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From bent wire to 3D printed cookie cutters

Abstract

With the advent of 3D printers in private homes, producing custom kitchen utensils such as cookie cutters becomes feasible. However, using existing interfaces – such as Autodesk Inventor, SolidWorks or SketchUp – to design a such customized kitchen artifact is out of reach for most users. In this work we present a system that takes a bent wire, or thick line drawing, as shape input and creates a producible cookie cutter model. We use computer vision and implement the idea of using household items for shape input, as well as fiducial markers.

Introduction

The creation and consumption of Christmas cookies is an essential activity during the holidays. For baking cookies one needs, besides the edible side of things, a cookie cutter – or potentially a few of them. They come in many shapes and sizes, however, stars, hearts and similar motives dominate the commercially available selection.
Creating custom cookie shapes is typically accomplished using a knife instead of the fixed-shape cookie cutters. The results of this creative endeavour depends highly on the cutting skills of the people involved and are seldom reproducible. So if one wants high-quality, reproducible, custom cookie shapes creating a custom cookie cutter seems inevitable.
One of the things that immediately comes to mind is 3D printing the cookie cutter. And indeed, quite a few people have done so already [1]. Also, the idea of building something like a cookie cutter creation tool is not new [2]. However, this tool (and others alike) suffer from the fact that judging the physical dimensions of a drawn shape remains difficult or that their expressiveness is rather limited.
This work makes three main points: it presents an easy system to design and build cookie cutters, it demonstrates the idea of using household items for shape input and dwells on the idea of maintaining a close relationship to the real world.
The process described here goes as follows (see figure 1):
  1. design cookie shape by bending a wire or drawing a thick black line
  2. place/draw the outline on an A4 sheet of paper
  3. take a photo of the outline and extract, smooth a polygon
  4. convert outline into a printable cookie cutter
(a) designing the cookie cutter shape by bending a wire, placing it on an A4 sheet of paper and taking a photo of it (b) filtering the photo by binarizing it, extracting the paper sheet corners, and using a canny edge detector (c) constructing a 3D model using OpenSCAD and extracted polygon (d) printing the cookie cutter on a 3D printer

Figure 1: the design process demonstrated with a user-designed shape: (a) designing the cookie cutter shape by bending a wire, placing it on an A4 sheet of paper and taking a photo of it (b) filtering the photo by binarizing it, extracting the paper sheet corners, and using a canny edge detector (c) constructing a 3D model using OpenSCAD and extracted polygon (d) printing the cookie cutter on a 3D printer

Shape definition

Many ways of defining 2D shapes are described in literature. From sketch based interfaces [3] to more traditional 2D CAD systems [4]. All of those approaches suffer from their disconnection to world they are designing for. It is hard to judge the dimensions and appeal of those virtual artifacts before they become physical reality.
Our approach in this work lets the user define the shape using a simple, tangible shape input controller: a piece of wire. Imagine there was something like a "cookie cutter band" that one could bend into the desired shape. Once bent, the shape would be fixed and additional struts would be introduced to strengthen the cutter. That’s exactly what this system does. The user bends a piece of wire into the desired shape and the system constructs a cookie cutter, which is then printed on a 3D printer.

Shape extraction

The wire shape has to fulfill a set of constraints, so that it makes sense as a cookie cutter:

  • planarity: the wire has to be bent flat, much like the cutter itself is going to be. This constraint is also imposed by the application domain, as cookie dough is generally flat.
  • not self-intersecting: a self intersecting cookie cutter would produce cookies which do not hold together as one piece – hence, we require the shape to be a simple polygon.

