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Sponsored Feature: Multi-Core Simulation of Soft-Body Characters Using Cloth
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# Sponsored Feature: Multi-Core Simulation of Soft-Body Characters Using Cloth

December 10, 2008 Page 2 of 4

Another interesting force to model on cloth is torsion. Torsion is like a spring that resists bending. This is intuitively present in many real-life cloth objects. A piece of paper is different from a handkerchief, in part, due to resistance to torsion. Clearly both objects resist stretching, but the handkerchief is easy to wad up into a ball, whereas the paper resists folding and attempts to remain flat. This can be modeled mathematically.

Figure 4: Torsion forces and normals on three connected points

Figure 4 shows the torsion force calculation for three points in a line. In the upper left diagram, the connection on the left half has a resting length d' and a torsion constant k'. The other half has length d'' and torsion k''. All points also have an identifying normal, pointing in an arbitrary, but consistent, direction. The diagram at the top right shows an intermediate state where the rightmost point has been moved relative to the other two points. Torsion forces are what attempt to bring the three points back into relative alignment.

In the bottom diagram for Figure 4, the normals have been recalculated for each point, where the left and right points have a local view of the outward pointing direction. The center node's normal is an average of the other two. The torsion force on the center point is opposite this normal and is proportional to the sum of each side's torsion constant multiplied by the resting length (the lever arm). There are also torsion forces on the end points (not drawn), which are aligned with their normals. The effect of these forces is to bring the middle point back between the two end points, returning them to a co-linear formation, although the whole line will be angled slightly clockwise from the original state.

Figure 5: Cloth with moderate torsion draped over a sphere

With the addition of torsion, more interesting effects are possible with the classic cloth drop over an invisible sphere. Figure 5 shows the drop of a cloth where torsion has been increased to a moderate level and the cloth ends stand out in broad folds - like a rubber sheet. Torsion allows us to create some interesting effects in manipulation of cloth.

Figure 6: An ooze created with both tension and torsion forces

Figure 6 shows an ooze created with a cloth with both tension and torsion forces. The ooze is a square piece of cloth that has a central area of additional tension and torsion which elevates it above the ground. The torsion between the center of the ooze and the outside edges allows it to turn in a swirling motion to track a new target.

Figure 7: A flying carpet

Figure 7 shows a flying carpet. The carpet is truly a classic cloth used in a new way. The manipulation of the leading edge of the carpet, with the help of some moderate torsion forces, allows the carpet to twist and swoop in a compelling fashion. The wireframe view shows that this is just the classic cloth mesh, with the leading edge defined by a set of fixed co-linear points.

Figure 8: A squishy ball

Figure 8 shows a character made with cloth that is a subdivided icosahedron, with strong tension forces on the surface, but a very weak tension force in the center. The result is something like a collapsed soufflé, which rolls around due to the torsion applied by the center as it turns. Very cool but kind of disturbing, which is why the demo artist decided to texture it with eyeballs.

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