Tag: Thing-O-Matic

With the Bash script and OpenSCAD source in hand, here’s how you go about producing a grayscale image that works as the height map file to produce a cookie press and matching cookie cutter.

The Big Picture description: the grayscale height map image looks a lot like a photo of the final cookie on a plate in front of you. The darkest regions mark the thinnest parts of the cookie: black lines emboss deep trenches. Gray regions denote thicker sections and very light gray will be thickest. Because image files are rectangular, a pure white area surrounds the region that will become the cookie press and acts as a mask to remove the rectangular border.

If you start by hand-drawing the shape of the cookie press at full size inside a 5 inch square (chosen to match the 3D printer’s build platform and in inches because that’s how it got measured; it’s not my printer) with a 1.5 or 2 mm black marker, then the marker lines will be just about exactly the right width to ensure good plastic fill (for a printer producing a 0.5 mm thread width, anyway) and printable walls. You can scale the drawing for smaller (my Thing-O-Matic) or larger (M2, Series One) platforms, but the thread width and minimum wall thickness do not scale: a tiny 1 inch push mold must still have 2 mm walls.

The workflow looks like this:

• Draw cookie press lines at full scale with fat black marker on white paper
• Scan a 5×5 inch (127×127 mm) square around the image at 300-ish dpi → 1500×1500 pixel image
• Convert a full-color scan to grayscale now (better to scan in grayscale)
• Resize image to 317×317 pixel, optionally set 2.5 pixel/mm = 63.5 dpi for proper display size
• Set color levels to blow out the contrast; auto probably works fine
• Threshold to reduce to just two colors: 0% = black and 100% = white
• Clean up the image: remove specks and single-pixel bumps, fill small gaps

Some sample images to show what happens along the way…

A hand-drawn image, derived from The Original Tux by crudely tracing the outline with a fat Sharpie, including some areas outside the box for pedagogic purposes:

The interior edge of the black box is exactly 5×5 inches. I created a 5×5 inch blank white image at 300 dpi, enlarged the canvas to 5.2×5.2 inches with the blank white image centered in the middle, set a black background, flattened the image to fill the border, and printed it out. That produces a piece of blank paper with a black square suitable for full-scale drawing.

It does not, however, confer any artistic eptitude whatsoever, so for this drawing I imported one of the Tux drawings, isolated the edges with one of The GIMP’s edge detectors, and traced over the thin lines with the aforementioned fat Sharpie. You can draw whatever you want, however you want it. If you already have an image file, you need not print it out and scan it back in; just resize it appropriately.

Pro tip: Ensuring that the drawing doesn’t touch the black square will greatly simplify the next half hour of your life.

A note on Sharpies. I used a Fine Point Marker, which is much fatter than a Fine Point Pen. The whole, uh, point is to produce a line about 2 mm wide that will become an actual plastic wall; you can’t print anything much finer than that.

A note on blackness. There’s no requirement for any black lines whatsoever. For most cookie presses, however, you want distinct walls that emboss lines into the dough, which is what the black lines will do. If you want to mold a cookie (or anything else, like a butter pat), you can produce a gently curved push mold by using only grayscale areas. For example, a circular area with a radial fill going from very light gray on the exterior to very dark gray in the center will produce a round cookie with a conical dent in the middle.

Given a drawn image, scan the area just inside the black square at 300 dpi to produce a nominally 1500×1500 pixel image, then resize it to 317×317 pixel at 63.5 dpi:

The magic number 317 comes from not wanting OpenSCAD to fall over dead after chewing on a larger image for an hour or two. Given the restriction to maybe 330×330 pixels, max, I picked a nice round 2.5 pixel/mm scaling factor that converts a 5 inch = 127 mm distance into 317 pixels:

317 pixel = 127 mm x 2.5 pixel/mm

The magic number 63.5 comes from wanting the image to print (on paper) and display (on screen) at the proper size:

5 inch = 317 pixel / 63.5 pixel/inch

Given a properly sized image, blow out the contrast so the background is mostly white and the lines are mostly black. This gets rid of background cruft:

Then apply a threshold to get rid of all the gray levels. The threshold level determines the line width (the edges shade from black to gray to white), so you can tune for best width. The result doesn’t look much different than the blown contrast version, but the lines will become thinner and more jagged.  Remember that you want the lines to be at least three pixels wide:

Do whatever cleanup is required; eliminate single-pixel bunps and dents, fatten (or, rarely, thin) lines as needed. If you draw with a 3 pixel wide pen, the line will print just over 1 mm wide, which is about the thinnest possible wall and may encounter problems at corners. Use pure 0% black and pure 100% white.

