User:Jholsenback

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Reference Section

These LaTex 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}

Note: This formula has been corrected!

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:

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

Product

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

render as:

$\prod _{{\textit {i}}{\textit {=}}{\textit {b}}}^{\textit {n}}{\textit {a}}$

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:

$\sum _{{\textit {i}}{\textit {=}}{\textit {b}}}^{\textit {n}}{\textit {a}}$

Tutorial Section

These LaTex segments appear 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: ${\sqrt {x^{2}+y^{2}+z^{2}}}=r$

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

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

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

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

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

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

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