Facade Functions
# Mathematical Equations
## Chair on Cliff
we can define "the surface of a particular chair" $ S $ formally;
$$ S := \{ (x,y,z) ; z = (x^2 + y^2 - 1)(x+y) \land x,y,z \in [-2,2] \} $$
~~~
$ gnuplot
> set terminal qt
> set contour
> set xrange[-2:2]
> set yrange[-2:2]
> set zrange[-2:2]
> set samples 50
> set isosamples 51
> splot (x**2+y**2-1)*(x+y)
~~~
on $ y = x $, we get;
$$ z = 4x(x-0.707)(x+0.707) $$
$$ z' = 12x(x-0.408)(x+0.408) $$
~~~
> plot 4*x**3 - 2*x
~~~
## Schwartz's P Surface
Schwartz's P surface is a 2-manifold whose homology is isomorphic to $ \mathbb{Z} ^ \infty $ .
Schwartz's P surface equation is simple .
$$ \cos(x) + \cos(y) + \cos(z) = 0 $$
This is actually a function with $ \infty $ floors
with 3 floors
~~~
$ gnuplot
> set terminal qt
> set xrange [0:8]
> set yrange [0:8]
> set zrange [-pi:2*pi]
> set contour // show zeropoints and so on
> set samples 200
> set isosamples 201
> splot acos(cos(x)+cos(y))-pi,acos(-cos(x)-cos(y)),acos(cos(x)+cos(y))+pi
~~~
with 2 floors
with 1 floor
~~~
$ gnuplot
> set terminal qt
> set xrange [0:10]
> set yrange [0:10]
> set samples 100
> set isosamples 100
> set pm3d ; set palette rgb 23,28,3
> set contour // projection to xy-plane for some z ( z=0 , ..)
> splot (acos(-cos(x)-cos(y))
~~~
other examples
## Haskell Implementation is underconstruction
with GLUT