If you possess powerful art-fu, you can draw that kind of image directly in the graphics program. Those of us with weak art-fu must rescale a found image of some sort. Should you draw a new image or rescale an old one, then:

• Start with a 317×317 pixel grayscale canvas in 100% white
• Draw lines with a 3 pixel (probably a square) 0% black pen

Now you have a clean black and white image of the cookie press lines; it’s still a grayscale image, but using only two colors.

• Use color levels to reduce the white to about 95% gray; this avoids interior islands
• Bucket-fill the exterior with 100% white (interior remains 95%): no anti-aliasing or blending
• Fill interior regions with grays to set cookie press depths: dark = low, light = high, no 100% white, no anti-aliasing
• Save as PNG to avoid compression artifacts

By reducing the overall white level to 95%, you get rid of all that pure white in the whole interior. Remember that pure white marks the area outside of the press, so any white inside the press will produce bizarre islands. You could pour 95% white into all the interior areas, but if you miss one, you have an island.

Having reduced all the whites, pouring pure 100% white around the press restores the exterior mask color. Turn off the anti-aliasing / blending / feathering options, because you want crisp edges rather than nice-looking gray transitions.

If all you want is a press with lines, you’re done. Save the image and proceed to make the cutter & press.

If you want a press that produces a cookie with different thicknesses, do some gray pours. For example:

That’s obviously contrived, but the general idea is that the feet and beak will be the thickest part of the cookie, the tummy next, and the body will be the thinnest part. The glint above one eye will become a bizarre peak, but that’s to show why you probably don’t want to do that. It’s not obvious, but the eyeball pupil and sclera areas will be recessed into the body.

If you’re doing a push mold, elaborate grayscaling will make a lot more sense. For a cookie press, black is where it’s at.

That process produces a clean grayscale image. Save it as a PNG file to avoid JPEG image compression artifacts: you want crisp lines and flat areas that define heights, not a small file. It’ll be small enough, anyway, compared to the eventual STL files.

To review, the grayscale height map image must satisfy this checklist:

• Maximum 317×317 pixels: smaller is OK and will print at 2.5 pixel/mm; larger may not work
• Exterior pure white: 100% = 255/255
• Four corners must be 100% white to allow proper auto-cropping
• No interior pixels are 100%: at most 99.6% = 254/255 will be fine
• All lines at least 3 pixels wide: will print at 1.2 mm = (3 pixel / 2.5 pixel/mm)
• No speckles or stray dots
• Clean lines with no single-pixel bumps or dents: they’re hard to print
• Saved as PNG to preserve crisp lines and areas

Then hand the file to the MakeCutter.sh Bash script, do something else for an hour, and get a pair of STL files.

To get higher resolution, you could use Shapeways’s online 2D-to-3D Converter, although it seems to produce STL files with many reversed normals. The press and cutter would require different height map images, of course, but I betcha ImageMagick could produce them for you. The PNG23D project may be of more than passing interest. Note that their recommended resolution matches up just about exactly with my 2.5 pixel/mm default, so higher resolution may not pay off the way you think.

In any event, for this example the height map file shown above is TuxTrace.png and all the output files use TuxTrace as a prefix.

The cookie press (TuxTrace-press.stl):

Notice that Tux has been reversed from left-to-right, the darkest parts of the original image correspond to the tallest lines, and that glint over the eye became a triangular depression. All that makes sense when you imagine pressing this shape onto a layer of dough rolled out over the kitchen cutting board.

The cookie cutter (TuxTrace-cutter.stl), with a stiffening lip extending on both sides of the cutting blade:

The press probably won’t slide into the cutter, because I set things up to use the same dimensions, and certainly won’t fit inside the inner lip on the build platform. Another Minkowski around the press to add half a millimeter or so would let them nest together, at the cost of even more computation time.

Those nicely shaded blue images come from MeshLab screenshots, which you can (and should!) install on your Linux box without any hassle at all.

The “blade” isn’t particularly sharp, due to the fact that we’re printing blocky pixels. I produced a very thin blade for the original Tux Cutter by using a finicky collection of settings, but that won’t produce a corresponding press.

The surface that OpenSCAD builds from the height map image has slightly tapering walls, because that’s how it ensures a 2-manifold 3D object. The base of the walls will be slightly wider than the grayscale line width and the top will be slightly narrower. This produces a tapered edge, which is probably what you want for a cookie cutter, but it means you must make the lines wide enough to ensure good fill along the top of the wall.

