Delta-like symbol in LaTeX

Question

I'd like to write a majuscule delta-like symbol in LaTeX but I can't find it's syntax anywhere. You can see the symbol on equation (12) of the following paper:

"Two-Frame Motion Estimation Based on Polynomial Expansion".

Answer 1

Note that the document uses Springer's LNCS style. In this style, all Greek letters are in italics, and vectors are denoted by boldface.

Most likely the bold italic Delta is produced in this particular case by something similar to this:

\documentclass{llncs}
\begin{document}
$\vec{\Delta}$
\end{document}

The result is:

Note that if you used the article class, the same code would produce a normal Delta with an arrow:

Answer 2

That is just $\Delta$ which is different from $\delta$. LateX symbols are case-sensitive. See any of the LaTeX cheat sheets as e.g. this one a U Colorado.

Answer 3

If one really wants a bold italic Delta, the way to go is

\usepackage{bm}
\newcommand{\bfitDelta}{\bm{\mathit{\Delta}}}

Of course, one could write every time \bm{\mathit{\Delta}}.

Answer 4

There are several such symbols in Unicode, and hence unicode-math. The Laplacian operator ∆ (U+2206) is \increment. This is semantically a math operator instead of a Greek letter. It provides △ as either the binary operator \bigtriangleup or the letter-like symbol \triangle, and ▵ as \vartriangle. There are also the letters Δ (\mupDelta or \symup\Delta), (\mitDelta or \symit\Delta), (\mbfDelta or \symbfup\Delta) and (\mbfitDelta or \symbfit\Delta). \Delta might mean either the upright or slanted letter. Finally, there are the sans-serif math letters (\mbfitsansDelta or \symbfsfup\Delta) and (\mbfsansdelta or \symbfsfit\Delta) for tensors.

You appear to want to use slanted capital Greek letters by default, including for the Δ symbol. You can acoomplish that with the following:

\documentclass{article}
% To fit into the width at TeX.SX:
\usepackage[paperwidth=10cm]{geometry}
\usepackage[math-style=ISO]{unicode-math}
\begin{document}
Scalar ( \Delta t ), vector ( \symbf{\Delta x} ),
Laplacian ( \increment f(p) ).
\end{document}

You might instead prefer to use upright Delta symbols even though Greek letters such as Γ are slanted in ISO style:

\documentclass{article}
% To fit into the width at TeX.SX:
\usepackage[paperwidth=10cm]{geometry}
\usepackage[math-style=ISO]{unicode-math}
\begin{document}
Scalar ( \symup\Delta t ), vector ( \symbfup\Delta\symbf{x} ),
Laplacian ( \increment \Gamma(p) ).
\end{document}

Although \symbf works only on the letters and not the operators, unicode-math supports \boldmath if you load a math font that has a bold weight (currently XITS Math, Libertinus Math and Minion Math). You can also \setmathfont[version=bold]{XITS Math Bold}. The \boldsymbol\increment (from amsbsy.sty) will work.

If you want a bold slanted Δ symbol for your bold slanted vector symbols in PDFTeX, I recommend the isomath package.

Answer 5

This looks very much like \Updelta (\usepackage{ upgreek })

As you can see here, when compared with the standard Delta, the Updelta has an italic look to it.