基于3D 正常扩散我想描绘出正态分布随着时间的推移而趋于平缓但又有所漂移的现象。
1 - 正如您在下面的 MWE 中看到的，橙色正态分布似乎在其底部被切断。为什么会这样？我实际上尝试沿黑线进行“阴影扩散”，但由于上述问题，我的分布在其基础上被切断。
2 - 我还尝试用浅色不透明度填充分布红色一侧的一半分布。简单的方法似乎不起作用。
3——分布顶部的连接处似乎有一个微小的白色间隙。
\documentclass[border =2mm]{standalone}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage{xintexpr}
\usetikzlibrary{decorations.pathmorphing,bending}
\usetikzlibrary{3d}
\usepackage{pgfplots, pgfplotstable}
%\pgfplotsset{compat=1.13} % for better axis label placement
\pgfplotsset{compat=1.15}
\usepgfplotslibrary{fillbetween}
\usepgfplotslibrary{groupplots}
\usepackage{graphicx}% Allows ding images
\begin{document}
\def\Fwd{1.5}
\def\Z{30}
\makeatletter
\pgfdeclareplotmark{dot} {\fill circle [x radius=0.02, y radius=0.08];}
\makeatother
\begin{tikzpicture}%[ % Define Normal Probability Function
\tikzset{
declare function={
normal(\x,\m,\s) = 1/(2*\s*sqrt(pi))*exp(-(\x-\m)^2/(2*\s^2));
invgauss(\a,\b) = sqrt(-2*ln(\a))*cos(deg(2*pi*\b));
forward(\a) = {\Fwd*(\a-0.5)+3};
call(\a,\b) = 0.35*max(\a-\b,0); %Facteur pour avoir un graphe de call plus haut
}}
\makeatletter
\pgfdeclareplotmark{dot}
{\fill circle [x radius=0.02, y radius=0.08];}
\makeatother
\tikzset{
distrib/.style={blue, ultra thick,opacity=0.40},
distribLeft/.style={distrib,red},
diffusion/.style={gray!50, only marks, mark=dot, mark layer=like plot, samples=200, domain=0.1:3.5, on layer=axis background},
Forward/.style={samples=2,domain=0:3,thick,red},
CallPayOff/.style={samples=200,cyan!50!black,thick}
}
\begin{axis}[
domain=0:8,
zmin=0, zmax=0.5,
ymin=0, ymax=8,
xmin=0, xmax=3,
samples=200,
samples y=0,
view={60}{30},
axis lines=middle,
enlarge y limits=true,
xtick={0.5,1.5,2.5},
xmajorgrids,
ytick=\empty,
xticklabels={$t_1$, $t_2$, $t_3$},
ztick=\empty,
xlabel=$time$, xlabel style={at={(rel axis cs:1,0,0)}, anchor=west,font=\small},
ylabel=$S$, ylabel style={at={(rel axis cs:0,1,0)}, anchor=south west,font=\small},
zlabel=Probability density, zlabel style={at={(rel axis cs:0,0,0.5)},font=\small, rotate=90, anchor=south},
set layers, mark=cube
]
\addplot3 [gray!50, only marks, mark=dot, mark layer=like plot, samples=200, domain=0.1:2.9, on layer=axis background] (x, {1.5*(x-0.5)+3+invgauss(rnd,rnd)*x}, 0);
\addplot3 [Forward] (x, {1.5*(x-0.5)+3}, 0);
%Forward flat, le spot
\addplot3 [Forward,black] (x, {forward(0)}, 0);
%Distributions centrées sur le forward
\addplot3 [distrib,domain=forward(0.5):10] (0.5, x, {normal(x, forward(0.5), 0.75)});
\addplot3 [distrib,domain=forward(1.5):10] (1.5, x, {normal(x, forward(1.5), 1.0)});
\addplot3 [distrib,domain=forward(2.5):10] (2.5, x, {normal(x, forward(2.5), 1.25)});
%Distributions centrées sur le forward
\addplot3 [distribLeft,domain=0:forward(0.5)] (0.5, x, {normal(x, forward(0.5), 0.75)});
