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Thank you Stefan,

I am actually not opposed to writing my paper on writeLaTex, it is rather nice. That being said I am afraid they will upgrade soon and break the drawing as well. I have followed your advise already and generated a PDF of the drawing I want. I will be able to include this in later ...

Link to latest version of the code on writelatex:
https://www.writelatex.com/read/vwhwddcvsgsh

Latest Minimal (I removed a couple of lines in preamble)
% Dominik Gothe
% Based on Marco Miani's work on "Spherical and cartesian grids"
\documentclass[12pt]{article}
\usepackage{tikz}
\usepackage ...

Hi gothed,
It's caused by a bug in a newer TikZ/pgf version. writeLaTeX still uses an older one, that's why the difference.

You can easily fix it by replacing .estyle by .style (styles for Longitudenal Planes, Latitudenal Planes, and at the beginning of the figure in the tikzpicture options).

We ...

Attempting to render the following MWE in MikTex via pdfLaTex results in no errors, however, incorrect rendering (see attachment: bad_render).
% Dominik Gothe
% Based on Marco Miani's work on "Spherical and cartesian grids"
\documentclass[12pt]{article}
\usepackage{tikz}
\usepackage{pgfplots ...