Carbon Tetrahedron

Carbon Tetrahedrons are controlled by segment and volume constraints, which allow the application of volume preservation on a local basis. Global volume preservation is achieved by guaranteeing local volume preservation for all the individual tetrahedrons. Along with Carbon Cloth, Carbon Tetrahedron is the most versatile product in the Carbon portfolio and its applications are endless. 

Houdini's native tetrahedron format is fully supported.

Simple Carbon Tetrahedron example.

 

Carbon Tetrahedrons work with all existing relationships, like Carbon Binding and Carbon Seaming, and can also be goal posed.

Typical use cases include deformable body parts, mattresses, pillows, shoes, plants and ropes. Also, using a coarsely tessellated tetrahedral mesh as collision geometry to cage a high resolution render geometry has proven to be an excellent way of quickly achieving the desired results.

 

Non-uniform Behavior

Just like Carbon Cloth, Carbon Tetrahedrons accepts paint maps for nodal customization of simulation behavior. Below is shown a mattress which is painted to identify soft and stiff regions. 

Painted tetrahedral mattress with non-uniform behavior.

 

 

Geometry Caging for Deformable Bodies

Body deformations rely on volume preservation. This deformable head is 100 percent volume preserving and realistically responds to the rods. For visualization purposes, the low resolution simulation tetra geometry can be captured with a high resolution render geometry.

 

Low resolution simulation geometry and high resolution render geometry.

 

 Result after the caging process.

 

Geometry Caging for Skin Layers

The following examples cover the main deformation cases, such as twisting, bending and poking.
These setups take advantage of Carbon's Soft Binding, which is a Binding constraint that has a non-zero radius to allow movement.
By binding a layer of Tetras to the surface of an animated Collider and filtering collision between those two objects,
the Tetras will follow the animation up to a point where the Tetra constraints win over the soft Binding constraints.

This handles situations where the tetrahedrons would otherwise be pushed inside each other and eventually corrupt or blow up.
Additionally, as you can see in twisting and poking, skin shearing/sliding is achieved as in real life. 

These skin layer .hip files are available on request for studios who are evaluating the Carbon Plug-in.

 

 In the video above, the simulation geometry is drawn directly. Additionally, all Binding constraints are drawn in yellow. 

 

 

 

 These skin layer .hip files are available on request for studios who are evaluating the Carbon Plug-in.

  

Geometry Caging for Ropes

There are multiple ways to simulate ropes: Using a very stiff Carbon Cloth, creating a long chain of Carbon Rigid Bodies which are connected by Carbon Joints, or using Carbon Tetrahedrons. It is not necessary to use a high resolution simulation geometry to capture characteristic behavior.

 

Low resolution simulation geometry and high resolution render geometry.

 

 

Result after the caging process.

 

Geometry Caging for Plants

Plants are very suitable for tetrahedral simulations if the intention is to show some deformations.
Very stiff plants are best modeled with low resolution tetra geometry and then simulated with a large numbers of iterations and subdivisions.
The low resolution plant simulation geometry can then be captured by high resolution render geometry.

 

Low resolution simulation geometry and high resolution render geometry.

Result after the caging process.

 

Shoes

The soles of modern sports shoes display a wide range of behavior. Some are very stiff, others deform while preserving their volume, and few show similar properties to sponges, i.e. non-volume preserving deformations due to air chambers within the material.

 

Shoe using a sole made from Carbon Tetra. Simulation geometry.

 

This shoe example is set up to lose a maximum of 10 percent volume during even the strongest deformations.

Another very interesting fact about this example is that it combines all major features in the Carbon portfolio. The shoe sole is made from tetrahedrons i.e. simulated using Carbon Tetra. All three straps (front, middle and back) are simulated as Carbon Cloth and the buckles are Carbon Rigid Bodies. The components are held together with Carbon Seaming and the floor and foot which deform the shoe are Carbon Colliders.

 

Rendered shoe simulation.

Raw Performance

The underlying Tet physics structure parallelizes extremely well and allows for real-time (24Hz) simulations of geometries containing 300,000 tets.
The noodle bowl below is simulating at 7.68million tets/sec. (and 10.6M segments/sec.), in the Carbon test bed on Dual 14 core system.
(Note: Houdini overhead will slow that down in the plug-in).

The versatility and speed of Carbon Tetra makes them the perfect solution for skin layers, deformable bodies, shoe soles, ropes and certain types of plants; and being a soft body, artists can take advantage of Carbon’s goal posing to art direct the Tet behavior they want, in the same way they goal pose cloth.