Table of Contents

Tutorial Overview
Merging
Intersecting
Differencing
Blobbing Functions

Tutorial Overview

Sometimes when making a complex isosurface, one wishes he/she could merge functions together or difference them in the same function. In this tutorial I will explain just how to do those things! We will learn how to merge, intersect and even difference functions.

Isosurface threshold, sign and contained_by box will be the same as in the beginning tutorial.

Merging

Let's make an isosurface cylinder with a radius of .5 units, a good shape to begin our exercise with. Will will encase it inside parenthesis as shown:

function{ ( sqrt(x^2+z^2)+.5 ) }

Next, we combine another function to it using | (it's the shift+backslash key on windows keyboards). We will use a diamond-shaped shaft for the second function:

function{ ( sqrt(x^2+z^2)+.5 ) | ( abs(x)+abs(y) +.5 ) }

Pretty simple, huh?

We could do the same exact thing by changing the function to this:

function{ min( ( sqrt(x^2+z^2)+.5 ), ( abs(x)+abs(y)+.5 ) ) }

Intersecting

We will do the same thing as before, but instead of using |, we we use an & sign:

function{ ( sqrt(x^2+z^2)+.5 ) & ( abs(x)+abs(y) +.5 ) }

An expected result, wouldn't you say? The cylinder intersected with the shaft to create a 'chip off the old block.'

The same thing could be achieved by typing:

function{ max( ( sqrt(x^2+z^2)+.5 ), ( abs(x)+abs(y)+.5 ) ) }

Differencing

For differencing we will have to alter the intersection code:

function{ ( sqrt(x^2+z^2)+.5 ) & -( abs(x)+abs(y) +.5 -2 )}

Pay close attention to what was changed. A minus sign was placed in front of the second function and a -2 was a placed inside the same function.

Again, we could get the same effect by typing:

function{ max( ( sqrt(x^2+z^2)+.5 ), -( abs(x)+abs(y)+.5 -2) ) }

Getting the idea? min and max allow you to do the same CSG operations as | and &. Why use min and max? I don't know. I think | and & are much more versatile, in that you can have more than 2 objects performing a CSG operation, and without making the code more messy.

By structuring your functions with logical placement of parenthesis, you can perform any complex CSG operation.

Blobbing Functions

Blobbing functions requires setting up a system for arranging your functions. First, we will make a threshold variable to preserve simplicity. Make sure you have this placed before the isosurface:

#declare Thr=.0001;

Next, inside our isosurface statement, we will set up our function using the cylinder and shaft from the above excercises:

function{
 ( 1+Thr )
 -Thr^( sqrt( x^2+z^2 )+.5 )
 -Thr^( abs(x)+abs(y)+.5 )
}

As you can see, it treated both functions as blob components. By changing Thr to other [decimal] numbers, you can get different blob thresholds, which means tighter transitions from one object to another, or more stretched, taffy-like transitions. Experiment!

What the heck! Let's try adding another cylinder to our blob:

function{
 (1+Thr)
 -Thr^( sqrt( x^2+z^2 )+.5 )
 -Thr^( abs(x)+abs(y)+.5 )
 -Thr^( sqrt( y^2+z^2 )+.5 )
}

You will see, no matter how many functions you add using this method, the threshold will always reamain constant.

Negative component blobbing has not been worked out completely using this method yet... sorry!

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