如何使用Tikz重建经典的观点插图

Question

我正在尝试使用Tikz复制这种原理图。我当前的代码是

\documentclass[tikz]{standalone}
\usetikzlibrary{intersections}

\begin{document}
    \begin{tikzpicture}
        \node[anchor = south west, inner sep = 0, minimum width = 1170 pt, minimum height = 500 pt] (image) at (0, 0) {};
        \begin{scope}[x = {(image.south east)}, y = {(image.north west)}]
%            \clip (0, 0) rectangle(1, 1);
            \coordinate (C) at (0.33, 1.05);
            \coordinate (R) at (1.6, 1.05);
            \coordinate (L) at (0.33 - 1.27, 1.05);
            \coordinate (P1) at (8 * 0.09, 0.07);
            \coordinate (P2) at (0.03 + 8 * 0.09, 0.07);
            \coordinate (P3) at (8 * 0.09, 0.9) node [above] {p3};
            \coordinate (P4) at (0.03 + 8 * 0.09, 0.9) node {p4};
            \draw [dashed, blue, name path = P3C] (P3) -- (C);
            \draw [dashed, blue] (P4) -- (C);
            \draw (L) -- (R);
            \foreach \x in {0, 0.09, ..., 1} {
                \draw [dashed, blue] (\x, 0.07) -- (C);
                \draw [dashed, violet] (\x, 0.07) -- (R);
                \draw [dashed, red] (\x, 0.07) -- (L);
            }
            \draw [name path = L1] (0, 0.2871) -- (1, 0.2871);
            \draw [name path = L2] (0, 0.19) -- (1, 0.19);

            \path [name path = P1C] (P1) -- (C);
            \coordinate [name intersections = {of = P1C and L1, by = P1a}];
            \draw [orange, thick] (P1) -- (P1a);

            \path [name path = P1aV] (C) -| (P1a);
            \coordinate [name intersections = {of = P1aV and P3C, by = P13}];
            \draw [orange, thick] (P13) circle (3 pt);
            
            \filldraw [gray] (0, 0) rectangle (11 * 0.09, 0.07);
            \filldraw [gray] (P1) rectangle (0.03 + 8 * 0.09, 0.9);

            \draw [red, fill] (P1) circle (2 pt);
            \draw [violet, fill] (P1a) circle (2 pt);
            \draw [green, fill] (P2) circle (2 pt);
            \draw [blue, fill] (P3) circle (2 pt);
            \draw [orange, fill] (P4) circle (2 pt);
        \end{scope}
    \end{tikzpicture}
\end{document}

在交叉点的详细信息中陷入困境，我正在寻找简化代码的方法，并有助于构造八角形平板及其投影。

这就是目前的样子：

Answer 1

这是代码：

\documentclass[tikz]{standalone}
\usetikzlibrary{calc, intersections}
\newcommand\w{0.03}
\newcommand\xx{0.09}
%%%%%%%
% \yy = thickness of floor
%%%%%%%
\newcommand\yy{0.07}
\begin{document}
    \begin{tikzpicture}
        \node[anchor = south west, inner sep = 0, minimum width = 1000 pt, minimum height = 500 pt] (image) at (0, 0) {};
        \begin{scope}[x = {(image.south east)}, y = {(image.north west)}]
            \clip (-0.12, -0.05) rectangle(1.2, 1);
            
