Technical‎ > ‎Houdini‎ > ‎Isosurface‎ > ‎

### 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))`