(p7),(p30),(p32)},%
{draw,fill=randomcolor}/closed polygon/{(p31),(p23),(p19)},%
{draw,fill=randomcolor}/closed polygon/{(p20),(p24),(p32)},%
{draw,fill=randomcolor}/closed polygon/{(p18),(p24),(p23)},%
{draw,fill=randomcolor}/closed polygon/{(p8),(p28),(p31)},%
{draw,fill=randomcolor}/closed polygon/{(p9),(p32),(p28)},%
{draw,fill=randomcolor}/closed polygon/{(p14),(p23),(p31)},%
{draw,fill=randomcolor}/closed polygon/{(p32),(p24),(p15)},%
{draw,fill=randomcolor}/closed polygon/{(p23),(p24),(p4)},%
{draw,fill=randomcolor}/closed polygon/{(p31),(p28),(p14)},%
{draw,fill=randomcolor}/closed polygon/{(p28),(p32),(p15)},%
{draw,fill=randomcolor}/closed polygon/{(p21),(p25),(p29)},%
{draw,fill=randomcolor}/closed polygon/{(p30),(p25),(p22)},%
{draw,fill=randomcolor}/closed polygon/{(p28),(p23),(p14)},%
{draw,fill=randomcolor}/closed polygon/{(p15),(p24),(p28)},%
{draw,fill=randomcolor}/closed polygon/{(p18),(p23),(p28)},%
{draw,fill=randomcolor}/closed polygon/{(p28),(p24),(p18)},%
{draw,fill=randomcolor}/closed polygon/{(p29),(p25),(p13)},%
{draw,fill=randomcolor}/closed polygon/{(p13),(p25),(p30)},%
{draw,fill=randomcolor}/closed polygon/{(p2),(p23),(p1)},%
{draw,fill=randomcolor}/closed polygon/{(p8),(p31),(p5)},%
{draw,fill=randomcolor}/closed polygon/{(p1),(p24),(p3)},%
{draw,fill=randomcolor}/closed polygon/{(p5),(p32),(p9)},%
{draw,fill=randomcolor}/closed polygon/{(p19),(p23),(p26)},%
{draw,fill=randomcolor}/closed polygon/{(p27),(p24),(p20)},%
{draw,fill=randomcolor}/closed polygon/{(p11),(p26),(p1)},%
{draw,fill=randomcolor}/closed polygon/{(p6),(p29),(p5)},%
{draw,fill=randomcolor}/closed polygon/{(p1),(p27),(p12)},%
{draw,fill=randomcolor}/closed polygon/{(p5),(p30),(p7)},%
{draw,fill=randomcolor}/closed polygon/{(p1),(p25),(p11)},%
{draw,fill=randomcolor}/closed polygon/{(p5),(p29),(p10)},%
{draw,fill=randomcolor}/closed polygon/{(p12),(p25),(p1)},%
{draw,fill=randomcolor}/closed polygon/{(p10),(p30),(p5)},%
{draw,fill=randomcolor}/closed polygon/{(p1),(p23),(p4)},%
{draw,fill=randomcolor}/closed polygon/{(p5),(p28),(p8)},%
{draw,fill=randomcolor}/closed polygon/{(p4),(p24),(p1)},%
{draw,fill=randomcolor}/closed polygon/{(p9),(p28),(p5)},%
{draw,fill=randomcolor}/closed polygon/{(p10),(p29),(p30)},%
{draw,fill=randomcolor}/closed polygon/{(p21),(p26),(p25)},%
{draw,fill=randomcolor}/closed polygon/{(p22),(p25),(p27)},%
{draw,fill=randomcolor}/closed polygon/{(p16),(p29),(p31)},%
{draw,fill=randomcolor}/closed polygon/{(p32),(p30),(p17)},%
{draw,fill=randomcolor}/closed polygon/{(p25),(p26),(p11)},%
{draw,fill=randomcolor}/closed polygon/{(p27),(p25),(p12)},%
{draw,fill=randomcolor}/closed polygon/{(p31),(p26),(p16)},%
{draw,fill=randomcolor}/closed polygon/{(p17),(p27),(p32)}}
% normal of screen (last row of the rotation matrix)
\path[overlay] ({sin(\tdplotmaintheta)*sin(\tdplotmainphi)},
{-1*sin(\tdplotmaintheta)*cos(\tdplotmainphi)},
{cos(\tdplotmaintheta)}) coordinate (n);
% build up the list of projections
\foreach \Style/\Poly/\CoordLst [count=\nC] in \PlaneData
{%
\pgfmathsetmacro{\mybarycenter}{barycenter("\CoordLst")}
\pgfmathsetmacro{\currproj}{TD("(n)o(\mybarycenter)")}
\foreach \Coord [count=\nP] in \CoordLst
{\expandafter\xdef\csname td@vertex@\romannumeral\nP\endcsname{\Coord}}
\pgfmathsetmacro{\mynormal}{TD("\td@vertex@i-\td@vertex@ii x\td@vertex@iii-\td@vertex@ii")}
\pgfmathtruncatemacro{\mysign}{ifthenelse(TD("(\mynormal)o(0,0,1)")<0,-1,1)}
\pgfmathtruncatemacro{\mylightproj}{60+\mysign*40*TD("(\mynormal)o(0.3,0.1,1)")}
%\pgfmathtruncatemacro{\mylightproj}{20+\nC}
\expandafter\xdef\csname tikz@td@saturation\romannumeral\nC\endcsname{\mylightproj}
\ifnum\nC=1
\xdef\LstProj{\currproj}
\else
\xdef\LstProj{\LstProj,\currproj}
\fi
\expandafter\gdef\csname tikz@td@layer\romannumeral\nC\endcsname{}%
\expandafter\xdef\csname tikz@td@poly\romannumeral\nC\endcsname{%
\noexpand\path[\Style,\Poly={\CoordLst}];}
\xdef\tikz@td@planes{\nC}%
}
\foreach \X [count=\nC] in \LstProj
{\pgfmathtruncatemacro{\mypos}{pos(\X,"\LstProj")}
\expandafter\edef\expandafter\tempa{\csname tikz@td@layer\romannumeral\mypos\endcsname}%
\edef\tempb{}%
\ifx\tempb\tempa\relax
\expandafter\xdef\csname tikz@td@layer\romannumeral\mypos\endcsname{\nC}%
\else
\expandafter\xdef\csname tikz@td@layer\romannumeral\mypos\endcsname{\tempa,\nC}%
\fi
}
\foreach \X in {1,...,\tikz@td@planes}
{\expandafter\edef\expandafter\tempa{\csname tikz@td@layer\romannumeral\X\endcsname}%
\edef\tempb{}%
\ifx\tempb\tempa\relax
\else
\foreach \Y in \tempa
{
\edef\mysaturation{\csname tikz@td@saturation\romannumeral\Y\endcsname}
\colorlet{randomcolor}{red!\mysaturation}
\csname tikz@td@poly\romannumeral\Y\endcsname
}
\fi}
\end{tikzpicture}}
\makeatother
\end{document}
它远不如 Mathematica 的版本那么花哨。绝对如此。这只是我的一个练习,看看一些 3d 排序例程的效果如何。到目前为止,我认为效果不错。