\addplot3 [distribLeft,domain=0:forward(1.5)] (1.5, x, {normal(x, forward(1.5), 1.0)});
\addplot3 [distribLeft,domain=0:forward(2.5)] (2.5, x, {normal(x, forward(2.5), 1.25)});
\pgfplotsextra{
\begin{pgfonlayer}{axis background}
\draw [gray, on layer=axis background]
(0.5, {forward(0)}, 0) -- (0.5, {forward(0)}, {normal(0,0,0.75)}) (0.5,0,0) -- (0.5,10,0)
(0.5, {forward(0.5)}, 0) -- (0.5, {forward(0.5)}, {normal(0,0,0.75)}) (0.5,0,0) -- (0.5,10,0)
(1.5, {forward(1.5)}, 0) -- (1.5, {forward(1.5)}, {normal(0,0,1)}) (1.5,0,0) -- (1.5,10,0)
(2.5, {forward(2.5)}, 0) -- (2.5, {forward(2.5)}, {normal(0,0,1.25)}) (2.5,0,0) -- (2.5,10,0);
\end{pgfonlayer}
}
%Distributions centrées sur 100
\addplot3 [distrib,fill=orange,domain=0:10,orange] (0.5, x, {normal(x, forward(0), 0.75)});
%mark=*,
\draw plot [mark=ball,mark size=2, ball color=blue] coordinates{(0, {forward(0)}, 0)};
\draw plot [mark=ball, mark size=2, ball color=red] coordinates{(0.5, {forward(0.5)}, 0)};
\draw plot [mark=ball, mark size=2, ball color=red] coordinates{(1.5, {forward(1.5)}, 0)};
\draw plot [mark=ball, mark size=2, ball color=red] coordinates{(2.5, {forward(2.5)}, 0)};
\coordinate[label=\tiny{Forward}] (B1) at (3,{forward(2.5)+0.2},0);
\coordinate[label=\tiny{Spot}] (B1) at (3.1,0.6,0);
\end{axis}
\end{tikzpicture}
\end{document}
这是我更新的版本，其中包含显示内容的条件。谢谢薛定谔！
\documentclass[border=2mm]{standalone}
\usepackage{pgfplots}
\usepackage{amssymb}
\pgfplotsset{compat=1.16}
\def\Fwd{1.1}
\def\Sig{0.4}
\def\Spot{1}
\def\Forward{1}
\def\PointDiffusion{0}
\pgfdeclareplotmark{dot}{\fill circle [x radius=0.02, y radius=0.08];}
\begin{document}
\begin{tikzpicture}[
declare function={
normal(\x,\m,\s) = 1/(2*\s*sqrt(pi))*exp(-(\x-\m)^2/(2*\s^2));
invgauss(\a,\b) = sqrt(-2*ln(\a))*cos(deg(2*pi*\b));
forward(\a) = {\Fwd*(\a-0.5)+3};
call(\a,\b) = 0.35*max(\a-\b,0); %Facteur pour avoir un graphe de call plus haut
},
distrib/.style={blue!40, ultra thick},
distribLeft/.style={distrib,red!40},
distribSpot/.style={distrib,domain=0:5,orange!50,thin},
diffusion/.style={gray!50, only marks, mark=dot, mark layer=like plot, samples=200, domain=0.1:3.5, on layer=axis background},
Forward/.style={samples=2,domain=0:3,thick,red},
CallPayOff/.style={samples=200,cyan!50!black,thick}
]
\begin{axis}[
domain=0:8,
zmin=0, zmax=0.75,
ymin=0, ymax=8,
xmin=0, xmax=3,
samples=200,
samples y=0,
view={60}{30},
axis lines=middle,
enlarge y limits=true,
xtick={0.5,1.5,2.5},
xmajorgrids,
ytick=\empty,
xticklabels={$t_1$, $t_2$, $t_3$},
ztick=\empty,
xlabel=$time$, xlabel style={at={(rel axis cs:1,0,0)}, anchor=west,font=\small},
ylabel=$S$, ylabel style={at={(rel axis cs:0,1,0)}, anchor=south west,font=\small},
zlabel=$\mathbb{P}$ density, zlabel style={at={(rel axis cs:0,0,0.75)},font=\small, rotate=90, anchor=south},
set layers=standard,% mark=cube
]
