Automated Cookie Cutters: OpenSCAD surface() Function

While pondering the notion of making cookie cutters, it occurred to me that the process could be automated: a grayscale height map image of the cookie should be enough to define the geometry. The existing height map solutions (like William Adams’s fine work) seem entirely too heavyweight, what with custom Windows or Java programs and suchlike. Some doodling indicates that a simpler solution may suffice for my simple needs, although the devil always hides in the details.

The overall problem with a cookie press involves producing a non-rectangular solid with a bumpy upper surface corresponding to the grayscale values of an image: dark pixels = low points of the surface, light pixels = peaks. The image size controls the XY extent of the solid and the pixel values control the Z, with some known value (likely either black or white) acting as a mask around the perimeter. Given such a solid, you can then wrap a cutter blade and handle around the outline, much as I did for the Tux cutter.

OpenSCAD has a lightly documented surface() function that reads an ASCII text file consisting of an array of numeric values. Each array element defines a 1 × 1 unit square of the resulting 3D object; the example in the doc shows a 10 x 10 array producing a 10 x 10 unit object. Each numeric value sets the height of the surface at the center of the square.

This array, slightly modified from the one in the doc, shows how that works:

9 9 8 7 6 5 5 5 5 1
9 9 7 6 6 4 3 2 1 0
8 7 6 6 4 3 2 1 0 0
7 6 6 4 3 2 1 0 0 0
6 6 4 3 2 1 1 0 0 0
6 6 3 2 1 1 1 0 0 0
6 6 2 1 1 1 9 9 9 0
6 6 1 0 0 0 9 8 9 0
3 1 0 0 0 0 9 9 9 0
9 8 7 6 5 4 3 2 1 0

Feeding that into this OpenSCAD program:

module ShowPegGrid(Space = 10.0,Size = 1.0) {

  Range = floor(50 / Space);

	for (x=[-Range:Range])
	  for (y=[-Range:Range])
		translate([x*Space,y*Space,Size/2])
		  %cube(Size,center=true);

}

ShowPegGrid();
surface("/tmp/test.dat",center=true,convexity=10);

Produces this object, surrounded by a few non-printing 1 unit alignment cubes on the Z=0 plane for scale:

Example Object

Example Object

Some things to note:

  • The text array looks like it builds downward from the upper left, but the solid model builds from the origin toward the +X and +Y directions, with the first line of the array appearing along Y=0. This reverses the object along the Y axis: the first line of the array is the front side of the object.
  • The “center=true” option centers the object in XY around the Z axis, with a 1 unit thick slab below the entire array; the top surface of that slab (at Z=0) represents the level corresponding to 0 elements in the array.
  • Each array element becomes a square one unit on a side; the RepRap software chain regards units as millimeters
  • The center point of each element’s square is at the nominal height
  • The Z coordinate of the edges of those squares linearly interpolate between adjacent centers
  • Vertical edges become slanted triangular facets

Remember that STL files contain a triangular tessellation (or whatever you call it in 3D) of the object surface, which means rectangles aren’t natural. The edge interpolation make the whole thing work, because an array of pure square pillars probably won’t be a 2-manifold object: some pillars would share only a common vertical edge. The interpolation does, however, produce a bazillion facets atop the object.

So the problem reduces to generating such an array from a grayscale image, for which some ImageMagick and Bash-fu should suffice, and then manipulating it into a model that will produce a cookie press and cutter. More on that tomorrow…

[Update: image file, height map file, solid modeling, printing]

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  1. Automated Cookie Cutters: Creating the Height Map Data File « The Smell of Molten Projects in the Morning
  2. Automated Cookie Cutters: Putting It All Together « The Smell of Molten Projects in the Morning
  3. Automated Cookie Cutters: OpenSCAD surface() Function #3dthursday « adafruit industries blog

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