5.4.1 Isosurface

A general method of describing an object is by an equation as implicitly given surface, called isosurface in Pov-Ray. Its syntax is

ISOSURFACE:
  isosurface { FLOAT_USER_FUNCTION [ISOSURFACE_ITEMS]
    [OBJECT_MODIFIERS] }

ISOSURFACE_ITEMS:
  [contained_by { CONTAINER }] & [threshold FLOAT] 
    & [accuracy FLOAT] & [max_gradient FLOAT 
    [evaluate MIN_ESTIMATE, MAX_ESTIMATE, 
    ATTENUATION]] & [open] & [INTERSECTION_LIMIT]

CONTAINER:
  sphere { CENTER, RADIUS } | 
	box { CORNER1, CORNER2 }

INTERSECTION_LIMIT:
  max_trace INT | all_intersections

See also:

• [pov:6.5.4]Isosurface Object
• [pov:3.6.3]Isosurface Object

• objects/isosurface
• St. Benge: Geometric Creations - Isosurface Tutorial - Part 3
  iso_tutorial3.html :
• St. Benge: Geometric Creations - Isosurface Tutorial - Beginning
  iso_tutorial1.html :
• St. Benge: Geometric Creations - Isosurface Tutorial - Part Two
  iso_tutorial2.html :
• :http://3dgallery.dhs.org/tutorials/iso_tutor.html :
• Smellenbergh: Isosurface manual: Overview
  isotutrs/iso_ind.html :
• :POV-Ray: Documentation: 6.5.4 Isosurface Object :

It is given as

$$\{\langle X,Y,Z\rangle: (X,Y,Z)=$$

$$\text{ for all }(X,Y,Z)\in\text{CONTAINER}. \}$$

The FLOAT_USER_FUNCTION is a user defined function $f$ which returns some float value for any point $\langle X,Y,Z\rangle$ in 3d-space. Note that mathematically we can guarantee (by the implicit function theorem) that the corresponding surface $f^{-1}($THRESHOLD$)$ is non-singular only in points $P$, where $f$ is $C^1$ and the derivative $f'(P)$ is non-vanishing.

With the optional CONTAINER one can restrict the object to a box or sphere. The other optional parameters control the numeric process used in solving the implicit equation.