Difference between revisions of "Documentation:LaTex Files"
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| Line 66: | Line 66: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
\mathit{density} = | \mathit{density} = | ||
\mathit{strength}\cdot | \mathit{strength}\cdot | ||
| Line 84: | Line 83: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
\begin{array}{l} | \begin{array}{l} | ||
b = M \cdot x, \mathrm{with:} | b = M \cdot x, \mathrm{with:} | ||
| Line 130: | Line 128: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
\mathit{attenuation} = | \mathit{attenuation} = | ||
\frac{2} | \frac{2} | ||
| Line 148: | Line 145: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
\mathit{attenuation} = | \mathit{attenuation} = | ||
\frac{1} | \frac{1} | ||
| Line 166: | Line 162: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
\prod_{i=b}^n a | \prod_{i=b}^n a | ||
\end{displaymath} | \end{displaymath} | ||
| Line 182: | Line 177: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
r^2 = f(h) = A\cdot h^3 + B\cdot h^2 + C\cdot h + D | r^2 = f(h) = A\cdot h^3 + B\cdot h^2 + C\cdot h + D | ||
\end{displaymath} | \end{displaymath} | ||
| Line 198: | Line 192: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
f(x,y,z) = (|x|^{(\frac{2}{e})} + |y|^{(\frac{2}{e})})^{(\frac{e}{n})} + |z|^{(\frac{2}{n})} - 1 = 0 | f(x,y,z) = (|x|^{(\frac{2}{e})} + |y|^{(\frac{2}{e})})^{(\frac{e}{n})} + |z|^{(\frac{2}{n})} - 1 = 0 | ||
\end{displaymath} | \end{displaymath} | ||
| Line 214: | Line 207: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
\sum^{\textit n}_{\textit i \textit = \textit b}\textit a | \sum^{\textit n}_{\textit i \textit = \textit b}\textit a | ||
\end{displaymath} | \end{displaymath} | ||
| Line 232: | Line 224: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
{\sqrt{x^2+y^2+z^2}} = r | {\sqrt{x^2+y^2+z^2}} = r | ||
\end{displaymath} | \end{displaymath} | ||
| Line 249: | Line 240: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
\displaystyle x^2+y^2+z^2-r = 0 | \displaystyle x^2+y^2+z^2-r = 0 | ||
\end{displaymath} | \end{displaymath} | ||
| Line 266: | Line 256: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
z = \frac{2xy^2}{x^2+y^4} | z = \frac{2xy^2}{x^2+y^4} | ||
\end{displaymath} | \end{displaymath} | ||
| Line 283: | Line 272: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
\displaystyle x^2z + y^4z - 2xy^2 = 0 | \displaystyle x^2z + y^4z - 2xy^2 = 0 | ||
\end{displaymath} | \end{displaymath} | ||
| Line 299: | Line 287: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
{\sqrt{(\sqrt{x^2+z^2}-r_1)^2+y^2}} = r_2 | {\sqrt{(\sqrt{x^2+z^2}-r_1)^2+y^2}} = r_2 | ||
\end{displaymath} | \end{displaymath} | ||
| Line 315: | Line 302: | ||
\begin{document} | \begin{document} | ||
\begin{displaymath} | \begin{displaymath} | ||
| − | |||
x^4+2x^2y^2+2x^2z^2-2(r_1^2+r_2^2)x^2+y^4+2y^2z^2+2(r_1^2-r_2^2)y^2+z^4-2(r_1^2+r_2^2)z^2+(r_1^2-r_2^2)^2 = 0 | x^4+2x^2y^2+2x^2z^2-2(r_1^2+r_2^2)x^2+y^4+2y^2z^2+2(r_1^2-r_2^2)y^2+z^4-2(r_1^2+r_2^2)z^2+(r_1^2-r_2^2)^2 = 0 | ||
\end{displaymath} | \end{displaymath} | ||
Revision as of 22:31, 22 March 2010
|
This document is protected, so submissions, corrections and discussions should be held on this documents talk page. |
Introduction
These images were generated using this TeX to GIF or PNG Converter for Web Documents, then resized using ImageMagick, and this is the shell script used to process them in a batch.
