Mel
Recursion

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Introduction

This tutorial addresses the issue of writing recursive procedures. A procedure is recursive when it calls or invokes itself. As a simple example consider the following procedure.

    proc foo(){
        sphere;
        foo(); // call ourself
        }

The color coded sequence shown below indicates what happens when the procedure is executed. Each time foo() is executed it would call a "copy" of itself, which in turn would call another "copy" - and so on. Each recursion ie. copy of the procedure, occupies a small allocation of memory. Eventually Maya would use up its memory and terminate!

Terminating Recursion

Recursive procedures must always be given a way of stopping the recursion process. Before they recursively call themself they test if a terminal condition is true or false. For example.

    proc foo(int $depth) 
    {
    sphere;
      
    // terminate the recursion...
    if($depth == 0)
        return;
      
    foo($depth - 1); // call ourself
    }

In a mel script this new version of the foo() procedure might be used as follows,
    foo(5);

The variable $depth determines the number of times recursion will occur. As soon as $depth equals 0, recursion is terminated. The new terminating version of foo() is equivalent to using a for-loop:

    for(int $n = 0; $n < 5; $n++)
        sphere;

So why bother with recursion? Why not use a for-loop to repeat a particular action - such as creating a sphere?

Why Use Recursion?

Recursion is particulary helpful when modeling branching and/or nested structures that consist of self-similar shapes. For example, the space filling Hilbert curve shown in fig 1 was created with a recursive procedure.

Example 1 - knobby sphere

The cluster of spheres in figure 1 was created with the procedure shown in listing 1.

Figure 1

Listing 1 (spheres.mel)

    proc spheres(int $depth, vector $pnt, float $rad)
    {
    if($depth == 0)
        return;
      
    // create a sphere
    sphere -p ($pnt.x) 0 ($pnt.z) -r $rad -esw 180;
      
    // find a random location on the surface of the sphere
    $pnt = unit(sphrand(1)) * $rad;
      
    // recurse...
    knobby($depth - 1, $pnt, $rad * 0.75);
    }

Line 7 includes the -esw flag (endSweep) flag so that hemi-spheres are produced. In addition the y coordinte is set to 0.0 to ensure the top edges of the spheres are aligned to the x-z plane. In this way it is easy to see that some "children" spheres are enclosed within the inner "parent" spheres.

For a more sophisticated examples of recursion refer to the tutorials "Mel: Recursion & Branching" and "Hilbert Curve: Mel Implementation"