% circles on the gound
\if 1\Spot
%Forward flat, le spot
\addplot3 [Forward,orange] (x, {forward(0)}, 0);
\if 1\PointDiffusion
\addplot3 [orange!50, only marks, mark=dot, mark layer=like plot, on layer=axis background,samples=300, domain=0.1:2.9]
(x,{forward(0)+invgauss(rnd,rnd)*x}, 0);
\fi
\fi
\if 1\Forward
\addplot3 [Forward] (x, {forward(x)}, 0);
\if 1\PointDiffusion
\addplot3 [gray!50, only marks, mark=dot, mark layer=like plot, on layer=axis background,samples=200, domain=0.1:2.9]
(x,{forward(x)+invgauss(rnd,rnd)*x}, 0);
\fi
\fi
%
%Distributions centrées sur 100
\addplot3 [distrib,domain=0:10,fill=orange,fill opacity=0.3,draw=none]
(0, x, {normal(x, forward(0), \Sig)}) -- (0, 10, 0) -- (0, 0, 0) ;
\addplot3 [only marks,mark=ball,mark size=2,mark options={color=orange,ball color=orange,line width=0pt}] coordinates {(0, {forward(0)}, 0)};
\addplot3 [distribSpot,ultra thick] (0, x, {normal(x, forward(0), \Sig)});
%Distributions centrées sur le spot
%Distributions centrées sur le forward
\pgfplotsinvokeforeach{1,2,3}{
\if 1\Spot
\addplot3 [distribSpot] (-0.5+#1, x, {normal(x, forward(0), \Sig+0.25*#1)});
\fi
\if 1\Forward
\addplot3 [distrib,domain=10:{forward(-0.5+#1)-0.01}]
(-0.5+#1, x, {normal(x, {forward(-0.5+#1)}, \Sig+0.25*#1)}) ;
\addplot3 [fill=red,fill opacity=0.2,domain=0:{forward(-0.5+#1)}]
(-0.5+#1, x, {normal(x, {forward(-0.5+#1)}, \Sig+0.25*#1)})
-- (-0.5+#1, {forward(-0.5+#1)},0) -- (-0.5+#1, 0,0);
\addplot3 [distribLeft,domain=0:{forward(-0.5+#1)}]
(-0.5+#1, x, {normal(x, {forward(-0.5+#1)}, \Sig+0.25*#1)});
\draw[gray] (-0.5+#1, {forward(0)}, 0) -- (-0.5+#1,10,0)
(-0.5+#1,{forward(-0.5+#1)},0) --
(-0.5+#1,{forward(-0.5+#1)},{normal({forward(-0.5+#1)}, {forward(-0.5+#1)}, \Sig+0.25*#1)});
\addplot3 [only marks,mark=ball,mark size=2,mark
options={color=red,ball color=red,line width=0pt}] coordinates
{(-0.5+#1, {forward(-0.5+#1)}, 0)};
\fi
}
\path (3, {1.5*(3-0.5)+3}, 0) coordinate (F);
\coordinate[label={[font=\tiny]Spot}] (B2) at (3.1,0.6,0);
\end{axis}
\path (F) node[below,font=\tiny] {Forward};
\end{tikzpicture}
\end{document}
答案1
这是解决您问题的方法。为了达到这个目的，我删除了不必要的包和定义。我决定使用“强力”填充，因为层使得 3d 排序很难通过库实现fillbetween。至于后者，我重新排序了图。要理解原因，请注意 pgfplots 在给定的范围内进行了一些排序\addplot3，但没有对图进行相互排序。
\documentclass[border=2mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
%\usepgfplotslibrary{fillbetween}
\begin{document}
\begin{tikzpicture}[
declare function={
normal(\x,\m,\s) = 1/(2*\s*sqrt(pi))*exp(-(\x-\m)^2/(2*\s^2));
invgauss(\a,\b) = sqrt(-2*ln(\a))*cos(deg(2*pi*\b));
forward(\a) = {\Fwd*(\a-0.5)+3};
call(\a,\b) = 0.35*max(\a-\b,0); %Facteur pour avoir un graphe de call plus haut
},
distrib/.style={blue!40, ultra thick},
distribLeft/.style={distrib,red!40},
diffusion/.style={gray!50, only marks, mark=dot, mark layer=like plot, samples=200, domain=0.1:3.5, on layer=axis background},
