User:Jholsenback

Projects

I'm currently working on migrating the current documentation set to this Wiki.

LaTex Markup

These Tex markup segments appear in the reference section. When they are wrapped in the <math></math> tags they ...

Blob Density

% 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:

${\textit {density}}={\textit {strength}}\cdot \left(1-\left({\frac {\min({\textit {distance}},{\textit {radius}})}{\textit {radius}}}\right)^{2}\right)^{2}$

Curve Math

  % 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:

${\begin{array}{l}b=M\cdot x,\mathrm {with:} \\\\b=\left[{\begin{array}{c}r(j)^{2}\\r(j+1)^{2}\\2\cdot r(j)\cdot (r(j+1)-r(j-1))\\\hline h(j+1)-h(j-1)\\2\cdot r(j+1)\cdot (r(j+2)-r(j))\\\hline h(j+2)-h(j)\end{array}}\right]\\\\M=\left[{\begin{array}{c c c c}h(j)^{3}&h(j)^{2}&h(j)&1\\h(j+1)^{3}&h(j+1)^{2}&h(j+1)&1\\3\cdot h(j)^{2}&2\cdot h(j)&1&0\\3\cdot h(j+1)^{2}&2\cdot h(j+1)&1&0\end{array}}\right]\\\\x=\left[{\begin{array}{c}A(j)\\B(j)\\C(j)\\D(j)\end{array}}\right]\end{array}}$

Light Fading

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

render as:

${\textit {attenuation}}={\frac {2}{1+\left({\frac {\textit {d}}{\textit {fade\_distance}}}\right)^{\textit {fade\_power}}}}$

Attenuation

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

render as:

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

Product

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

render as: $\prod _{i=b}^{n}a$

Surface of Revolution

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

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

Superquadric Ellipsoid

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

Sum

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

render as: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum^{n}_{i=b} a}

These Tex segments in the tutorial section. When they are wrapped in the <math></math> tags they ...

Creating the polynomial function

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

render as: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\sqrt{x^2+y^2+z^2}} = r}

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

render as: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2+y^2+z^2-r = 0}

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

render as: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z = \frac{2xy^2}{x^2+y^4}}

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

render as: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2z + y^4z - 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: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\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: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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}