%%%%%%%
% left (L), center (C), & right (R) vanishing points to create the framework of the picture
%%%%%%%
            \coordinate (C) at (0.33, 1.05);
            \coordinate (R) at (1.6, 1.05);
            \coordinate (L) at (0.33 - 1.27, 1.05);
%%%%%%%
% connect left (L), & right (R) to draw horizon
%%%%%%%
            \path [name path = horizon] (L) -- (R); % node [above = 10 pt, left = 2 em, midway] {\huge horizon};
%%%%%%%
% PP
%%%%%%%
    %%%%%%%
    % vertices of front of PP
    %%%%%%%
            \coordinate (p1) at (8 * \xx, \yy);
            \coordinate (p2) at (\w + 8 * \xx, \yy);
            \coordinate (p3) at (8 * \xx, 0.9);
            \coordinate (p4) at (\w + 8 * \xx, 0.9);
    %%%%%%%
    % name paths connecting visible points on front of PP to vanishing point C
    %%%%%%%
            \path [name path = p1C] (p1) -- (C);
            \path [name path = p3C] (p3) -- (C);
            \path [name path = p4C] (p4) -- (C);
%%%%%%%
% draw divergent rays from L, C, R to equidistant points at the top of the floor slab
%%%%%%%
            \foreach \x in {-1, 0, 1, ..., 13, 18} {
                \path [dashed, thin, blue, name path global/.expanded = lineC\x] (\x*9/100, \yy) -- (C);
                \path [dashed, thin, violet, name path global/.expanded = lineR\x] (\x*9/100, \yy) -- (R);
                \path [dashed, thin, red, name path global/.expanded = lineL\x] (\x*9/100, \yy) -- (L);
            }
%%%%%%%
% FLOOR
%%%%%%%
    %%%%%%%
    % l2, the distant horizontal line
    %%%%%%%
            \draw [name intersections = {of = lineL3 and lineC-1, by = L3C-1}]; % (intersection-1) circle (5 pt);
            \draw [name intersections = {of = lineR9 and lineC13, by = R9C13}]; % (intersection-1) circle (5 pt);
            \draw [name path = l2] (L3C-1) -- (R9C13); % node [above, midway] {\huge l2};
    %%%%%%%
    % l1, the middle horizontal line
    %%%%%%%
            \draw [name intersections = {of = lineL1 and lineC-1, by = L1C-1}]; % (intersection-1) circle (5 pt);
            \path [name intersections = {of = lineR11 and lineC13, by = R11C13}]; % (intersection-1) circle (5 pt);
            \draw [name path = l1] (L1C-1) -- (R11C13); % node [above, midway] {\huge l1};
    %%%%%%%
    % intersection of floor line in PP with distant horizontal line l2
    %%%%%%%
            \coordinate [name intersections = {of = p1C and l2, by = p1a}];
    %%%%%%%
    % intersections of divergent rays from C with distant horizontal line l2
    %%%%%%%
            \foreach \x in {-1, 0, 1, ..., 13} {
                \coordinate [name intersections = {of = l2 and lineC\x, by = l2_C\x}];
                \draw (\x * \xx, \yy) -- (l2_C\x);
            }
    %%%%%%%
    % draw front of floor
    %%%%%%%
            \filldraw [gray!50] (-1 * \xx, 0) rectangle (13 * \xx, \yy);
            
            
            \path [name path = p1p1a, red, very thick] (p1) -- (p1a); % node [midway, below] {\huge p1p1a};
            \path [name path = p1aV] (p1a) -- ($(L)!(p1a)!(R)$);
            \coordinate [name intersections = {of = p1aV and p3C, by = p1b}];
            \path [red, very thick] (p1a) -- (p1b); % node [above] {\huge p1b};
%%%%%%%
% HEXAGON
%%%%%%%
    % name hexagon vertices
            \path [name intersections = {of = lineC10 and lineR8, by = h1}] (intersection-1) circle (5 pt);
            \path [name intersections = {of = lineC11 and lineR8, by = h2}] (intersection-1) circle (5 pt);
            \path [name intersections = {of = lineC12 and lineR9, by = h3}] (intersection-1) circle (5 pt);
            \path [name intersections = {of = lineC13 and lineR11, by = h4}] (intersection-1) circle (5 pt);
            \path [name intersections = {of = lineC12 and lineR11, by = h5}] (intersection-1) circle (5 pt);
            \path [name intersections = {of = lineC11 and lineR10, by = h6}] (intersection-1) circle (5 pt);
    % draw hexagon
            \fill [blue] (h1) -- (h2) -- (h3) -- (h4) -- (h5) -- (h6) -- cycle;
%%%%%%%
% CoP
%%%%%%%
    % p1m: projection of centric point onto the floor line of the PP
            \path [name intersections ={of = l1 and p1p1a, by = p1m}] (intersection-1); % circle (5 pt) node [above] {\huge p1m};
    % p1mV: vertical line from p1m
            \path [brown!50!red, name path = p1mV] (p1m) -- ($(L)!(p1m)!(R)$); % node [midway, right] {\huge p1mV};
    % centric: intersection of vLine with horizon
            \path [name intersections = {of = lineC18 and p1mV, by = centric}] (intersection-1) circle (5 pt) node [above] {\huge centric};
    % vLine: vertical line through CoP
            \path [purple, name path = vLine] (L1C-1) -- ($(L)!(L1C-1)!(R)$); % node [midway, left] {\huge vLine};
    % vLineH: intersection of vLine with horizon
            \path [name intersections = {of = vLine and horizon, by = vLineH}] (intersection-1) circle (5 pt);
%%%%%%%
% name intersections of hexagon sides (orthogonals) with ground line in PP
%%%%%%%
            \path [name intersections = {of = lineC8 and lineR5, by = o1}] (intersection-1) circle (5 pt);
            \path [name intersections = {of = lineC8 and lineR7, by = o2}] (intersection-1) circle (5 pt);
%%%%%%%
% converging lines from o1 & o2 to vanishing point (centric) in PP
%%%%%%%
            \path [name path = orth1] (o1) -- (centric);
            \path [name path = orth2] (o2) -- (centric);
%%%%%%%
% PP
%%%%%%%
    % horizontal line back of top of PP
            \path [name path = p1bH] (p1b) -- ($(p1)!(p1b)!(p3)$);
    % point at top back right of PP
            \path [draw, name intersections = {of = p1bH and p4C, by = p1c}];
    % draw top of PP
            \fill [gray!50, very thick] (p1b) -- (p1c) -- (p4) -- (p3) -- cycle;
    % draw surface of PP
            \draw [black, fill = white, very thick] (p1) -- (p1a) -- (p1b) -- (p3)  -- cycle;
    % draw edge of PP
            \fill [gray!50, very thick] (p1) -- (p2) -- (p4) -- (p3) -- cycle;