Forward/.style={samples=2,domain=0:3,thick,red},
CallPayOff/.style={samples=200,cyan!50!black,thick}
]
\def\Fwd{1.5}
\pgfdeclareplotmark{dot}{\fill circle [x radius=0.02, y radius=0.08];}
\begin{axis}[
domain=0:8,
zmin=0, zmax=0.5,
ymin=0, ymax=8,
xmin=0, xmax=3,
samples=200,
samples y=0,
view={60}{30},
axis lines=middle,
enlarge y limits=true,
xtick={0.5,1.5,2.5},
xmajorgrids,
ytick=\empty,
xticklabels={$t_1$, $t_2$, $t_3$},
ztick=\empty,
xlabel=$time$, xlabel style={at={(rel axis cs:1,0,0)}, anchor=west,font=\small},
ylabel=$S$, ylabel style={at={(rel axis cs:0,1,0)}, anchor=south west,font=\small},
zlabel=Probability density, zlabel style={at={(rel axis cs:0,0,0.5)},font=\small, rotate=90, anchor=south},
set layers=standard,% mark=cube
]
% circles on the gound
\addplot3 [gray!50, only marks, mark=dot, mark layer=like plot,
on layer=axis background,samples=200, domain=0.1:2.9] (x,
{1.5*(x-0.5)+3+invgauss(rnd,rnd)*x}, 0);
\addplot3 [Forward] (x, {1.5*(x-0.5)+3}, 0);
%Forward flat, le spot
\addplot3 [Forward,black] (x, {forward(0)}, 0);
%
%Distributions centrées sur 100
\addplot3 [distrib,domain=0:10,fill=orange,fill opacity=0.4,draw=none]
(0.5, x, {normal(x, forward(0), 0.75)}) --
(0.5, 10, 0) -- (0.5, 0, 0) ;
\addplot3 [distrib,domain=0:10,orange] (0.5, x, {normal(x, forward(0), 0.75)});
\addplot3 [only marks,mark=ball,mark size=2,mark size=2,mark
options={color=red,line width=0pt}] coordinates {(0, {forward(0)}, 0)};
%Distributions centrées sur le forward
\pgfplotsinvokeforeach{1,2,3}{
\addplot3 [distrib,domain=10:{forward(-0.5+#1)-0.01}]
(-0.5+#1, x, {normal(x, {forward(-0.5+#1)}, 0.5+0.25*#1)}) ;
\addplot3 [fill=red,fill opacity=0.3,domain=0:{forward(-0.5+#1)}]
(-0.5+#1, x, {normal(x, {forward(-0.5+#1)}, 0.5+0.25*#1)})
-- (-0.5+#1, {forward(-0.5+#1)},0) -- (-0.5+#1, 0,0);
\addplot3 [distribLeft,domain=0:{forward(-0.5+#1)}]
(-0.5+#1, x, {normal(x, {forward(-0.5+#1)}, 0.5+0.25*#1)});
\draw[gray] (-0.5+#1, {forward(0)}, 0) -- (-0.5+#1,10,0)
(-0.5+#1,{forward(-0.5+#1)},0) --
(-0.5+#1,{forward(-0.5+#1)},{normal({forward(-0.5+#1)}, {forward(-0.5+#1)}, 0.5+0.25*#1)});
\addplot3 [only marks,mark=ball,mark size=2,mark
options={color=red,line width=0pt}] coordinates
{(-0.5+#1, {forward(-0.5+#1)}, 0)};
}
%
\coordinate[label={[font=\tiny]Forward}] (B1) at (3,{forward(2.5)+0.2},0);
\coordinate[label={[font=\tiny]Spot}] (B2) at (3.1,0.6,0);
\end{axis}
\end{tikzpicture}
\end{document}
结果看起来部分还不错。但是，有一件事我无法理解：橙色图和其中一个蓝红色图似乎共享相同的时间坐标。这是故意的吗？对我来说，下面的看起来更好。
\documentclass[border=2mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
%\usepgfplotslibrary{fillbetween}
\begin{document}
\begin{tikzpicture}[
declare function={
normal(\x,\m,\s) = 1/(2*\s*sqrt(pi))*exp(-(\x-\m)^2/(2*\s^2));
