# How to draw (Cartesian, cylindrical, and spherical) coordinates and differential elements?

How to draw the following figures?

I tried to do it myself, not an easy job, apparently! I did also find these relevant posts:

However, the drawings are a little bit weird and not so accurate. Any help would be appreciated.

• Each of those drawings is a complicated work all by itself, I don't think they should all be asked in the same question because the answer will have to contain all of them. At least, you should ask a question for each one, and if you could provide some code, it would be appreciated. I mean setting up the axes will allow the users to have something to start from instead of typing everything from scratch. Feb 2, 2016 at 18:12
• Even better: you linked to questions with similar diagrams, one is basically the same except for some detail. You definitely could start from those and see if you can obtain yours with some modifications and then ask questions when you get stuck. Feb 2, 2016 at 18:14

The figure in spherical coordinates can be found here

The code for cylindrical coordinates is next:

  \documentclass{article}
\usepackage[pdftex]{graphicx}
\usepackage{tikz}
\usepackage{amssymb,amsfonts,amsmath}
\usepackage{tikz,tkz-euclide}
\usetikzlibrary{arrows,calc,patterns}

\begin{document}
\begin{figure}
\begin{center}
\begin{tikzpicture}
\coordinate (O) at (0,0);
\coordinate (Ox) at (-3,-3);
\coordinate (Oy) at (4.243,0);  % sqrt{18}
\coordinate (Oz) at (0, 6);

% draw axis
\draw[-latex, line width=1] (O)-- (Ox) node[below] {$x$};
\draw[-latex, line width=1] (O)-- (Oy) node[right] {$y$};
\draw[-latex, line width=1] (O)-- (Oz) node[above] {$z$};

% draw arcs
\draw[thick] ($(0, 0) + (236:3cm and 2cm)$(P) arc
(236:360:3cm and 2cm);
\draw[thick] ($(0, 0) + (236:3cm and 2cm)$(P) arc
(236:360:3cm and 2cm);

\draw[thick] ($(0, 5) + (236:3cm and 2cm)$(P) arc
(236:360:3cm and 2cm);

\draw[thick, -latex] ($(0, 0) + (236:1.5cm and 1cm)$(P) arc
(236:310:1.5cm and 1cm);

\coordinate (Phi) at (0,-1) ;
\node[below] at (Phi) {$\theta$};

\coordinate (A1) at (0, 5);
\coordinate (B) at (3, 5);
\coordinate (C) at (-1.7, 3.3);
\draw[thick] (A1)--(B);
\draw[thick] (A1)--(C);

\coordinate (D) at (1.9,-1.5);
\coordinate (P) at (1.9,3.5);
\draw[thick] (O)--(D);
\draw[thick, dashed] (A1)--(P) node[right, yshift=-1mm] {$P$};
\draw[thick] (D)--(P);
\fill[black] (P) circle (3pt);

\coordinate (A) at (2.6, 4.0);
\draw[thick, dashed] (A1)--(A) node[right, yshift=-1mm, xshift=-1mm] {$A$};

% arcs
\draw[thick] ($(0, 5) + (310:1.8cm and 1.2cm)$(P) arc
(310:330:1.8cm and 1.2cm);

\draw[thick] ($(0, 3.5) + (310:1.8cm and 1.2cm)$(P) arc
(310:330:1.8cm and 1.2cm);

\draw[thick] ($(0, 3.5) + (310:3cm and 2cm)$(P) arc
(310:330:3cm and 2cm);

\coordinate (Q) at (1.9,1.97);
\node[below,xshift=2mm] at (Q) {$Q$};
% \fill[black] (Q) circle (3pt);

\coordinate (B) at (2.6, 2.5);
\node[below,xshift=1mm] at (B) {$B$};
% \fill[black] (B) circle (3pt);
\draw[thick] (A) --(B);

\coordinate (S) at (1.15, 4.1);
\node[below, xshift=-2mm] at (S) {$S$};
% \fill[black] (S) circle (3pt);

\coordinate (R) at (1.15, 2.6);
\node[below, xshift=-2mm] at (R) {$R$};
%\fill[black] (R) circle (3pt);

\coordinate (D) at (1.52, 4.42);
\node[above] at (D) {$D$};
% \fill[black] (D) circle (3pt);

\coordinate (C) at (1.54, 2.86);
\node[below] at (C) {$C$};
%\fill[black] (C) circle (3pt);

\draw[thick] (S) --(R);
\draw[thick] (D) --(C);
\draw[thick] (R) --(Q);
\draw[thick] (C) --(B);

% verticals on the planes
\coordinate (H) at (-1.65,-1.65);
%\fill[black] (H) circle (3pt);
%
\coordinate (I) at (-1.65,3.35);
%\fill[black] (I) circle (3pt);
\draw[thick] (H) --(I);

\coordinate (J) at (3,0);
%\fill[black] (J) circle (3pt);
\coordinate (K) at (3,5);
%\fill[black] (K) circle (3pt);
\draw[thick] (J) --(K);

% filling
\filldraw[opacity=0.2]
(D)--(A) arc (325:306:3cm and 2.2cm)--(S)
arc (305:325:1.8cm and 1.2cm)--cycle;

\filldraw[opacity=0.2]
(P) arc (306:325:3cm and 2.2cm)--(B)
arc (325:306:3.0cm and 2.2cm)--cycle;

\filldraw[opacity=0.2]
(P)--(Q)--(R)--(S)--cycle;

% differential labels
\node[right, yshift=1mm,xshift=2mm, rotate=-20] at (Q) {$\rho d \theta$};
\node[right, yshift=6mm, xshift=-1mm ] at (B) {$dz$};
\node[right,xshift=3mm, yshift=2mm, rotate=-20] at (D) {$d \rho$};

\end{tikzpicture}
\end{center}
\end{figure}
\end{document}


The picture is The cube, is easy and left as homework.