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| 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 (p3) without changing its length is:
| T(p, c) = p ⋅ | [ | cos c⋅p3 −sin c⋅p3 0 |
sin c⋅p3 cos c⋅p3 0 |
0 0 1 |
] |
Vector p = [p1, p2, p3]. 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 p1×p2 plane by an amount proportional to its p3 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 |
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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! | |