The G-Code produced from the height map image above looks like this at the base of the walls on the press (as always, clicky for more dots):

The same walls become much thinner on the top layer, including a few single-thread sections:

Moral of the story: draw with a chunky marker!

Bonus lesson: always analyze the G-Code before you build anything…

The Bash script produces several intermediate images and data files along the way; delete them if you like.

A cropped / rotated / de-commented / contrast-stretched image (TuxTrace_prep.png):

An image (TuxTrace_plate.pgm and .dat) that defines the outside edge, with no interior detail, to shape the cutter outline:

An image (TuxTrace_map.pgm and .dat) that defines the height map for the press surface:

That one is actually identical to the incoming PNG file, just converted to an ASCII image file format.

Yummy!

Running more grayscale images through the cookie cutter process revealed some problems and solutions…

It seems OpenSCAD (or the underlying CGAL library) chokes while creating a 3D surface from a bitmap image more than about 350-ish pixels square: it gradually blots up all available memory, fills the entire swap file, then crashes after a memory allocation failure. As you might expect, system response time rises exponentially and, when the crash finally occurs, everything else resides in the swap file. The only workaround seems to be keeping the image under about 330-ish pixels. That’s on a Xubuntu 12.04 box with 4 GB of memory and an 8 GB swap partition.

So I applied 2.5 pixel/mm scaling factor to images intended for a 5 inch build platform:

317 pixel = (5 inch × 25.4 mm/inch) * 2.5 pixel/mm

Any reasonable scaling will work. For smaller objects or platforms, use 3 pixel/mm or maybe more. If you have a larger build platform, scale accordingly. I baked the default 2.5 factor into the Bash script below, but changing it in that one spot will do the trick. Remember that you’re dealing with a 0.5 mm extrusion thread and the corresponding 1 mm minimum feature size, so the ultimate object resolution isn’t all that great.

Tomorrow I’ll go through an image preparation checklist. However, given a suitable grayscale height map image as shown above, the rest happens automagically:

./MakeCutter.sh filename.png

That process required some tweakage, too …

Auto-cropping the image may leave empty borders: the canvas remains at the original size with the cropped image floating inside. Adding +repage to the convert command shrinkwraps the canvas around the cropped image.

If the JPG file of the original scanned image has an embedded comment (Created by The GIMP, for example), then so will the PNG file and so will the ASCII PGM files, much to my astonishment and dismay. The comment line (# Created by The GIMP) screwed up my simplistic assumption about the file’s header four-line header layout. The +set Comment squelches the comment; note that the word Comment is a keyword for the set option, not a placeholder for an actual comment.

It turns out that OpenSCAD can export STL files that give it heartburn when subsequently imported, so I now process the height map and outline images in the same OpenSCAD program, without writing / reading intermediate files. That requires passing all three image dimensions into the program building the cutter and press, which previously depended on the two incoming STL files for proper sizing. This seems much cleaner.

The original program nested the cookie press inside the cutter on the build platform as a single STL file, but it turns out that for large cutters you really need a T-shaped cap to stabilize the thin plastic shape; the press won’t fit inside. The new version produces two separate STL files: one for the press and one for the cutter, in two separate invocations. The command-line options sort everything out on the fly.

Because the cutter lip extends outward from the press by about 6 mm, you must size the press to keep the cutter completely on the build platform. The 5 inch outline described above produces a cutter that barely fits on a 5.5 inch platform; feel free to scale everything as needed for your printer.

The time commands show that generating the press goes fairly quickly, perhaps 5 to 10 minutes on a 3 GHz Core 2 Duo 8400. The multiple Minkowski operations required for the cutter, however, run a bit over an hour on that machine. OpenSCAD saturates one CPU core, leaving the other for everything else, but I wound up getting a cheap off-lease Dell Optiplex 760 as a headless graphics rendering box because it runs rings around my obsolete Pentium D desktop box.

