User:Jholsenback

Random Scratchings

I'm currently working on migrating the current documentation set to this Wiki. There isn't any content yet, so I've just planted at flag for now.

LaTex

These appear in the reference section, and when they are wrapped in the <math></math> tags they ...

% FILE: blobdens
% --------
\begin{displaymath}
  \mathit{density} =
  \mathit{strength}\cdot
  \left(1-\left(\frac{\mathit{distance}}{\mathit{radius}}\right)^2\right)^2
\end{displaymath}

render as: $density=strength\cdot (1-({\frac {distance}{radius}})^{2})^{2}$

  % FILE: curvmath
% --------
\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}

render as: not done yet!

% FILE: lattenua
% --------
\begin{displaymath}
  \mathit{attenuation} =
  \frac{2}
  {1+\left(\frac{d}{\mathit{fade\_distance}}\right)^\mathit{fade\_power}}
\end{displaymath}

render as: ${attenuation}={\frac {2}{1+({\frac {d}{fade\_distance}})^{fade\_power}}}$

% FILE: medatten
% --------
\begin{displaymath}
  \mathit{attenuation} =
  \frac{1}
  {1+\left(\frac{d}{\mathit{fade\_distance}}\right)^\mathit{fade\_power}}
\end{displaymath}

render as: ${attenuation}={\frac {1}{1+({\frac {d}{fade\_distance}})^{fade\_power}}}$

% FILE: prod
% ----
\begin{displaymath}
  \prod_{i=b}^n a
\end{displaymath}

render as: $prod_{i=b}^{n}a$

% sormath
% -------
\begin{displaymath}
  r^2 = f(h) = A\cdot h^3 + B\cdot h^2 + C\cdot h + D
\end{displaymath}

render as: $r^{2}=f(h)=A\cdot h^{3}+B\cdot h^{2}+C\cdot h+D$

% FILE: sqemath
% -------
\begin{displaymath}
  f(x,y,z) =
  \left(|x|^{\left(\frac{2}{e}\right)} + |y|^{\left(\frac{2}{e}\right)}
  \right)^{\left(\frac{e}{n}\right)} + |z|^{\left(\frac{2}{n}\right)} - 1 = 0
\end{displaymath}

render as: $f(x,y,z)=(|x|^{({\frac {2}{e}})}+|y|^{({\frac {2}{e}})})^{({\frac {e}{n}})}+|z|^{({\frac {2}{n}})}-1=0$

% FILE: sum
% ---
\begin{displaymath}
  \sum_{i=b}^n a
\end{displaymath}

render as: $sum_{i=b}^{n}a$

These appear in the tutorial section, and when they are wrapped in the <math></math> tags they ...

% FILE: polyfunc1
% ---------
\begin{displaymath}
  \sqrt{x^2+y^2+z^2} = r
\end{displaymath}

render as: $sqrt{x^{2}+y^{2}+z^{2}}=r$

% FILE: polyfunc2
% ---------
\begin{displaymath}
  x^2+y^2+z^2-r = 0
\end{displaymath}

render as: $x^{2}+y^{2}+z^{2}-r=0$

% FILE: polyfunc3
% ---------
\begin{displaymath}
  z = \frac{2xy^2}{x^2+y^4}
\end{displaymath}

render as: $z={\frac {2xy^{2}}{x^{2}+y^{4}}}$

% FILE: polyfunc4
% ---------
\begin{displaymath}
  x^2z + y^4z - 2xy^2 = 0
\end{displaymath}

render as: $x^{2}z+y^{4}z-2xy^{2}=0$

% FILE: polyfunc5
% ---------
\begin{displaymath}
  \sqrt{\left(\sqrt{x^2+z^2}-r_1\right)^2+y^2} = r_2
\end{displaymath}

render as: $sqrt{({\sqrt {x^{2}+z^{2}}}-r_{1})^{2}+y^{2}}=r_{2}$

% FILE: polyfunc6
% ---------
\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}

render as: $x^{4}+2x^{2}y^{2}+2x^{2}z^{2}-2(r_{1}^{2}+r_{2}^{2})x^{2}+y^{4}+2y^{2}z^{2}+2(r_{1}^{2}-r_{2}^{2})y^{2}+z^{4}-2(r_{1}^{2}+r_{2}^{2})z^{2}+(r_{1}^{2}-r_{2}^{2})^{2}=0$