To pag. 81 of the asymptote tutorial there are spherical arrows tips:
I like the tips of the first image and of the 2nd image arrow=Arrow3() that it can be used also in 2D. Do this tips exists only in asymptote or also in TikZ, pstricks, or into a specific symbols or packages?
This is just for fun. Some considerations concerning the projection of a 3d cone on the screen. The main purpose is to explain why I think that the extremal rays from the tip are in general on tangents to the ellipse that emerges from projecting the base circle on the screen. The projection of the cone is a triangle. One can compute the intersection of the cone with the base analytically to obtain
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{shadings}
\tikzset{pics/3d cone/.style={code={
\tikzset{3d cone/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/3d cone/##1}}%
% \itest determines whether the projection of the tip of the cone is inside
% the projection of the base circle, in which case \itest=1
\pgfmathtruncatemacro{\itest}{-1*sign(\pv{h}*abs(cos(\pv{theta}))-\pv{r}*abs(sin(\pv{theta})))}
% \ttest checks whether we look at the cone from the bottom or top,
% in the latter case \ttest=1
\pgfmathtruncatemacro{\ttest}{sign(sin(\pv{theta}))}%
% alpha crit
\pgfmathsetmacro{\alphacrit}{90-atan2((2*\pv{h}*\pv{r}*sin(\pv{theta})*cos(\pv{theta}))/(pow(\pv{h}*cos(\pv{theta}),2) + pow(\pv{r}*sin(\pv{theta}),2)),
(pow(\pv{h}*cos(\pv{theta}),2) - pow(\pv{r}*sin(\pv{theta}),2))/(pow(\pv{h}*cos(\pv{theta}),2) +
pow(\pv{r}*sin(\pv{theta}),2))}%
\begin{scope}[rotate=\pv{phi}]
\ifnum\itest=1
\ifnum\ttest=1
\path[3d cone/base] (0,0)
circle[x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}];
\path[3d cone/mantle]
circle[x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}];
\else
\path[3d cone/mantle]
circle[x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}];
\path[3d cone/base] (0,0)
circle[x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}];
\fi
\else
\ifnum\ttest=1
\path[3d cone/base] (0,0)
circle[x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}];
\path[3d cone/mantle]
plot[variable=\t,domain=\alphacrit:360-\alphacrit,smooth,samples=51]
({\pv{r}*sin(\pv{theta})*cos(\t)},{\pv{r}*sin(\t)})
-- ({\pv{h}*cos(\pv{theta})},0) -- cycle;
\else
\path[3d cone/mantle]
plot[variable=\t,domain=\alphacrit:360-\alphacrit,smooth,samples=51]
({\pv{r}*sin(\pv{theta})*cos(\t)},{\pv{r}*sin(\t)})
-- ({\pv{h}*cos(\pv{theta})},0) -- cycle;
\path[3d cone/base] (0,0)
circle[x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}];
\fi
\fi
\end{scope}
}},3d cone/.cd,h/.initial=1,r/.initial=1,theta/.initial=0,phi/.initial=90,
base/.style={fill=gray},
mantle/.style={shading=bilinear interpolation,
lower left=gray, upper left=gray!60!black, upper right=gray, lower
right=white,shading angle=\pv{phi}-135,opacity=0.7,
postaction={left color=gray,right color=gray,middle color=gray!20,
shading angle=\pv{phi},opacity=0.7}},
mantle contour/.style={draw=gray,very thin},
from top/.style={inner color=gray!20,outer color=gray,opacity=0.7}}
\begin{document}
\foreach \Angle in {5,15,...,355}
{\begin{tikzpicture}
\path[use as bounding box] (-4,-4) rectangle (4,4);
\path (0,0) pic{3d cone={theta=\Angle,phi={90+30*sin(\Angle)},h=3,r=2}};
\end{tikzpicture}}
\end{document}
This can be used to construct an arrow. The shading is stolen from here.