invgauss(\a,\b) = sqrt(-2*ln(\a))*cos(deg(2*pi*\b));
forward(\a) = {\Fwd*(\a-0.5)+3};
call(\a,\b) = 0.35*max(\a-\b,0); %Facteur pour avoir un graphe de call plus haut
},
distrib/.style={blue!40, ultra thick},
distribLeft/.style={distrib,red!40},
diffusion/.style={gray!50, only marks, mark=dot, mark layer=like plot, samples=200, domain=0.1:3.5, on layer=axis background},
Forward/.style={samples=2,domain=0:3,thick,red},
CallPayOff/.style={samples=200,cyan!50!black,thick}
]
\def\Fwd{1.5}
\pgfdeclareplotmark{dot}{\fill circle [x radius=0.02, y radius=0.08];}
\begin{axis}[
domain=0:8,
zmin=0, zmax=0.75,
ymin=0, ymax=8,
xmin=0, xmax=3,
samples=200,
samples y=0,
view={60}{30},
axis lines=middle,
enlarge y limits=true,
xtick={0.5,1.5,2.5},
xmajorgrids,
ytick=\empty,
xticklabels={$t_1$, $t_2$, $t_3$},
ztick=\empty,
xlabel=$time$, xlabel style={at={(rel axis cs:1,0,0)}, anchor=west,font=\small},
ylabel=$S$, ylabel style={at={(rel axis cs:0,1,0)}, anchor=south west,font=\small},
zlabel=Probability density, zlabel style={at={(rel axis cs:0,0,0.5)},font=\small, rotate=90, anchor=south},
set layers=standard,% mark=cube
]
% circles on the gound
\addplot3 [gray!50, only marks, mark=dot, mark layer=like plot,
on layer=axis background,samples=200, domain=0.1:2.9] (x,
{1.5*(x-0.5)+3+invgauss(rnd,rnd)*x}, 0);
\addplot3 [Forward] (x, {1.5*(x-0.5)+3}, 0);
%Forward flat, le spot
\addplot3 [Forward,black] (x, {forward(0)}, 0);
%
%Distributions centrées sur 100
\addplot3 [distrib,domain=0:10,fill=orange,fill opacity=0.4,draw=none]
(0, x, {normal(x, forward(0), 0.5)}) --
(0, 10, 0) -- (0, 0, 0) ;
\addplot3 [distrib,domain=0:10,orange] (0, x, {normal(x, forward(0), 0.5)});
\addplot3 [only marks,mark=ball,mark size=2,mark size=2,mark
options={color=red,line width=0pt}] coordinates {(0, {forward(0)}, 0)};
%Distributions centrées sur le forward
\pgfplotsinvokeforeach{1,2,3}{
\addplot3 [distrib,domain=10:{forward(-0.5+#1)-0.01}]
(-0.5+#1, x, {normal(x, {forward(-0.5+#1)}, 0.5+0.25*#1)}) ;
\addplot3 [fill=red,fill opacity=0.3,domain=0:{forward(-0.5+#1)}]
(-0.5+#1, x, {normal(x, {forward(-0.5+#1)}, 0.5+0.25*#1)})
-- (-0.5+#1, {forward(-0.5+#1)},0) -- (-0.5+#1, 0,0);
\addplot3 [distribLeft,domain=0:{forward(-0.5+#1)}]
(-0.5+#1, x, {normal(x, {forward(-0.5+#1)}, 0.5+0.25*#1)});
\draw[gray] (-0.5+#1, {forward(0)}, 0) -- (-0.5+#1,10,0)
(-0.5+#1,{forward(-0.5+#1)},0) --
(-0.5+#1,{forward(-0.5+#1)},{normal({forward(-0.5+#1)}, {forward(-0.5+#1)}, 0.5+0.25*#1)});
\addplot3 [only marks,mark=ball,mark size=2,mark
options={color=red,line width=0pt}] coordinates
{(-0.5+#1, {forward(-0.5+#1)}, 0)};
}
%
\path (3, {1.5*(3-0.5)+3}, 0) coordinate (F);
\coordinate[label={[font=\tiny]Spot}] (B2) at (3.1,0.6,0);
\end{axis}
\path (F) node[below,font=\tiny] {Forward};
\end{tikzpicture}
\end{document}
