LaTeX: Figures - Scaling, Rotating & Trimming

Document 1

Scaling, Rotating & Trimming

LaTeX Source Ready

\documentclass{article}
\usepackage{graphicx}
\usepackage{amsmath}

\begin{document}

\section{Tensor Transformations: Rotated Figure Orientation}

In Minkowski spacetime with metric $\eta_{\mu\nu} = \text{diag}(1, -1, -1, -1)$, an orthogonal rotation or coordinate boost transforms tensor field components. When embedding wide schematic diagrams, the \texttt{angle} option in \texttt{\textbackslash includegraphics} performs exact rotation:

\begin{figure}[htbp]
    \centering
    \includegraphics[angle=90, width=0.45\textwidth]{em_tensor.png}
    \caption{Electromagnetic tensor diagram rotated counter-clockwise by $90^\circ$ for landscape display.}
    \label{fig:rotated_tensor}
\end{figure}

Under a Lorentz transformation matrix $\Lambda^\mu{}_\alpha$, the field-strength tensor transforms as:
\begin{equation}
    F'^{\mu\nu} = \Lambda^\mu{}_\alpha \Lambda^\nu{}_\beta F^{\alpha\beta}
\end{equation}
preserving the gauge invariants $I_1 = -\frac{1}{2}F_{\mu\nu}F^{\mu\nu} = \mathbf{E}^2 - c^2\mathbf{B}^2$ and $I_2 = -\frac{1}{4}F_{\mu\nu}\tilde{F}^{\mu\nu} = c\mathbf{E}\cdot\mathbf{B}$.

\end{document}

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Formulation Guide

Rotate graphics by an angle in degrees: \includegraphics[angle=90, width=...]{...}
Positive angles rotate counter-clockwise; negative angles rotate clockwise
Order of parameters matters: [angle=90, width=0.45\textwidth] first rotates then rescales

The graphicx package supports geometric transformations on imported figures. Specifying angle=90 rotates the graphic by 90 degrees counter-clockwise before scaling it to fit the specified width.

Document 2

Scaling, Rotating & Trimming

.tex

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Formulation Guide

Crop unwanted margins: trim=left bottom right top
Enforce clipping: clip parameter
Preserve proportional dimensions: keepaspectratio

The trim option specifies dimensions (in PostScript points by default or explicit units like 10mm) to shave off from the left, bottom, right, and top edges. The companion clip boolean ensures that pixels outside the trimmed bounding box are masked from display.

LaTeX 8.7 Scaling, Rotating & Trimming

Scaling, Rotating & Trimming

Rendered Output Preview

Formulation Guide

Scaling, Rotating & Trimming

Rendered Output Preview

Formulation Guide