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{shadings}
\tikzset{pics/3d arrow/.style={code={
\tikzset{3d arrow/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/3d arrow/##1}}%
% \itest determines whether the projection of the tip of the cone is inside
% the projection of the base circle, in which case \itest=1
\pgfmathtruncatemacro{\itest}{-1*sign(\pv{h}*abs(cos(\pv{theta}))-\pv{R}*abs(sin(\pv{theta})))}
% \ttest checks whether we look at the cone from the bottom or top,
% in the latter case \ttest=1
\pgfmathtruncatemacro{\ttest}{sign(sin(\pv{theta}))}%
% alpha crit
\pgfmathsetmacro{\alphacrit}{90-atan2((2*\pv{h}*\pv{R}*sin(\pv{theta})*cos(\pv{theta}))/(pow(\pv{h}*cos(\pv{theta}),2) + pow(\pv{R}*sin(\pv{theta}),2)),
(pow(\pv{h}*cos(\pv{theta}),2) - pow(\pv{R}*sin(\pv{theta}),2))/(pow(\pv{h}*cos(\pv{theta}),2) +
pow(\pv{R}*sin(\pv{theta}),2))}%
%\pgfmathsetmacro{\alphacrit}{min(\alphacrit,180-\alphacrit)}
% \path (-4,4) node[below right]
% {$t=\ttest,i=\itest,\alpha_\mathrm{crit}=\alphacrit,\theta=\pv{theta},\phi=\pv{phi}$};
\begin{scope}[rotate=\pv{phi}]
\path ({\pv{h}*cos(\pv{theta})},0) coordinate (tip);
\ifnum\itest=1
\ifnum\ttest=1
\tikzset{3d arrow/shaft}
\path[3d arrow/base] (0,0)
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\path[3d arrow/mantle]
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\tikzset{3d arrow/mantle extra}
\else
\path[3d arrow/mantle]
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\tikzset{3d arrow/mantle extra}
\path[3d arrow/base] (0,0)
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\tikzset{3d arrow/shaft}
\fi
\else
\ifnum\ttest=1
\tikzset{3d arrow/shaft}
\path[3d arrow/base] (0,0)
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\pgfmathsetmacro{\alphamax}{(\alphacrit<90 ? 360-\alphacrit :-\alphacrit)}
\path[3d arrow/mantle]
plot[variable=\t,domain=\alphacrit:\alphamax,smooth,samples=51]
({\pv{R}*sin(\pv{theta})*cos(\t)},{\pv{R}*sin(\t)})
-- ({\pv{h}*cos(\pv{theta})},0) -- cycle;
\tikzset{3d arrow/mantle extra}
\else
\path[3d arrow/mantle]
plot[variable=\t,domain=\alphacrit:360-\alphacrit,smooth,samples=51]
({\pv{R}*sin(\pv{theta})*cos(\t)},{\pv{R}*sin(\t)})
-- ({\pv{h}*cos(\pv{theta})},0) -- cycle;
\tikzset{3d arrow/mantle extra}
\path[3d arrow/base] (0,0)
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\tikzset{3d arrow/shaft}
\fi
\fi
\end{scope}
}},3d arrow/.cd,h/.initial=1,% height of cone
R/.initial=1,% radius of cone
r/.initial=0.5,% radius of shaft
L/.initial=2,% length of shaft
theta/.initial=0,phi/.initial=90,
base/.style={fill=gray!70},
mantle/.style={fill=gray!20},
mantle contour/.style={draw=gray,very thin},
from top/.style={inner color=gray!20,outer color=gray,opacity=0.7},
mantle extra/.code={
\ifnum\itest=1
\foreach \XX in {-45,45,135,225}
{\foreach \YY [evaluate = {\ZZ=30;}] in {0,2,...,30}
{\fill [black, fill opacity = 1/50]
(tip) --
plot[variable=\t,domain=-\ZZ:\ZZ]