After bending the shape, the user places the piece of wire on an A4 sheet of paper and takes a photo of that assembly. The photo is then fed into this system which extracts the shape using computer vision. Since the outcome is going to be produced for the real world, the polygon has to be translated into real world units. We map the image to real world coordinates by detecting the corners of the A4 paper. This leads to the following processing pipeline (implemented in C++ using the OpenCV [5]):

  1. threshold filter to binarize the image
  2. find paper corners and compute the homography
  3. warp perspective of the input image based on the homography
  4. canny filter the warped image
  5. erode the image to connect spurious lines
  6. find contours in eroded image
  7. select contour with largest area that is not the whole image
  8. if no contour is found, exit
  9. find center of the polygon using the enclosing circle
  10. approximate outline using Douglas-Pecker to smooth the polygon

Model creation and printing

The polygon coming from the shape extraction stage is then scaled into a smaller and a bigger version, which are assembled to form the cutter using CSG operations, implemented in OpenSCAD [6]. Scaling a concave polygon to build an outline is not as straight forward as scaling a convex one. While a convex polygon can be adequately scaled by multiplying each vertex with a scalar value, scaling a concave polygon that way is unsuitable for creating the model (see figure 2, b). To properly scale a concave polygon P = \mathbf{p}_0, \dots, \mathbf{p}_n for our needs, we translate each \mathbf{p}_i by the edge normal

    \[\lambda\frac{\mathbf{n}}{\vert \mathbf{n} \vert}, \mathbf{n}=(\mathbf{p}_{i+1} - \mathbf{p}_i)\]

with results as depicted in figure 2,c.

(a) the polygon to be scaled (b) the naively scaled version, drawn as dotted line (c) the properly scaled polygon

Figure 2: Scaling a concave polygon to create a thin outline: (a) the polygon to be scaled (b) the naively scaled version, drawn as dotted line (c) the properly scaled polygon

The correctly scaled polygons are then extruded into 3D space using OpenSCADs 2D subsystem. Additional struts are added to stiffen the cookie cutter and ease its handling. Strut size is determined by computing the bounding box of the polygon.

Discussion

We implemented this system using simple computer vision algorithms. While this implementation is sufficient in many cases, it is not particularly robust. The paper sheet corner detection does not always work and the whole process depends on proper parameter choice – parameters which are image dependent. A more sophisticated processing pipeline or some form of automated parameter choice could be explored.
Also, the line extraction depends on the characteristics of the shape being extracted. While the erosion stage somewhat mitigates this effect, e.g. glossy wires or "sketchy" are still unsuited for this system.

Our system does not enforce the constraints imposed by the domain (i.e. simple, not self-intersecting polygon). Users can input such a shape and the system will try to create a cookie cutter from it, regardless if such a cutter makes sense or not. The system could inform the user when a shape is not meaningful and suggest corrections.
The concave polygon scaling algorithm we used in this work, results in very thin shells around sharp corners. Some 3D printers, or their slicing software, can not reproduce such corners – or even strips close to those corners. As a result, the cutter can have gaps in its perimeter yielding an unclean cutting result. A more constant perimeter thickness could be achieved by sampling the polygon at a finer rate (better normal computation) or by employing post model generation algorithms, such as the one described by Stava et. al. [7]
Future work could investigate the suitability of certain media as shape input controllers. A question that comes to mind is, if it is easier to bend a wire into shape rather than to draw the shape with a thick pen? An investigation of this question should take the tangibility and affordance of the wire *as compared to a drawing on a sheet of paper) into account.
Also, the importance of real-time feedback could be explored. Is it enough to get feedback on the producability/constraint enforcement at discrete points in time, e.g. when we feed an image into the system? Or should the system provide continuous feedback? Also, what is the relationship between constraint system complexity and real-time feedback need?

Conclusion

In this work, we described the idea of using household items for modeling, specifically investigating wire as shape input sensor and A4 paper as fiducial marker. We implemented a system for designing cookie cutters as case study, targeting 3D printing as production technique. Our system is easy to use, as it is situated in the real world.

Download

The source code can be found here [8], including a few test pictures. I’ve only tested it on Linux, however, it should run on OSX as well. To compile/run the stuff run:

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tar xvfz contours.tar.gz && cd contours
mkdir build && cd build
cmake .. && make
./contours ../test4.jpg && openscad main.scad

References

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