Optimization

Optimization Problem Statement

Working from the metaphor of fabric, the approached I took in setting up this optimization was to utilize a surface or target point as a representation of the "site". Using single or multiple distance evaluations I was able to have the algorithm minimize those distances while obeying the tile-to-tile constraints of the system.

Tile and Target

As proof of concept, and to work bugs out of my methods, a number of simplified models were run through the optimization routine. Here a singe target point is used to evaluate the distance while the opposite end of the strip is fully anchored. In other words, the strip has one free end and attempts to reach the target point.

Geometric Constraints

Here the point is placed on the off-hand side of the strip. These are multiple views of the same optimization result.

Additional Strip Optimization

Here the target point is on the on-hand side and can nearly reach the target point.

Multiple Direction Strip

The complexity is greatly increased when a 90 degree strip is arrainged with strategically placed distance evaluations.

Converged Top

The final result. The orange lines are offsets of the surface which is turned off for visual clarity.

Converged Side View

The final result. The orange lines are offsets of the surface which is turned off for visual clarity.

Converged Front

The final result. The orange lines are offsets of the surface which is turned off for visual clarity.

Working Surface

The process to complete the surface is to fill tiles in between the strips allowing the constraints of the two edges to determine the infill tile positions.