({\pv{R}*sin(\pv{theta})*cos(\XX-\YY+\t)},{\pv{R}*sin(\XX-\YY+\t)})
-- cycle;}}
\else
\pgfmathsetmacro{\pft}{(cos(\pv{theta})>0 ? 0 :180)}
\foreach \XX in {135,225}
{\foreach \YY [evaluate = {\ZZ=30;}] in {0,2,...,30}
{\fill [black, fill opacity = 1/50]
(tip) --
plot[variable=\t,domain=-\ZZ:\ZZ]
({\pv{R}*sin(\pv{theta})*cos(\pft+\XX-\YY+\t)},{\pv{R}*sin(\pft+\XX-\YY+\t)})
-- cycle;}}
\fi
},
shaft/.code={
\pgfmathsetmacro{\betamax}{(cos(\pv{theta})>0 ? 270 :-90)}
\path[top color=gray!80,bottom color=black,middle color=gray!10,
shading angle=\pv{phi}] (0,\pv{r}) arc[start angle=90,end angle=\betamax,
x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}] --
({-\pv{L}*cos(\pv{theta})},-\pv{r})
arc[start angle=\betamax,end angle=90,
x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}] -- cycle;
\ifnum\ttest=-1
\fill[gray] ({-\pv{L}*cos(\pv{theta})},0) circle[x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}];
\fi
}}
\begin{document}
\foreach \Angle in {5,15,...,355}
{\begin{tikzpicture}
\path[use as bounding box] (-4,-4) rectangle (4,4);
\path (0,0) pic{3d arrow={theta=\Angle,phi={90+30*sin(\Angle)},h=3,R=2}};
\end{tikzpicture}}
\end{document}
This can be used in the usual way to create a symbol.
\documentclass{article}
\usepackage{tikz}
\usepackage{scalerel}
\tikzset{pics/3d arrow/.style={code={
\tikzset{3d arrow/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/3d arrow/##1}}%
% \itest determines whether the projection of the tip of the cone is inside
% the projection of the base circle, in which case \itest=1
\pgfmathtruncatemacro{\itest}{-1*sign(\pv{h}*abs(cos(\pv{theta}))-\pv{R}*abs(sin(\pv{theta})))}
% \ttest checks whether we look at the cone from the bottom or top,
% in the latter case \ttest=1
\pgfmathtruncatemacro{\ttest}{sign(sin(\pv{theta}))}%
% alpha crit
\pgfmathsetmacro{\alphacrit}{90-atan2((2*\pv{h}*\pv{R}*sin(\pv{theta})*cos(\pv{theta}))/(pow(\pv{h}*cos(\pv{theta}),2) + pow(\pv{R}*sin(\pv{theta}),2)),
(pow(\pv{h}*cos(\pv{theta}),2) - pow(\pv{R}*sin(\pv{theta}),2))/(pow(\pv{h}*cos(\pv{theta}),2) +
pow(\pv{R}*sin(\pv{theta}),2))}%
%\pgfmathsetmacro{\alphacrit}{min(\alphacrit,180-\alphacrit)}
% \path (-4,4) node[below right]
% {$t=\ttest,i=\itest,\alpha_\mathrm{crit}=\alphacrit,\theta=\pv{theta},\phi=\pv{phi}$};
\begin{scope}[rotate=\pv{phi}]
\path ({\pv{h}*cos(\pv{theta})},0) coordinate (tip);
\ifnum\itest=1
\ifnum\ttest=1
\tikzset{3d arrow/shaft}
\path[3d arrow/base] (0,0)
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\path[3d arrow/mantle]
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\tikzset{3d arrow/mantle extra}
\else
\path[3d arrow/mantle]
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\tikzset{3d arrow/mantle extra}
\path[3d arrow/base] (0,0)
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\tikzset{3d arrow/shaft}
\fi
\else
\ifnum\ttest=1
\tikzset{3d arrow/shaft}
\path[3d arrow/base] (0,0)