    % centricLine: horizontal line through centric
            \path [draw, name path = centricLine] (centric) -- ($(L1C-1)!(centric)!(vLineH)$);
    % CoP: intersection of vLine & centricLine
            \path [name intersections = {of = vLine and centricLine, by = CoP}] (intersection-1) node [left] {\huge CoP};
    % Extract coordinates of CoP
            \path (CoP); \pgfgetlastxy{\xCoP}{\yCoP};
            \path [draw, name intersections = {of = l1 and p1p1a, by = p1m}] (intersection-1); % circle (5 pt) node [above] {\huge p1m};

    % virtual horizon: lineC18
            \path [name path = p1a_p1b] (p1a) -- (p1b);
            \draw [name path = p1_p3] (p1) -- (p3);
            \path [name intersections = {of = lineC18 and p1a_p1b, by = z1}]; % (intersection-1) circle (5 pt);
            \path [name intersections = {of = lineC18 and p1_p3, by = z2}]; % (intersection-1) circle (5 pt);
            \draw [shorten  > = 1 em, shorten  < = 1 em] (z1) -- (z2);

%%%%%%%
% hexagon image
%%%%%%%
    % name hexagon vertices images
            \foreach \x in {1, ..., 6} \draw [dotted, thick, name path global/.expanded = CoP_h\x] (CoP) -- (h\x);
    % draw hexagon vertices images
            \path [draw, name intersections = {of = CoP_h1 and p1mV, by = h1x}] (intersection-1); % node [below] {\huge h1x};
            \path [draw, name intersections = {of = CoP_h2 and orth1, by = h2x}] (intersection-1); % node [left] {\huge h2x};
            \path [draw, name intersections = {of = CoP_h3 and orth1, by = h3x}] (intersection-1); % circle (10 pt); % node [left] {\huge h3x};
            \path [draw, name intersections = {of = CoP_h4 and p1mV, by = h4x}] (intersection-1); % node [above] {\huge h4x};
            \path [draw, name intersections = {of = CoP_h5 and orth2, by = h5x}] (intersection-1); % circle (10 pt); % node [right] {\huge h5x};
            \path [draw, name intersections = {of = CoP_h6 and orth2, by = h6x}] (intersection-1); % node [right] {\huge h6x};
    % draw image of hexagon
            \draw [very thick, fill = blue!25] (h1x) -- (h2x) -- (h3x) -- (h4x) -- (h5x) -- (h6x) -- cycle;
    % hexagon image to VP
            \path [draw, loosely dashed] (h3x) -- (centric) -- (h5x);
%%%%%%%
% eye
%%%%%%%
            \pgfmathsetmacro{\eyeSize}{0.05}
            \pgfmathsetmacro{\ex}{0}
            \pgfmathsetmacro{\ey}{1}
            \pgfmathsetmacro{\eRot}{0}
            \pgfmathsetmacro{\eAp}{-70}
            \draw [red, rotate around = {\eRot : (CoP)}]
                (CoP) -- ++(-.5 * \eAp : \eyeSize)
                (CoP) -- ++(.5 * \eAp : \eyeSize);
            \draw [red] (CoP) ++(\eRot + \eAp : .75 * \eyeSize) arc (\eRot + \eAp : \eRot - \eAp : .75 * \eyeSize);
    % IRIS
            \draw [fill = red!50] (CoP) ++(\eRot + \eAp / 3 : .75 * \eyeSize) % start point
              arc (\eRot + 180 - \eAp : \eRot + 180 + \eAp : .28 * \eyeSize);
    %PUPIL, a filled arc 
            \draw [fill = black] (CoP) ++(\eRot + \eAp / 3 : .75 * \eyeSize) % start point
              arc (\eRot + \eAp / 3 : \eRot - \eAp / 3 : .75 * \eyeSize);
%%%%%%%
        \end{scope}
    \end{tikzpicture}
\end{document}

ps：如果有人可以弄清楚如何移动眼睛的图像，以使虹膜处于警察处，我会感激不已。