The MakeCutter.sh Bash script controlling the whole show:

#!/bin/bash
DotsPerMM=2.5
MapHeight=5
ImageName="${1%%.*}"
rm ${ImageName}_* ${ImageName}-press.stl ${ImageName}-cutter.stl
echo Normalize and prepare grayscale image...
convert $1 -type Grayscale -depth 8 -auto-level -trim +repage -flip -flop -negate +set Comment ${ImageName}_prep.png
echo Create PGM files...
convert ${ImageName}_prep.png -compress none ${ImageName}_map.pgm
convert ${ImageName}_prep.png -white-threshold 1 -compress none ${ImageName}_plate.pgm
echo Create height map data files...
ImageX=`identify -format '%[fx:w]' ${ImageName}_map.pgm`
ImageY=`identify -format '%[fx:h]' ${ImageName}_map.pgm`
echo Width: ${ImageX} x Height: ${ImageY}
cat ${ImageName}_map.pgm | tr -s ' \012' '\012' | tail -n +5 | column -x -c $((8*$ImageX)) > ${ImageName}_map.dat
cat ${ImageName}_plate.pgm | tr -s ' \012' '\012' | tail -n +5 | column -x -c $((8*$ImageX)) > ${ImageName}_plate.dat
echo Create cookie press...
time openscad -D BuildPress=true \
-D fnPlate=\"${ImageName}_plate.dat\" \
-D fnMap=\"${ImageName}_map.dat\" -D Height=$MapHeight \
-D ImageX=$ImageX -D ImageY=$ImageY -D DotsPerMM=$DotsPerMM \
-o ${ImageName}-press.stl Cookie\ Cutter.scad
echo Create cookie cutter...
time openscad -D BuildCutter=true \
-D fnPlate=\"${ImageName}_plate.dat\" \
-D ImageX=$ImageX -D ImageY=$ImageY -D DotsPerMM=$DotsPerMM \
-o ${ImageName}-cutter.stl Cookie\ Cutter.scad

The Cookie Cutter.scad OpenSCAD source code:

// Cookie cutter from grayscale height map using Minkowski sum
// Ed Nisley KE4ZNU - November 2012

//-----------------
// Cookie cutter files

BuildPress = false;						// override with -D Buildxxx=true
BuildCutter = false;

fnMap = "no_map.dat";					// override with -D 'fnMap="whatever.dat"'
fnPlate = "no_plate.dat";				// override with -D 'fnPlate="whatever.dat"'

DotsPerMM = 2.5;						// overrride with -D DotsPerMM=number

MapHeight = 5.0;						// overrride with -D MapHeight=number

ImageX = 10;							// overrride with -D ImageX=whatever
ImageY = 10;

MapScaleXYZ = [1/DotsPerMM,1/DotsPerMM,MapHeight/255];
PlateScaleXYZ = [1/DotsPerMM,1/DotsPerMM,1.0];

echo("Press File: ",fnMap);
echo("Plate File: ",fnPlate);

echo("ImageX:",ImageX," ImageY: ", ImageY);
echo("Map Height: ",MapHeight);
echo("Dots/mm: ",DotsPerMM);
echo("Scale Map: ",MapScaleXYZ,"  Plate: ",PlateScaleXYZ);

//- Extrusion parameters - must match reality!

ThreadThick = 0.25;
ThreadWidth = 2.0 * ThreadThick;

//- Cookie cutter parameters

TipHeight = IntegerMultiple(8.0,ThreadThick);		// cutting edge
TipWidth = 5*ThreadWidth;

WallHeight = IntegerMultiple(4.0,ThreadThick);		// center section
WallWidth = IntegerMultiple(4.0,ThreadWidth);

LipHeight = IntegerMultiple(2.0,ThreadThick);		// cutter handle
LipWidth = IntegerMultiple(3.0,ThreadWidth);

PlateThick = IntegerMultiple(4.0,ThreadThick);	// solid plate under press relief

//- Useful info

function IntegerMultiple(Size,Unit) = Unit * ceil(Size / Unit);

Protrusion = 0.1;						// make holes & unions work correctly

MaxConvexity = 5;						// used for F5 previews in OpenSCAD GUI

ZFuzz = 0.2;							// numeric chaff just above height map Z=0 plane

//-----------------
// Import plate height map, slice off a slab to define outline

module Slab(Thick=1.0) {
	intersection() {
		translate([0,0,Thick/2])
			cube([2*ImageX,2*ImageY,Thick],center=true);
		scale(PlateScaleXYZ)
			difference() {
				translate([0,0,-ZFuzz])
					surface(fnPlate,center=true,convexity=MaxConvexity);
				translate([0,0,-1])
					cube([2*ImageX,2*ImageY,2],center=true);
			}
	}
}