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\pgfmathsetmacro{\alphamax}{(\alphacrit<90 ? 360-\alphacrit :-\alphacrit)}
\path[3d arrow/mantle]
plot[variable=\t,domain=\alphacrit:\alphamax,smooth,samples=51]
({\pv{R}*sin(\pv{theta})*cos(\t)},{\pv{R}*sin(\t)})
-- ({\pv{h}*cos(\pv{theta})},0) -- cycle;
\tikzset{3d arrow/mantle extra}
\else
\path[3d arrow/mantle]
plot[variable=\t,domain=\alphacrit:360-\alphacrit,smooth,samples=51]
({\pv{R}*sin(\pv{theta})*cos(\t)},{\pv{R}*sin(\t)})
-- ({\pv{h}*cos(\pv{theta})},0) -- cycle;
\tikzset{3d arrow/mantle extra}
\path[3d arrow/base] (0,0)
circle[x radius={\pv{R}*sin(\pv{theta})},y radius=\pv{R}];
\tikzset{3d arrow/shaft}
\fi
\fi
\end{scope}
}},3d arrow/.cd,h/.initial=1,% height of cone
R/.initial=1,% radius of cone
r/.initial=0.5,% radius of shaft
L/.initial=2,% length of shaft
theta/.initial=0,phi/.initial=90,
base/.style={fill=gray!70},
mantle/.style={fill=gray!20},
mantle contour/.style={draw=gray,very thin},
from top/.style={inner color=gray!20,outer color=gray,opacity=0.7},
mantle extra/.code={
\ifnum\itest=1
\foreach \XX in {-45,45,135,225}
{\foreach \YY [evaluate = {\ZZ=30;}] in {0,2,...,30}
{\fill [black, fill opacity = 1/50]
(tip) --
plot[variable=\t,domain=-\ZZ:\ZZ]
({\pv{R}*sin(\pv{theta})*cos(\XX-\YY+\t)},{\pv{R}*sin(\XX-\YY+\t)})
-- cycle;}}
\else
\pgfmathsetmacro{\pft}{(cos(\pv{theta})>0 ? 0 :180)}
\foreach \XX in {135,225}
{\foreach \YY [evaluate = {\ZZ=30;}] in {0,2,...,30}
{\fill [black, fill opacity = 1/50]
(tip) --
plot[variable=\t,domain=-\ZZ:\ZZ]
({\pv{R}*sin(\pv{theta})*cos(\pft+\XX-\YY+\t)},{\pv{R}*sin(\pft+\XX-\YY+\t)})
-- cycle;}}
\fi
},
shaft/.code={
\pgfmathsetmacro{\betamax}{(cos(\pv{theta})>0 ? 270 :-90)}
\path[top color=gray!80,bottom color=black,middle color=gray!10,
shading angle=\pv{phi}] (0,\pv{r}) arc[start angle=90,end angle=\betamax,
x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}] --
({-\pv{L}*cos(\pv{theta})},-\pv{r})
arc[start angle=\betamax,end angle=90,
x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}] -- cycle;
\ifnum\ttest=-1
\fill[gray] ({-\pv{L}*cos(\pv{theta})},0) circle[x radius={\pv{r}*sin(\pv{theta})},y radius=\pv{r}];
\fi
}}
\newsavebox\SBTikzTDrightarrow
\newsavebox\SBTikzTDleftarrow
\sbox\SBTikzTDrightarrow{\begin{tikzpicture}
\pic{3d arrow={theta=-20,phi=0,h=3,R=2,L=8}};
\end{tikzpicture}}
\sbox\SBTikzTDleftarrow{\begin{tikzpicture}
\pic{3d arrow={theta=20,phi=180,h=3,R=2,L=8}};
\end{tikzpicture}}
\newcommand{\TDrightarrow}{\mathrel{\scalerel*{\usebox\SBTikzTDrightarrow}{\rightarrow}}}
\newcommand{\TDleftarrow}{\mathrel{\scalerel*{\usebox\SBTikzTDleftarrow}{\leftarrow}}}
\begin{document}
$a\TDrightarrow b\TDleftarrow c$
$a\rightarrow b\leftarrow c$
\end{document}
symbolsit has to besymbol 1. ;-) – Apr 12 '20 at 19:40tikzpicture. I guess if you rewrite your question in this way, it is not a duplicate. Also call the arrowssphericalwithph. – Apr 12 '20 at 19:44