textogif -dpi 200 -res 0.1 -png blobdens convert blobdens.png -resize 385 blobdens.png textogif -dpi 200 -res 0.1 -png curvmath convert curvmath.png -resize 450 curvmath.png textogif -dpi 200 -res 0.1 -png lattenua convert lattenua.png -resize 395 lattenua.png textogif -dpi 200 -res 0.1 -png medatten convert medatten.png -resize 395 medatten.png textogif -dpi 200 -res 0.1 -png polyfunc1 convert polyfunc1.png -resize 170 polyfunc1.png textogif -dpi 200 -res 0.1 -png polyfunc2 convert polyfunc2.png -resize 185 polyfunc2.png textogif -dpi 200 -res 0.1 -png polyfunc3 convert polyfunc3.png -resize 110 polyfunc3.png textogif -dpi 200 -res 0.1 -png polyfunc4 convert polyfunc4.png -resize 195 polyfunc4.png textogif -dpi 200 -res 0.1 -png polyfunc5 convert polyfunc5.png -resize 275 polyfunc5.png textogif -dpi 200 -res 0.1 -png polyfunc6 convert polyfunc6.png -resize 780 polyfunc6.png textogif -dpi 200 -res 0.1 -png prod convert prod.png -resize 45 prod.png textogif -dpi 200 -res 0.1 -png sormath convert sormath.png -resize 360 sormath.png textogif -dpi 200 -res 0.1 -png sqemath convert sqemath.png -resize 445 sqemath.png textogif -dpi 200 -res 0.1 -png sum convert sum.png -resize 45 sum.png mv blobdens.png RefImgBlobdens.png mv curvmath.png RefImgCurvmath.png mv lattenua.png RefImgLattenua.png mv medatten.png RefImgMedatten.png mv polyfunc1.png TutImgPolyfunc1.png mv polyfunc2.png TutImgPolyfunc2.png mv polyfunc3.png TutImgPolyfunc3.png mv polyfunc4.png TutImgPolyfunc4.png mv polyfunc5.png TutImgPolyfunc5.png mv polyfunc6.png TutImgPolyfunc6.png mv prod.png RefImgProd.png mv sormath.png RefImgSormath.png mv sqemath.png RefImgSqemath.png mv sum.png RefImgSum.png
Reference Section
These images appear in the reference section.
Blob Density
% FILE: blobdens
% --------
% textogif -dpi 200 -res 0.1 -png blobdens
% convert blobdens.png -resize 385 blobdens.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
\mathit{density} =
\mathit{strength}\cdot
\left(1-\left(\frac {\min (\textit{distance}, \textit{radius})} {\textit{radius}} \right)^2\right)^2
\end{displaymath}
\end{document}
Curvmath
% FILE: curvmath
% --------
% textogif -dpi 200 -res 0.1 -png curmath
% convert curvmath.png -resize 450 curvmath.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
\begin{array}{l}
b = M \cdot x, \mathrm{with:}
\\ \\
b = \left[
\begin{array}{c}
r(j)^2 \\
r(j+1)^2 \\
2 \cdot r(j) \cdot (r(j+1)-r(j-1)) \\
\hline
h(j+1)-h(j-1) \\
2 \cdot r(j+1) \cdot (r(j+2)-r(j)) \\
\hline
h(j+2)-h(j)
\end{array}
\right]
\\ \\
M = \left[
\begin{array}{c c c c}
h(j)^3 & h(j)^2 & h(j) & 1 \\
h(j+1)^3 & h(j+1)^2 & h(j+1) & 1 \\
3\cdot h(j)^2 & 2\cdot h(j) & 1 & 0 \\
3\cdot h(j+1)^2 & 2\cdot h(j+1) & 1 & 0
\end{array}
\right]
\\ \\
x = \left[
\begin{array}{c}
A(j)\\ B(j)\\ C(j)\\ D(j)
\end{array}
\right]
\end{array}
\end{displaymath}
\end{document}
Lattenua
% FILE: lattenua
% --------
% textogif -dpi 200 -res 0.1 -png lattenua
% convert lattenua.png -resize 395 lattenua.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
\mathit{attenuation} =
\frac{2}
{1+\left(\frac{\textit d}{\textit{fade\_distance}}\right)^\textit{fade\_power}}
\end{displaymath}
