i_algbr Library part 3© Mike Williams 2001,2002,2003,2004 

See here for details of "Field Strength", "Field Limit", "SOR switch", "SOR offset" and "SOR angle" parameters  
The Quartic paraboloid is similar to a paraboloid, but has a squarer shape.
The parameters are:
function { f_quartic_paraboloid(x,y,z,1)}  
The Quartic saddle is similar to a saddle, but has a squarer shape.
The parameters are:
function { f_quartic_saddle(x,y,z,1)}  
The Quartic cylinder looks a bit like a cylinder that's swallowed an egg.
The parameters are:
function {  f_quartic_cylinder(x,y,z,1,0.6,0.3)}  
The "Steiners Roman" is composed of four identical triangular pads which together make up
a sort of rounded tetrahedron. There are creases along the X, Y and Z axes where the pads meet. It is a model of the projective plane. The parameters are:
function { f_steiners_roman(x,y,z,1)+0}  
The Strophoid is like an infinite plane with a bulb sticking out of it.
The parameters are:
When the Size parameter is 3 times the Sharpness, the surface is given the special name "trisectrix of Maclaurin". function { f_strophoid(x,y,z,1,1.5,1,1.2)}  
The 2d strophid curve can be extruded in the Z direction
or rotated about various axes by using the SOR parameters.
The parameters are:
function { f_strophoid_2d(x,y,z,1,1.5,1,1.2,1,1,180)}  
I've rotated this Glob function through z*90 so that it looks like
a falling drip of thick liquid.
The parameters are:
function { f_glob(x,y,z,1)}  
This "pillow" surface apparently featured on the back cover of the 1992
Siggraph proceedings.
The parameters are:
function { f_pillow(x,y,z,1)}  
This is the "Crossed Trough" surface.
The parameters are:
function {  f_crossed_trough(x,y,z,1)+0}  
The "Witch of Agnesi" surface looks something like a witches hat.
The parameters are:
function {  f_witch_of_agnesi(x,y,z,1,0.02)}  
The 2d version of the Witch of Agnesi curve can be extruded in the Z direction
or rotated about various axes by use of the SOR parameters.
The parameters are:
function { f_witch_of_agnesi_2d (x,y,z,1, 0.2, 0.04, 1, 0, 0)}  
The "Mitre" surface looks a bit like an ellipsoid which has been
nipped at each end with a pair of sharp nosed pliers.
The parameters are:
function { f_mitre(x,y,z,1)}  
One odd thing about the "Odd" surface is that it's identical to the "Cushion" surface. This time I've cut it in half so that you can see the way that the rear face puckers forward to meet the dimple from the front face. The parameters are:
function { f_odd(x,y,z,1)}  
The "Heart"  a surface for Valentine's Day.
The parameters are:
function { f_heart(z,x,y,1)}  
The Nodal Cubic is something like what you'd get if you were to extrude the Stophid2D curve
along the X axis and then lean it over.
The parameters are:
function { f_nodal_cubic(x,y,z,0.1)}  
This is the "Umbrella" surface
The parameters are:
function { f_umbrella(x,y,z,1)}  
This is the Enneper surface.
The parameters are:
function { f_enneper(x,y,z,0.1)}  

Download a zip file containing the POV source files for all the images that appear on this page. 
