Iso Surface SOP
Summary[edit]
The Iso Surface SOP uses implicit functions to create 3D visualizations of isometric surfaces found in Grade 12 Functions and Relations textbooks.
An implicit function is defined so that it = 0. For example with:
x2 + y2 = r2
the implicit function is:
f(x, y) = x2 + y2 - r2 = 0
Parameters - Page
Implicit Function func - Enter the function for implicit surface building here.
Example 1: (me.curPos.x**2) / (4*4) - (me.curPos.y**2) / (3*3) + me.curPos.z
This formula creates a hyperbolic paraboloid, or saddle shape.
Example 2: (me.curPos.x**2) / 0.1 + (me.curPos.y**2) / 2 + (me.curPos.z**2) / 6 - 1
This formula creates an ellipsoid.
Try loading some of the sample functions in $TFS/touch/presets.
Minimum Bound min - ⊞ - Determines the minimum clipping plane boundary for display of iso surface.
- X
minx-
- Y
miny-
- Z
minz-
Maximum Bound max - ⊞ - Determines maximum clipping plane boundary for display of iso surfaces.
- X
maxx-
- Y
maxy-
- Z
maxz-
Divisions divs - ⊞ - The density, or resolution of the iso surface polygons in X, Y and Z.
- X
divsx-
- Y
divsy-
- Z
divsz-
Compute Normals normals - Adds normals to the surface.
Example
The action of the Iso Surface sop is conceptually simple - it takes a user specified expression in R3 (a mathematical term meaning, "having three dimensions, each taking a Real value), and creates a surface where the function goes from being positive to being negative. In the case of the default expression ( $X2 + $Y2 + $Z2 ), the expression is less than zero within a unit sphere, and greater than zero outside. As the sop cooks, it marches through the bounding volume specified (by default from -1 to +1 in X, Y and Z), and creates geometry where the expression equals zero.
This may seem like a difficult way to define a sphere, but there's much potential beyond this simple example using the rich array of mathematical functions (see the Expressions section). A simple illustration is with the noise() function. Try inputing the following expression. 
TouchDesigner Build:
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