Unexpected TikZ Output In Let \n1={2pt}

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Introduction

When working with TikZ, a powerful drawing package in LaTeX, users often encounter unexpected output due to various reasons. In this article, we will discuss a specific issue related to the let command in TikZ, specifically when using the syntax let \n1={2pt}. This problem arises when trying to perform calculations or transformations on coordinates in a TikZ plot.

The Problem

In the following code, in the first plot, we manually entered the rotated coordinates. In other words, each coordinate is transformed by the rotation matrix (using cos 25 and sin 25) as the function is being plotted.

\documentclass[tikz,border=10pt]{standalone}
\begin{document}
\begin{tikzpicture}
\draw[->] (0,0) -- (4,0) node[right] {$x$};
\draw[->] (0,0) -- (0,4) node[above] {$y$};
\draw[domain=0:4,smooth,variable=\x,red] plot (\x, {sin(25*\x)});
\draw[domain=0:4,smooth,variable=\x,blue] plot (\x, {sin(25*\x+90)});
\draw[domain=0:4,smooth,variable=\x,green] plot (\x, {sin(25*\x+180)});
\draw[domain=0:4,smooth,variable=\x,orange] plot (\x, {sin(25*\x+270)});
\end{tikzpicture}
\end{document}

However, when we try to use the let command to perform the same transformation, we get unexpected output.

\documentclass[tikz,border=10pt]{standalone}
\begin{document}
\begin{tikzpicture}
\draw[->] (0,0) -- (4,0) node[right] {$x$};
\draw[->] (0,0) -- (0,4) node[above] {$y$};
\draw[domain=0:4,smooth,variable=\x,red] plot (\x, {sin(25*\x)});
\draw[domain=0:4,smooth,variable=\x,blue] plot (\x, {sin(25*\x+90)});
\draw[domain=0:4,smooth,variable=\x,green] plot (\x, {sin(25*\x+180)});
\draw[domain=0:4,smooth,variable=\x,orange] plot (\x, {sin(25*\x+270)});
\draw[domain=0:4,smooth,variable=\x,black] plot (\x, {let \n1={2pt} in \n1});
\end{tikzpicture}
\end{document}

The Issue with let \n1={2pt}

The problem lies in the way TikZ handles the let command. When we use let \n1={2pt}, TikZ creates a new coordinate system with the specified value, but it does not update the current coordinate system. As a result, the subsequent calculations are performed in the original coordinate system, leading to unexpected output.

Workaround

To avoid this issue, we can use the `` command with the shift option, which updates the current coordinate system.

\documentclass[tikz,border=10pt]{standalone}
\begin{document}
\begin{tikzpicture}
\draw[->] (0,0) -- (4,0) node[right] {$x$};
\draw[->] (0,0) -- (0,4) node[above] {$y$};
\draw[domain=0:4,smooth,variable=\x,red] plot (\x, {sin(25*\x)});
\draw[domain=0:4,smooth,variable=\x,blue] plot (\x, {sin(25*\x+90)});
\draw[domain=0:4,smooth,variable=\x,green] plot (\x, {sin(25*\x+180)});
\draw[domain=0:4,smooth,variable=\x,orange] plot (\x, {sin(25*\x+270)});
\draw[domain=0:4,smooth,variable=\x,black] plot (\x, {let \n1={2pt} in \n1+shift (\n1,0)});
\end{tikzpicture}
\end{document}

Conclusion

In conclusion, the let command in TikZ can be tricky to use, especially when performing calculations or transformations on coordinates. By understanding the behavior of the let command and using the shift option, we can avoid unexpected output and create accurate plots.

Tips and Variations

  • To perform more complex calculations, you can use the let command with multiple assignments, such as let \n1={2pt}, \n2={\n1+1pt} in \n2.
  • To update the current coordinate system, you can use the shift option with the let command, such as let \n1={2pt} in \n1+shift (\n1,0).
  • To create a new coordinate system, you can use the scope environment with the let command, such as scope let \n1={2pt} in \n1.

Example Use Cases

  • Creating a plot with rotated coordinates
  • Performing calculations on coordinates in a plot
  • Updating the current coordinate system in a plot

Common Issues and Solutions

  • Issue: Unexpected output when using the let command.
  • Solution: Use the shift option with the let command to update the current coordinate system.
  • Issue: Inaccurate calculations when using the let command.
  • Solution: Use the let command with multiple assignments to perform more complex calculations.
    TikZ Q&A: Understanding the let Command =====================================================

Introduction

TikZ is a powerful drawing package in LaTeX, used for creating a wide range of graphics, from simple diagrams to complex plots. However, its syntax can be complex and sometimes confusing, especially for beginners. In this article, we will answer some frequently asked questions about the let command in TikZ, a command that is often misunderstood.

Q: What is the let command in TikZ?

A: The let command in TikZ is used to assign a value to a variable, which can then be used in subsequent calculations or transformations.

Q: How do I use the let command in TikZ?

A: The basic syntax of the let command is let \n1={value} in {expression}, where \n1 is the variable name, {value} is the value assigned to the variable, and {expression} is the expression that uses the variable.

Q: What is the difference between let and let \n1={value} in {expression}?

A: The let command without the in keyword is used to assign a value to a variable, but it does not update the current coordinate system. The let \n1={value} in {expression} syntax, on the other hand, updates the current coordinate system with the assigned value.

Q: Why do I get unexpected output when using the let command?

A: The let command can produce unexpected output if the assigned value is not a valid coordinate or if the expression using the variable is not correctly formatted.

Q: How do I avoid unexpected output when using the let command?

A: To avoid unexpected output, make sure to use the correct syntax and format for the let command, and ensure that the assigned value is a valid coordinate.

Q: Can I use the let command with multiple assignments?

A: Yes, you can use the let command with multiple assignments by separating the assignments with commas, such as let \n1={value1}, \n2={value2} in {expression}.

Q: How do I update the current coordinate system using the let command?

A: To update the current coordinate system using the let command, use the shift option, such as let \n1={value} in \n1+shift (\n1,0).

Q: Can I use the let command in a scope environment?

A: Yes, you can use the let command in a scope environment to create a new coordinate system with the assigned value.

Q: What are some common issues with the let command?

A: Some common issues with the let command include unexpected output, incorrect calculations, and invalid coordinates.

Q: How do I troubleshoot issues with the let command?

A: To troubleshoot issues with the let command, check the syntax and format of the command, ensure that the assigned value is a coordinate, and verify that the expression using the variable is correctly formatted.

Conclusion

In conclusion, the let command in TikZ is a powerful tool for performing calculations and transformations on coordinates. However, its syntax can be complex and sometimes confusing. By understanding the behavior of the let command and using the correct syntax and format, you can avoid unexpected output and create accurate plots.

Tips and Variations

  • Use the let command with multiple assignments to perform more complex calculations.
  • Use the shift option with the let command to update the current coordinate system.
  • Use the scope environment with the let command to create a new coordinate system.
  • Verify that the assigned value is a valid coordinate.
  • Check the syntax and format of the let command.

Example Use Cases

  • Creating a plot with rotated coordinates
  • Performing calculations on coordinates in a plot
  • Updating the current coordinate system in a plot

Common Issues and Solutions

  • Issue: Unexpected output when using the let command.
  • Solution: Use the shift option with the let command to update the current coordinate system.
  • Issue: Inaccurate calculations when using the let command.
  • Solution: Use the let command with multiple assignments to perform more complex calculations.