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曲线合成 - 添加许多（大部分是分段线性）曲线

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曲线合成 - 添加许多（大部分是分段线性）曲线

这是上一个问题。如果我能从那里的解决方案中获得一个宏，那就太好了，但我做不到。

  1. 以下代码（将添加到上一个主题中 Paul Gaborit 的回答中的代码）尚未运行，如何修复它？

    % one + two + three
\foreach \c in {0,...,100} {
   \pgfmathsetmacro{\x}{\c/10}
   \path[name path=line] (\x,0) -- (\x,6);
   \path[name intersections={of=one and line,name=inter}];

   % How to initialize sum?

   \foreach \curve in {two,three}{ 

      \path[name intersections={of=curve and line,name=newinter}];
      \path let \p1=(inter-1), \p2=(newinter-1) in 
      (\x1,\y1+\y2) coordinate (sum-\c);
  }
}
\draw[red!50!green!50!black]
(sum-0) \foreach \x in {1,...,100}{-- (sum-\x)} node[right]{one + two + three};

  2. 如何传递样本数量（此处为 100）作为输入？更好的方法是能够传递垂直相交线所在的 x 坐标（扭结位置）列表。

对于分段线性曲线，更好的方法确实是合并所有曲线的 x 坐标，对它们进行排序，然后只在这些点相交。

答案1

这是我的答案的增强版本，使用通用方法添加多条曲线（命名路径）。

你会注意到整体的缓慢！对于这些计算，TeX 确实不是合适的工具。

结果

在此处输入图片描述

代码

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc,intersections}

\newcommand\addcurves[7]{
  % samples, xmin, xmax, ymin, ymax, list of paths, prefix
  \bgroup
  \edef\samples{#1}
  \edef\xmin{#2}
  \edef\xmax{#3}
  \edef\ymin{#4}
  \edef\ymax{#5}
  \def\listofpaths{#6}
  \edef\prefix{#7}
  %
  \foreach \c in {0,...,\samples} {
    \pgfmathsetmacro{\x}{\c/\samples * (\xmax-\xmin)+\xmin}
    % verticale line
    \path[name path=line] (\x,\ymin) -- (\x,\ymax);
    % initialize sum (y=0)
    \coordinate (\prefix-\c) at (\x,0);
    % add each path
    \foreach \curve in \listofpaths {
      \path[name intersections={of=line and \curve,name=inter}];
      \path let \p1=(inter-1), \p2=(\prefix-\c) in
      (\x2,\y1+\y2) coordinate (\prefix-\c);
    }
  }
  \egroup
}

\begin{document}
\begin{tikzpicture}[line width=1pt]
  \def\samples{100}

  % a grid
  \draw[help lines] (0,-.5) grid (10,10);
  % x axis
  \draw[-latex,thick] (0,0) -- (10,0) node[right]{$x$};

  % one (red line)
  \def\lineone{(0,4),(4,1),(8,6),(10,6)}
  \foreach \point[count=\c] in \lineone {%
    \coordinate[at=\point] (one-\c);%
    %\fill[red] (one-\c) circle (0.1);%
  }
  \draw[red,name path=one] (one-1)
  \foreach \i in {2,...,\c}{-- (one-\i)} node[right]{one};

  % two (blue line)
  \def\linetwo{(0,1),(3.33,5),(4,2),(6,5),(10,2)}
  \foreach \point[count=\c] in \linetwo {%
    \coordinate[at=\point] (two-\c);%
    %\fill[blue] (two-\c) circle (0.1);%
  }
  \draw[blue,name path=two] (two-1)
  \foreach \i in {2,...,\c}{-- (two-\i)} node[right]{two};

  % one + two
  \addcurves{\samples}{0}{10}{0}{6}{one,two}{sum}
  \draw[red!50!blue]
  (sum-0) \foreach \x in {1,...,\samples}{-- (sum-\x)} node[right]{one + two};

  % three (a green function)
  \draw[green!50!black,name path=three]
  plot[domain=0:10.001,samples=\samples,smooth]
  (\x,{sin(3*\x r)+2}) node[right]{three};

  % one + three
  \addcurves{\samples}{0}{10}{0}{6}{one,three}{sum}
  \draw[red!50!green!50!black]
  (sum-0) \foreach \x in {1,...,\samples}{-- (sum-\x)} node[right]{one + three};

  % four (orange function)
  \draw[orange,name path=four]
  plot[domain=0:10.001,samples=\samples,smooth]
  (\x,{cos(1*\x r)+4}) node[right]{four};

  % four + three
  \addcurves{\samples}{0}{10}{0}{6}{three,four}{sum}
  \draw[orange!50!green!50!black]
  (sum-0) \foreach \x in {1,...,\samples}{-- (sum-\x)} node[right]{three + four};

  % one + two + three
  \addcurves{\samples}{0}{10}{0}{6}{one,two,three}{sum}
  \draw[red!50!green!50!black] (sum-0)
  \foreach \x in {1,...,\samples}{-- (sum-\x)} node[right]{one + two + three};

\end{tikzpicture}
\end{document}

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