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
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|
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!|