Super-Quadratic Formulas

       r          s          t

|X|+ |Y|+ |Z| = 1

R,S,T = numbers that determine the features of the quadratic.

X,Y,Z = your constant variables.

A basic super-quadratic formula will be equal to 1. However, there are cases where this is not true. In these cases, the super-quadratic will change shape.

 A value that equals less than 1:  This value will create a pointy octahedron shape that will have concave faces and sharp edges.

A value that equals 1: This value will create a normal octahedron.

A value that is between 1 and 2: This value will create an octahedron will convex faces, and blunt edges and faces.

A value that equals 2: This value will generate a sphere.

 

A value that is greater than 2: This value will create a cube with round edges.

 A value that is infinite, or that goes on forever beyond 2:  This value will create a basic cube.

So now that we understand what's going on behind the scenes of our density field, lets dive deeper.

In Houdini,the way we adjust these field shapes is by adjusting our XY, and Z parameters. In turn, this adjusts our quadratic formula.

We know already that two meta-balls together will overlap if combined together. However, when two meta-balls combine the density of their force fields join together to include the area where they intersected, as well as their sphere of influence.

  • display primitive hulls You can view a meta-ball's sphere of influence by turning on in the display options.

  • display options When using a meta-ball you may notice that the level of detail may be lower than you might like. One way to fix this is to go into the and adjusting the level of detail inside those options.

  • facet node When shading a meta-ball remember to include or promote the normal attribute. You can include the normal by adding a and clicking post-compute normals

 

A Quadratic: A shape that follows the basic structure of squares. From it's formula, to it's shape. If you've heard of a quadratic formula in high school, this theory is what we are building upon.

A Octahedron: A shape that contains; 8 faces, 12 edges, and 6 vertices. For example: a diamond.

 

 

 

 

 

Some quick definitions:

The Density Field of a meta-ball can either be a Ellipsoid or a Super-Quadratic. So for fun, lets break down one of those, and understand what a Super-Quadratic is. I'm choosing Super-Quadratic for now, as it is the most applicable to other functions and objects in Houdini. Plus, an ellipsoid is much more easier to understand.

By adjusting the Weight Function, you can shift where the density is located in the meta-ball. By adjusting this, it will move the density further or closer away from the center.

The way to control a meta-ball's density field is to adjust it's Kernel Function.  The kernel function is designed to control the density, by adjusting it's weight from 0 to 1

A meta-ball by itself will not do much. However, two meta-balls added together will overlap their density fields. They are designed to change shape, the position of their density, and fuse together if one meta-ball has a higher density than another. You can also modify a meta-ball to push another meta-ball away. 

 

Meta-balls are fields of density that represented by surface blobs in Houdini.

Meta-balls are interesting mathematical objects in Houdini. They are mostly used for organic simulations. Such as two cells dividing, fleshy separations between objects, or organic surfaces.

 

MetaBalls