http://people.csail.mit.edu/jaffer/Marbling/Pattern-Welding | |

## Pattern Welding |

Bladesmiths John D. Smith and Zack Jonas had a booth at the 2011 Lowell Folk Festival where they showed their beautiful pattern-welded steel knives. Inquiring about their techniques, I realized that what they do is 3-dimensional marbling!

First, they forge a bar of alternating steel (longways) layers having two different compositions (and appearance).

There are several techniques which can be combined to create a variety of patterns. A simple one is to twist a (heated) bar tightly, so that it looks like a cable. The blade is then created by slicing it out of the twisted bar.

The transform to twist a bar along its axis (*p*_{3})
without changing its length is:

T(p, c) = p
⋅ | [ | cos c⋅p_{3}−sin c⋅p_{3}0 |
sin c⋅p_{3}cos c⋅p_{3}0 |
0 0 1 |
] |

Vector **p** = [*p*_{1}, *p*_{2}, *p*_{3}].
Large *c* values twist tightly.
The inverse transform
*T*^{ −1}(**p**,*c*)=*T*(**p**,−*c*).
*T*(**p**,*c*)−**p** is not a vector field
because its magnitude becomes unbounded with distance from the axis
of rotation. However, for finite volumes, *T* is
volume-preserving; the transform simply rotates
each *p*_{1}×*p*_{2} plane by an
amount proportional to its *p*_{3} coordinate.

Below are slices through simulated pattern-welded bars with 0, 1/2, 1, 2, and 4 full twists. The left two columns are sliced midway between the center and minimum radius. The right column is sliced through the center.

13 layers | 12 layers | 12 layers, sliced through center |
---|---|---|

PostScript code | PostScript code | PostScript code |

I am a guest and not a member of the MIT Computer Science and Artificial Intelligence Laboratory.
My actions and comments do not reflect in any way on MIT. | ||

Topological Computer Graphics | ||

agj @ alum.mit.edu | Go Figure! |