//- Put peg grid on build surface

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);
}

//- Build it

//ShowPegGrid();

if (BuildPress) {
	echo("Building press");
	union() {
		Slab(PlateThick + Protrusion);
		translate([0,0,PlateThick])							// cookie press height map
			scale(MapScaleXYZ)
			difference() {
				translate([0,0,-ZFuzz])
					surface(fnMap,center=true,convexity=MaxConvexity);
				translate([0,0,-1])
					cube([2*ImageX,2*ImageY,2],center=true);
			}
	}
}

if (BuildCutter) {
	echo("Building cutter");
	union() {
		difference() {
			union() {										// stack cutter layers
				translate([0,0,(WallHeight + LipHeight - 1)])
					minkowski() {
						Slab(TipHeight);
						cylinder(r=TipWidth,h=1);
					}
				translate([0,0,LipHeight - 1])
					minkowski() {
						Slab(WallHeight);
						cylinder(r=WallWidth,h=1);
					}
			}
			translate([0,0,-1])								// punch central hole for plate
				Slab(TipHeight + WallHeight + LipHeight + 2);
		}
		minkowski() {										// put lip around base
			difference() {
				minkowski() {
					Slab(LipHeight/3);
					cylinder(r=WallWidth,h=LipHeight/3);
				}
				translate([0,0,-2*LipHeight])
					Slab(4*LipHeight);
			}
			cylinder(r=LipWidth,h=LipHeight/3);
		}
	}
}

And then it Just Works…

That process produces a grayscale height map PNG image in the proper orientation:

OpenSCAD, however, requires a flat ASCII data file to build a 3D model, as described there.

It turns out that a PGM (“Portable Graymap”) file is almost exactly what we need: a fixed format header in ASCII text, followed by the pixel data in either ASCII or binary. To get an ASCII-formatted PGM file from that PNG image:

convert jellyfish_prep.png -compress None jellyfish.pgm

The top of the PGM file looks like this:

P2
149 159
255
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 255 255 255 255 255 255 255 255 255 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 255 255 255 255 255 255 255 255 255 255
... more data ...

The data isn’t in the XY array layout that OpenSCAD expects; It Would Be Very Nice If OpenSCAD could read PGM files, including the header describing the array size, but it doesn’t. Fortunately, some Bash-fu can handle the reformatting.

First, store the number of pixels along the X axis in a Bash variable:

ImageX=`identify -format '%[fx:w]' ${imagename}_prep.png`

Note the backticks around the whole mess that tell Bash to execute what’s inside and return the value. The -format operation returns the width as an integer, which is what we need.

Now, returning our attention to the PGM file, convert multiple blanks and line ends to single line ends, thus putting one entry on each output line with no other whitespace:

cat filename.pgm | tr -s ' \012' '\012'

Nota bene: there’s a leading blank in the first character string and the escape sequences should read “reverse-slash zero one two” to denote the Unix-style line end character (ASCII 10 = newline). I think the meta-markup works around the usual WordPress formatting, but ya never know what can go wrong.

The first four lines then contain the magic number, X size, Y size, and the maximum data value, respectively:

P2
149
159
255

Those values are all known, because:

• The magic number is P2 for ASCII PGM files. It would be useful to verify this, but …
• The XY values correspond to the image size
• The maximum data value will be 255 because of  the auto-level operation applied to the image’s 8-bit grayscaleness

Strip off the first four lines and wrap the remaining data into an array corresponding to the image size:

tail -n +5 | column -x -c $((8*${ImageX})) > filename.dat

The $((8*${ImageX)) magic comes from the way the column command works: it’s right-aligning each data values in an 8 character column, so you specify the total width of the result in character columns. Think of the parameter as specifying the screen width and you’ll be on the right track.

That fits neatly into a single line of Bash gibberish:

cat filename.pgm | tr -s ' \012' '\012' | tail -n +5 | column -x -c $((8*${ImageX})) > filename.dat

The first complete line of that file goes on basically forever, but it actually has the right stuff. You can examine it thusly:

head -1 filename.dat

The file should then Just Work when sucked into OpenSCAD with the surface() function:

surface("filename.dat",center=true,convexity=10);

And, indeed, it does:

Note that it’s oriented with the head in the +Y direction, the tentacles (or whatever) in the -Y direction, and the freckle over the eye on the proper side. Here’s the original PNG image of the cookie for reference:

Using center=true centers the object on the XY plate, but the base of the solid remains at Z=-1. That makes some sense, as the “solid” part of the model lies below the Z values set by the data: the model includes a one unit thick slab below Z=0 for all points.

The convexity=10 parameter helps OpenSCAD’s quick rendering code (invoked by hitting F5 in the GUI) determine when it can stop looking for intersections between the visible ray and the object. It doesn’t affect the F6 CGAL compilation & export to STL. Because this routine will eventually be used only from the command line, the value doesn’t matter.

That works and the height map looks OK, but the model is too large in all directions and the slab below Z=0 has got to go. But it’s looking good…