Difference between revisions of "User:Jholsenback"

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\end{displaymath}
 
\end{displaymath}
 
</pre>
 
</pre>
 +
<p class="Note">'''Note:''' This formula has been corrected!</p>
 
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>
 
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>
<p class="Note">'''Note:''' This formula has been corrected!</p>
 
  
 
====Curve Math====
 
====Curve Math====

Revision as of 14:58, 14 October 2009

Projects

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

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:

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:

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:

Attenuation

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

render as:

Product

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

render as:

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:

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:

Sum

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

render as:

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:

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

render as:

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

render as:

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

render as:

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

render as:

% 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: