Saturday, April 29, 2017

[avkthzdj] Generalized engraving

Divide a region into a tessellation of equilateral triangles.  Divide each equilateral triangle into a grid of small equilateral triangles.  To each internal vertex of the larger triangles, assign a height value.  Vertices on the edges of the larger triangles remain at height zero, to establish boundaries between the larger triangles.  Interpolate a plane between each small triangle of vertices.  Each larger triangle represents a letter in an alphabet.

This could also be done with a small equilateral triangles dividing regular hexagons in tessellation.  The simplest size has only one internal vertex per hexagon.

Square grid requires more work in interpolating a surface between vertices of specified heights, e.g., bilinear interpolation.

3D print or mill the surface, encoding information into a physical object.

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