\end{document}
Medatten
% FILE: medatten
% --------
% textogif -dpi 200 -res 0.1 -png medatten
% convert medatten.png -resize 395 medatten.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
\mathit{attenuation} =
\frac{1}
{1+\left(\frac{d}{\mathit{fade\_distance}}\right)^\mathit{fade\_power}}
\end{displaymath}
\end{document}
Prod
% FILE: prod
% --------
% textogif -dpi 200 -res 0.1 -png prod
% convert prod.png -resize 45 prod.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
\prod_{i=b}^n a
\end{displaymath}
\end{document}
Sormath
% FILE: sormath
% --------
% textogif -dpi 200 -res 0.1 -png sormath
% convert sormath.png -resize 360 sormath.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
r^2 = f(h) = A\cdot h^3 + B\cdot h^2 + C\cdot h + D
\end{displaymath}
\end{document}
Sqemath
% FILE: sqemath
% -------
% textogif -dpi 200 -res 0.1 -png sqemath
% convert sqemath.png -resize 445 sqemath.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
f(x,y,z) = (|x|^{(\frac{2}{e})} + |y|^{(\frac{2}{e})})^{(\frac{e}{n})} + |z|^{(\frac{2}{n})} - 1 = 0
\end{displaymath}
\end{document}
Sum
% FILE: sum
% ---
% textogif -dpi 200 -res 0.1 -png sum
% convert sum.png -resize 45 sum.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
\sum^{\textit n}_{\textit i \textit = \textit b}\textit a
\end{displaymath}
\end{document}
Tutorial Section
These images appear in the tutorial section.
Polyfunc1
% FILE: polyfunc1
% ---------
% textogif -dpi 200 -res 0.1 -png polyfunc1
% convert polyfunc1.png -resize 170 polyfunc1.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
{\sqrt{x^2+y^2+z^2}} = r
\end{displaymath}
\end{document}
Polyfunc2
% FILE: polyfunc2
% ---------
% textogif -dpi 200 -res 0.1 -png polyfunc2
% convert polyfunc2.png -resize 185 polyfunc2.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
\displaystyle x^2+y^2+z^2-r = 0
\end{displaymath}
\end{document}
Polyfunc3
% FILE: polyfunc3
% ---------
% textogif -dpi 200 -res 0.1 -png polyfunc3
% convert polyfunc3.png -resize 110 polyfunc3.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
z = \frac{2xy^2}{x^2+y^4}
\end{displaymath}
\end{document}
Polyfunc4
% FILE: polyfunc4
% ---------
% textogif -dpi 200 -res 0.1 -png polyfunc4
% convert polyfunc4.png -resize 195 polyfunc4.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
\displaystyle x^2z + y^4z - 2xy^2 = 0
\end{displaymath}
\end{document}
Polyfunc5
% FILE: polyfunc5
% ---------
% textogif -dpi 200 -res 0.1 -png polyfunc5
% convert polyfunc5.png -resize 275 polyfunc5.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
{\sqrt{(\sqrt{x^2+z^2}-r_1)^2+y^2}} = r_2
\end{displaymath}
\end{document}
Polyfunc6
% FILE: polyfunc6
% ---------
% textogif -dpi 200 -res 0.1 -png polyfunc6
% convert polyfunc6.png -resize 780 polyfunc6.png
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
\begin{displaymath}
x^4+2x^2y^2+2x^2z^2-2(r_1^2+r_2^2)x^2+y^4+2y^2z^2+2(r_1^2-r_2^2)y^2+z^4-2(r_1^2+r_2^2)z^2+(r_1^2-r_2^2)^2 = 0
\end{displaymath}
\end{document}
| Main Table of Contents | Main Table of Contents |
|
This document is protected, so submissions, corrections and discussions should be held on this documents talk page. |