Reference:Isosurface

See the isosurface tutorial for more about working with isosurfaces. The syntax basics are as follows:

isosurface {
  function { FUNCTION_ITEMS }
  [contained_by { SPHERE | BOX }]
  [threshold FLOAT_VALUE]
  [accuracy FLOAT_VALUE]
  [max_gradient FLOAT_VALUE]
  [evaluate P0, P1, P2]
  [open]
  [max_trace INTEGER] | [all_intersections]
  [polarity on | +VALUE | off | -VALUE] 
  [OBJECT_MODIFIERS...]
  }

Isosurface default values:

contained_by : box{-1,1}
threshold    : 0.0
accuracy     : 0.001
max_gradient : 1.1
polarity     : off

Since isosurfaces are defined by a user supplied function { ... } it must be specified as the first item of the isosurface statement. Here you place all the mathematical functions that will describe the surface.

The contained_by object limits the area where POV-Ray samples for the surface of the function. This container can either be a sphere or a box both of which use the standard POV-Ray syntax. If nothing is specified a default box, as noted above, will be used. See additional usage examples below:

contained_by { sphere { CENTER, RADIUS } }
contained_by { box { CORNER1, CORNER2 } }

Using threshold specifies how much strength, or substance to give the isosurface. The surface appears where the function value equals the threshold value. See above for the listed default value.

The isosurface resolver uses a recursive subdivision method. This subdivision goes on until the length of the interval where POV-Ray finds a surface point is less than the specified accuracy. See above for the listed default value. Be aware that smaller values produce more accurate surfaces, but takes longer to render.

POV-Ray can find the first intersecting point between a ray and the isosurface of any continuous function if the maximum gradient of the function is known. To that end you can specify a max_gradient for the function. See above for the listed default value. When the max_gradient used to find the intersecting point is too high, the render slows down considerably. Conversely, when it is too low, artifacts or holes may appear on the isosurface, and in some cases when it is way too low, the surface does not show at all. While rendering the isosurface POV-Ray stores the found gradient values and issues a warning, if these values are either higher or much lower than the specified max_gradient value:

Warning: The maximum gradient found was 5.257, but max_gradient of
the isosurface was set to 5.000. The isosurface may contain holes!
Adjust max_gradient to get a proper rendering of the isosurface.

Warning: The maximum gradient found was 5.257, but max_gradient of
the isosurface was set to 7.000. Adjust max_gradient to
get a faster rendering of the isosurface.

For best performance you should specify a value close to the real maximum gradient.

Isosurfaces can also dynamically adapt the used max_gradient. To activate this technique you have to specify the evaluate keyword followed by these three parameters:

• P0: the minimum max_gradient in the estimation process.
• P1: an over-estimating factor. That is, the max_gradient is multiplied by the P1 parameter.
• P2: an attenuation parameter of 1 or less

In this case POV-Ray starts with the max_gradient value P0 and dynamically changes it during the render using P1 and P2. In the evaluation process, the P1 and P2 parameters are used in quadratic functions. This means that over-estimation increases more rapidly with higher values and attenuates more rapidly with lower values. It should also be noted that when using dynamic max_gradient, there can be artifacts or holes.

If you are unsure what values to use, just start a render without using evaluate to get a value for the max_gradient, then use that value with evaluate like this:

• P0: max_gradient * Min_Factor
• P1: sqrt(max_gradient/(max_gradient * Min_Factor))
• P2: should be 1 or less use 0.7 as a good starting point.

Where Min_Factor is a float between 0 and 1 to reduce the max_gradient to a minimum max_gradient. The ideal value for P0 would be the average of the found maximum gradients, but we do not have access to that information. A good starting point for Min_Factor is 0.6

If there are artifacts or holes in the isosurface, you can just increase Min_Factor and / or P2. For Example: when the first run gives a found max_gradient of 356, start with:

#declare Min_factor= 0.6;
isosurface {
  ...
  evaluate 356*Min_factor,  sqrt(356/(356*Min_factor)),  0.7
  //evaluate 213.6, 1.29, 0.7
  ...
  }

This method is only an approximation of what happens internally, but it gives faster rendering speeds with the majority of isosurfaces.

When the isosurface is not fully contained within the contained_by object, there will be a cross section. When this happens, you will see the surface of the container. Using the open keyword, these cross section surfaces are removed, and the inside of the isosurface becomes visible.

Note: Using open slows down the render speed, and it is not recommended for use with CSG operations.

Isosurfaces can be used in CSG shapes since they are solid finite objects - if not finite by themselves, they are through the cross section with the container. By default POV-Ray searches only for the first surface which the ray intersects. However, when using an isosurface in CSG operations, the other surfaces must also be found. Consequently, the keyword max_trace followed by an integer value, must be added to the isosurface statement. To check for all surfaces, use the keyword all_intersections instead. With max_trace it only checks until that number is reached.

Note: The current implementation has a limit of 10 intersections in all cases.

By default, the inside of an isosurface is defined as the set of all points inside the contained_by shape where the function values are below the threshold. New in version 3.7.1 this can be changed via the polarity keyword. Specifying a positive setting or on will instead cause function values above the threshold to be considered inside. Specifying a negative setting or off will give the default behavior.