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Math

Here is describe some basic mathematical functions

Algebra:

($X^4/$PI+$Y^4/$PI)*$Z/$PI/3+$X*$Y+1/10^2.4
Black Hole:

$X*$X - 2/($Y*$Y) + $Z*$Z
Cayley Ruled Cubic:

$Y*$Y*$Y - $X*$Y*$Z - $Z*$Z
Duplin Cyclides:

(2^2 - 0^2 - (2 + 2.1)^2) * (2^2 - 0^2 - (2 - 2.1)^2)*($X^4+$Y^4+$Z^4)+ 2*((2^2 - 0^2 - (2 + 2.1)^2 )*(2^2 - 0^2 - (2 - 2.1)^2)* ($X^2 * $Y^2+$X^2 * $Z^2+$Y^2 * $Z^2))+2* 2^2 *((-0^2-2^2+2^2+2.1^2)* (2 *$X *2+2* $Y* 0-2^2)-4*0 *2.1^2 *$Y)*($X^2+$Y^2+$Z^2)+ 4 * 2^4 * (2 *$X+0 *$Y)* (-2^2+0 * $Y+2 * $X)+4* 2^4 * 2.1^2 * $Y^2+2^8
Fanfare:

-$X^3 + $Z^2 + $Y^2
Helicoid:

$X*tan($Z/0.01)-$Y
HourGlass:

(sqrt($X^2+$Z^2)*ch("c")) - (sqrt($X^2+$Z^2)-ch("r")) + $Y^2 - (ch("R")^2)

Channel c, r and R need to be created as parameters.
Hyperbolic:

$X * $X + $Y - $Z*$Z
Hyperboloid One Sheet:

$X*$X - $Y*$Y + $Z*$Z - 0.5
Hyperboloid Two Sheet:

- 2*$X*$X +$Y*$Y - 2*$Z*$Z - 0.05
Hyper Knife:

ch("a") -($X*$X + $Y - $Z*$Z)^2+(cos($X+sin($X)/ch("b")) +cos($Y+sin($Y)/ch("b")) +cos($Z+sin($Z)/ch("b")))

Parameters a and b must be set.
Moebius:

-ch("b")^2 * $Y + $X^2 * $Y + $Y^3 - 2*ch("b") * $X* $Z - 2 * $X^2*$Z -2*$Y^2 * $Z+$Y*$Z^2

Parameter b net to be set.
Monkey Saddle:

$X*($X^ch("a") - ch("b") *$Y^2) - $Z

Parameters a and b must be set.
Nebelgebilde:

($X-ch("b")-ch("a")^6)*($X-ch("b")+ch("a")^4)*($X+ch("b")-ch("a")^4)*($X+ch("b")+ch("a")^4)+$Y^4-$Z^6

a and b parameters need to be set.
Paraboloid:

$X*$X - $Y + $Z*$Z
Plucker's Conoid:

$X*$X - $X*$X*$Z - $Y*$Y*$Z
Roman Surface:

$X^2*$Y^2 + $X^2*$Z^2 + $Y^2*$Z^2 + 2*ch("a")*$X*$Y*$Z
Saddle:

$X*$X - $Y - $Z*$Z
Stairs:

$X*cos(deg($Y*ch("c")))+ $Z*sin(deg($Y*ch("c")))
Or
atan2($Y*cos(deg($Z))+$X*sin(deg($Z)),$X*cos(deg($Z))-$Y*sin(deg($Z)))

Parameter c must be added.
Steiner 01:

$X^2*$Y^2 - $X^2*$Z^2 + $Y^2*$Z^2 -$X*$Y*$Z
Steiner 02:

$Y^2 - 2 * $X*$Y^2 -$X*$Z^2 + $X^2*$Y^2 + $X^2*$Z^2 - $Z^4
Whitney Umbrella:

$X*$X - $Y*$Y*$Z
4 Leaf 01:

($X*$X + $Y*$Y)*sqrt($X*$X+$Y*$Y)/(2*sqrt(1-$Z*$Z)) * $Y*$Y + $X*$X - $Y*$Y + $X*$X - ($X*$X + $Y*$Y)*sqrt($X*$X+$Y*$Y)/(2*sqrt(1-$Z*$Z))
4 Leaf 02:

- $Y*$Y + $X*$X - ($X*$X + $Y*$Y)*sqrt($X*$X+$Y*$Y)/(2*sqrt(1-$Z*$Z))

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