Arrange Rectangles with Python to Design a Carton

Recently I've been interested in cardboard boxes and how to design and model them.  In my last blog post I described how to create a box in Fusion 360.  It works but it's a cumbersome, frustrating, and time consuming process.  What was needed was a way to go from concept to template quickly.  After looking around and not finding a tool for the job, I designed one.  It's called rectangleBuilder.

Laying out a template isn't too hard once you get the hang of it.  Draw all the rectangles that make up the box you intend to build and then dimension them.  Then define relationships between all the rectangles.  An example of a relationship can be seen in the plan below.  The bottom middle of rectangle B is in the same location as the top middle of rectangle A.

Box Template Plan

This can be done by defining a Rectangle class in python,  It is initialized with its width and height and by default is placed with its bottom left corner at (0,0).  The Rectangle object is also aware of the position of all its corners and edge midpoints.  When called with a code for one of these points it returns the xy coordinates in list form.  For example, calling an object with the argument 'TM' will return the coordinates of the top middle.  All of this shorthand is explained in the code.

Define rectangle sizes

This is the part that I think is really cool.  Positioning the rectangles by defining geometric relationships.  In the code below the bottom middle of rectangle A is positioned at the origin.  Rectangle B is then positioned so that it's bottom middle is in the same position as the top middle of rectangle A.  The last line demonstrates the offset feature.  It essentially says, place rectangle M so that its bottom left corner is in the same position as the bottom right of rectangle B then shift it in the y direction by an amount (t+b).  The few lines of code above and below completely describe the template for the box.

Position rectangles

This data can then be used to generate an SVG template in python to see if everything is as expected.  The outline to cut is in black and the bend lines are marked in red.

Box template

That's all well and good but how do we transfer that to cardboard?  I don't have a plotter or laser cutter so it has to be done by hand.  After some experimenting, the below instructions are the easiest way to describe the rectangle edges so that they can be easily drawn.  The y coordinate and the start and end x coordinates of the horizontal lines are listed in increasing y order.

Stats and Horizontal lines

The same process is repeated for the vertical lines as well.

Vertical lines

Take the piece of cardboard that you plan to use and draw a base line in the direction of the x axis.  At each end of this line draw perpendicular guides in the direction of the y axis.  Along each of these lines mark all the y coordinates from the horizontal line list using the base line as the zero point.  You can then draw the line segments in the following manner.  77.0 , (84.0 - 124.5) means place a ruler on the 77.0 marks you would have drawn in the last step with the 0 mark on the left guide.  Then draw a line from 84.0 to 124.5 on the ruler.  By working through the list the design will gradually appear.  The vertical list is supplied just to be complete and isn't really needed as the ends of the horizontal lines can be joined to form the rectangles.

Edge guides

The layout looks like the SVG file so everything worked out OK.

Box to cut out

The bend lines can be perforated with a tool like the one below that's used for transferring dressmaking patterns.

Perforated Bend Lines

Cut out the outlines with a scalpel.

Flattened box

When folded together everything works quite well.  You can see in the image below what my intention was.  The top extends over to cover the entire top and although not necessary is a fun little design challenge.

Top overlap

As it's a tight fit, the box needs to be taped together to stop it springing open.

Assembled Box

Everything seems to fit nicely.  A little tweaking could make things better, but I'm happy with it.  In the end the fit all comes down to how accurately the template is drawn and bent.  Folding across the corrugations is easy to get right, but folding in the same direction as the corrugations is hard and I need to come up with a better way to do it.  When folding with the corrugation it's not uncommon for the fold to follow the middle of the corrugation.  This could be a couple mm away from from the line.

Get The Code!

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