Difference between revisions of "User:Jholsenback"

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===Projects===
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===Organization===
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I'm currently working on migrating the current [[Documentation:Contents|documentation]] set to this Wiki.
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<p align="justify">
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===Reference Section===
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Basically, I've been using this area as a scratch pad of sorts. As I complete things, and clean-up I'll probably just add a link [[User:Jholsenback#Links|here]] of reference. </p>
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These LaTex markup segments appear in the reference section. When they are wrapped in the <nowiki><math></math></nowiki> tags they ...
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===Scratch Pad===
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====Blob Density====
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===Links===
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<pre>
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:*The source and notes on the [[Documentation:LaTex_Files|LaTex]] markup used in the documentation.
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% FILE: blobdens
 
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% --------
 
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\begin{displaymath}
 
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  \mathit{density} =
 
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  \mathit{strength}\cdot
 
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  \left(1-\left(\frac{\mathit{distance}}{\mathit{radius}}\right)^2\right)^2
 
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\end{displaymath}
 
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</pre>
 
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<p class="Note">'''Note:''' This formula has been corrected!</p>
 
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render as: <p><math>{\textit{density}} = {\textit{strength}}\cdot \left(1-\left(\frac {\min (\textit{distance}, \textit{radius})} {\textit{radius}} \right)^2\right)^2</math></p>
 
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====Curve Math====
 
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<pre>
 
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% FILE: curvmath
 
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% --------
 
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\begin{displaymath}
 
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  \begin{array}{l}
 
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    b = M \cdot x, \mathrm{with:}
 
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    \\ \\
 
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    b = \left[
 
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      \begin{array}{c}
 
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        r(j)^2 \\
 
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        r(j+1)^2 \\
 
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        2 \cdot r(j) \cdot (r(j+1)-r(j-1)) \\
 
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        \hline
 
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        h(j+1)-h(j-1) \\
 
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        2 \cdot r(j+1) \cdot (r(j+2)-r(j)) \\
 
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        \hline
 
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        h(j+2)-h(j)
 
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      \end{array}
 
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    \right]
 
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    \\ \\
 
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    M = \left[
 
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      \begin{array}{c c c c}
 
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        h(j)^3 & h(j)^2 & h(j) & 1 \\
 
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        h(j+1)^3 & h(j+1)^2 & h(j+1) & 1 \\
 
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        3\cdot h(j)^2 & 2\cdot h(j) & 1 & 0 \\
 
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        3\cdot h(j+1)^2 & 2\cdot h(j+1) & 1 & 0
 
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      \end{array}
 
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    \right]
 
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    \\ \\
 
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    x = \left[
 
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      \begin{array}{c}
 
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        A(j)\\ B(j)\\ C(j)\\ D(j)
 
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      \end{array}
 
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    \right]
 
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  \end{array}
 
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\end{displaymath}
 
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</pre>
 
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render as:<p>
 
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<math>
 
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\begin{array}{l}
 
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    b = M \cdot x, \mathrm{with:}
 
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    \\ \\
 
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    b = \left[
 
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      \begin{array}{c}
 
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        r(j)^2 \\
 
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        r(j+1)^2 \\
 
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        2 \cdot r(j) \cdot (r(j+1)-r(j-1)) \\
 
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        \hline
 
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        h(j+1)-h(j-1) \\
 
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        2 \cdot r(j+1) \cdot (r(j+2)-r(j)) \\
 
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        \hline
 
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        h(j+2)-h(j)
 
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      \end{array}
 
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    \right]
 
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    \\ \\
 
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    M = \left[
 
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      \begin{array}{c c c c}
 
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        h(j)^3 & h(j)^2 & h(j) & 1 \\
 
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        h(j+1)^3 & h(j+1)^2 & h(j+1) & 1 \\
 
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        3\cdot h(j)^2 & 2\cdot h(j) & 1 & 0 \\
 
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        3\cdot h(j+1)^2 & 2\cdot h(j+1) & 1 & 0
 
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      \end{array}
 
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    \right]
 
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    \\ \\
 
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    x = \left[
 
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      \begin{array}{c}
 
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        A(j)\\ B(j)\\ C(j)\\ D(j)
 
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      \end{array}
 
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    \right]
 
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  \end{array}
 
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</math>
 
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</p>
 
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====Light Fading====
 
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<pre>
 
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% FILE: lattenua
 
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% --------
 
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\begin{displaymath}
 
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  \mathit{attenuation} =
 
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  \frac{2}
 
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  {1+\left(\frac{d}{\mathit{fade\_distance}}\right)^\mathit{fade\_power}}
 
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\end{displaymath}
 
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</pre>
 
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render as:
 
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<p>
 
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<math>
 
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  \textit{attenuation} =
 
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  \frac{2}
 
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  {1+\left(\frac{\textit d}{\textit{fade\_distance}}\right)^\textit{fade\_power}}
 
