stuff growing and crawling - L-Systems

In this nth experiment I wanted to create a way to wrap a growing geometry on the surface of another geometry without relying upon UVs on the target geometry.

The OTL I created takes 3 inputs:

1. lsystem (this will be wrapped on top of 2)
2. poly geometry
3. one point

L-System (points and edges)

The L-System provided as first input can be any L-System where the root point of a new branch overlaps the point it generates from. In other words if you 'window' select the first point of a branch in your L-System you should end up selecting 2 points. Inside the OTL the L-System is pre-processed adding point attributes (like an attr that specifies if a certain point is a branch root, or the direction of each segment) that will make traversing it's hierarchy later on way faster. Something like this:

Wrapped Geometry (any geometry)

The OTL wraps the original L-System around this geometry. It can be any geometry. This geometry will be converted into a VDB SDF in the OTL, sample and gradient volume vops are used to quickly find the closest point on this surface. Because of this approach, the OTL doesn't require any UV coordinate to locate positions on this geometry and it's super fast since the SDF is calculate only once at the beginning of the whole simulation and contains already all the info to calculate the closest point on the surface with just a couple of multiplications and sums.

Start Point (one point)

The closest point of the Start Point on the Wrapped Geometry is where the root of the 'wrapped' L-System will sit. This point must be as close as possible to the the Wrapped Geometry surface (in order to have it within the Wrapped Geometry SDF VDB voxels).

How it works

simple otl interface

The original L-System is flattened on the XY plane before being processed. The root (the first point calculated) of the wrapped L-System (WL) is the closest point of the Start Point (SP) on the Wrapped Geometry (WG).The initial direction is given by the vector specified in the OTL UI (see image above).Every 'next' point position is calculated starting from the position of the previous point. For this reason I used a foreach loop making sure to uncheck the parameter "merge", since I want the same data to be processed and provided to the next cycle after adding a new point.To calculate the closest point on the surface from a certain point in the world space, I've used VDB SDF. SDF are already a blessing provided by Houdini but they've always had a certain level of imprecision. VDB SDF are way faster to calculate, and much more precise (thank you DreamWorks Animation for this gift !). The following is the VOP SOP structure to calculate the closest point on surface, given an SDF volume and a sample location in world space:

In this example I've created the wrapped L-System, and then used a Ray Sop to make sure each point really was on the surface, once per frame (Ray Sop is very fast).

I made sure to preserve the Width attribute calculated by default in the L-System Sop and I used it in the PolyWire Sop to drive the width of the Tubes as explained in the PolyWire documentation:

....This node works like the Wireframe node, but this node creates more complex tube geometry from curves, with smoother bends and intersections than Wireframe, especially for L-systems. The four numerical parameters support all the local variables of the Point operation, plus the LSYSTEM specific variables of $WIDTH, $SEGS, $DIV, $LAGE, $GEN, and $ARC....

WL has been calculated on a static WG (I choose the first frame of the hand animation). Then I used a Lattice Sop to wrap WL on the animated version of WG. Before applying the Lattice Sop I've calculated and stored the density of the points on a point attribute on the animated WG via VOP SOP where I used Point Cloud vex nodes to access the same geometry and return the number of points within a certain radius. Then I've used the density attribute to drive the size of the metaballs internally used by Lattice Sop.

Note: L-Systems are perfect to create intricate veins systems. Because L-Systems are a parallel rewriting systems, their size might get huge very fast. For instance in the previous example the original L-System had 95 generations and ~66k points. Nevertheless the generation of the L-System itself was very fast (less than 1s per frame for 95 generations).

OTL processing time to calculate the Wrapped L-System in this example:

Frames 1-84 (83 frames) : less than 2 minutes
Frames 85-91 (7 frames) : ~1 minute
Frames 92-96 (4 frames) : ~1 minute
Frames 97-99 (2 frames) : ~1 minute
Frames 100-102 (2 frames) : ~1 minute
Frames 103-104 (1 frame): ~1 minute
Frame 116 : ~2 minutes
Frame 122 : ~3 minutes
Frame 131 : ~5 minutes
Frame 138: ~10 minutes
Frame 145: ~21 minutes

Time to calculate 145 frames ~ 3h 40m.

on an Intel Core i7 3.0Ghz - 4 cores - 8 logical All VOP SOPs are set to 1 thread per proc.

As you can see , processing times increase exponentially when the number of L-System generation starts getting crazy so if the idea is, for instance, to cover a full animated character with veins, the best approach is divide and conquer, instead of using one single massive L-System.

Now, I guess this is just a way to accomplish this effect, I am sure there are many others I've not thought about. So, feel free to comment and pitch ideas !