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</math>
 
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</p>
 
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====Attenuation====
 
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<pre>
 
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% FILE: medatten
 
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% --------
 
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\begin{displaymath}
 
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  \mathit{attenuation} =
 
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  \frac{1}
 
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  {1+\left(\frac{d}{\mathit{fade\_distance}}\right)^\mathit{fade\_power}}
 
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\end{displaymath}
 
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</pre>
 
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render as:<p><math>\textit {attenuation} = \frac{1}{1+\left(\frac \textit {d} \textit {fade\_distance}\right)^\textit {fade\_power}}</math></p>
 
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====Product====
 
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<pre>
 
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% FILE: prod
 
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% ----
 
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\begin{displaymath}
 
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  \prod_{i=b}^n a
 
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\end{displaymath}
 
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</pre>
 
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render as:<p><math>\prod^\textit {n}_{\textit i \textit = \textit b}\textit  a</math></p>
 
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====Surface of Revolution====
 
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<pre>
 
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% sormath
 
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% -------
 
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\begin{displaymath}
 
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  r^2 = f(h) = A\cdot h^3 + B\cdot h^2 + C\cdot h + D
 
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\end{displaymath}
 
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</pre>
 
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render as:<p><math>r^2 = f(h) = A\cdot h^3 + B\cdot h^2 + C\cdot h + D</math></p>
 
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====Superquadric Ellipsoid====
 
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<pre>
 
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% FILE: sqemath
 
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% -------
 
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\begin{displaymath}
 
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  f(x,y,z) =
 
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  \left(|x|^{\left(\frac{2}{e}\right)} + |y|^{\left(\frac{2}{e}\right)}
 
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  \right)^{\left(\frac{e}{n}\right)} + |z|^{\left(\frac{2}{n}\right)} - 1 = 0
 
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\end{displaymath}
 
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</pre>
 
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render as:<p><math>f(x,y,z) = (|x|^{(\frac{2}{e})} + |y|^{(\frac{2}{e})})^{(\frac{e}{n})} + |z|^{(\frac{2}{n})} - 1 = 0</math></p>
 
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====Sum====
 
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<pre>
 
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% FILE: sum
 
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% ---
 
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\begin{displaymath}
 
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  \sum_{i=b}^n a
 
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\end{displaymath}
 
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</pre>
 
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render as:<p><math>\sum^{\textit n}_{\textit i \textit = \textit b}\textit a</math></p>
 
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===Tutorial Section===
 
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<p>These LaTex segments appear in the tutorial section. When they are wrapped in the <nowiki><math></math></nowiki> tags they ...</p>
 
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====Creating the polynomial function====
 
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<pre>
 
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% FILE: polyfunc1
 
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% ---------
 
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\begin{displaymath}
 
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  \sqrt{x^2+y^2+z^2} = r
 
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\end{displaymath}
 
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</pre>
 
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render as: <math>{\sqrt{x^2+y^2+z^2}} = r</math>
 
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<pre>
 
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% FILE: polyfunc2
 
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% ---------
 
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\begin{displaymath}
 
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  x^2+y^2+z^2-r = 0
 
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\end{displaymath}
 
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</pre>
 
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render as: <math>\displaystyle x^2+y^2+z^2-r = 0</math>
 
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<pre>
 
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% FILE: polyfunc3
 
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% ---------
 
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\begin{displaymath}
 
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  z = \frac{2xy^2}{x^2+y^4}
 
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\end{displaymath}
 
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</pre>
 
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render as: <math>z = \frac{2xy^2}{x^2+y^4}</math>
 
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<pre>
 
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% FILE: polyfunc4
 
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% ---------
 
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\begin{displaymath}
 
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  x^2z + y^4z - 2xy^2 = 0
 
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\end{displaymath}
 
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</pre>
 
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render as: <math>\displaystyle x^2z + y^4z - 2xy^2 = 0</math>
 
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<pre>
 
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% FILE: polyfunc5
 
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% ---------
 
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\begin{displaymath}
 
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  \sqrt{\left(\sqrt{x^2+z^2}-r_1\right)^2+y^2} = r_2
 
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\end{displaymath}
 
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</pre>
 
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render as: <math>{\sqrt{(\sqrt{x^2+z^2}-r_1)^2+y^2}} = r_2</math>
 
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<pre>
 
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% FILE: polyfunc6
 
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% ---------
 
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\begin{displaymath}
 
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  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+
 
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  z^4-2(r_1^2+r_2^2)z^2+(r_1^2-r_2^2)^2 = 0
 
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\end{displaymath}
 
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</pre>
 
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render as: <math>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</math>
 

Revision as of 13:29, 23 March 2010

Organization

Basically, I've been using this area as a scratch pad of sorts. As I complete things, and clean-up I'll probably just add a link here of reference.

Scratch Pad

Links

  • The source and notes on the LaTex markup used in the documentation.
Retrieved from "https://wiki.povray.org/content?title=User:Jholsenback&oldid=2158"