Creating a symmetrical design for a coffee table

[WillAdams (William Adams (Carbide 3D))]

If one wanted to create a symmetrical design of parts which could be assembled on a base so as to create a marquetry design for a 24" round coffee table which had:

• 8 partial circles (lunes)
• 8 pointed star sections
• 8 flower petals (for overlapping (complete) and 4 which are notched so as to allow the others to seem to overlay)
• a central circle

one would do this by:

• creating a 24" x 24" working area:

Putting the origin at the center will make rotation and so forth easier.

We start w/ a 1/2" dowel at the center:

We will then add a line down the center:

Done

We then use circular array to rotate this to create the 8 reference points:

Select Center in Window

click at the center:

increase to 8 elements:

Ok

Draw in circles to represent the outside of the table, and the inset for the marquetry:

Draw in a circle for the crescents around the edge:

Draw in a second on the opposite side:

Select both:

rotate 22.5 degrees:

Done

Use Circular Array to duplicate it around the circle:

Ok

Select the circle for the edge of the marquetry and duplicate it in place:

Add the array of circles to the selection:

Note that there are twice as many as there should be, so select the top 8 and delete them.

and use Trim Vectors:

and remove what is not wanted:

Until one arrives at:

Ok

Ok

Join Vectors

Yes

[WillAdams (William Adams (Carbide 3D))]

Next we will create the points for the stars.

Select the 8 lines:

and duplicate them in place, then select them

and add the marquetry circle to the selection:

and use Trim Vectors:

to trim them short:

Ok

Draw in pairs of lines on either side of each opposing lune:

Done

Done

add the outer circle to the selection and again use Circular Array to duplicate:

Ok

Select one set of the lines for the center:

and use Trim Vectors:

to remove the inner geometry:

arriving at:

Ok

OK

[WillAdams (William Adams (Carbide 3D))]

Next we draw an 8-pointed flower — see:

Practical Shop Math: Simple Solutions to Workshop Fract…

Draw a circle from the center to an inner point of the 8-sided star:

Then draw a line from the center to the top of that circle:

Done

Duplicate the circle:

then drag the center to align with the top of the original:

Add the outermost circle to the selection:

Ok

Select the 8 circles:

and use Trim Vectors:

and remove all but the 8 leaves (4 complete, 4 overlayed)

Ok

Remove the 8 outer arcs from the selection:

and group

Then select and delete the 8 outer arcs:

Select the circle which is inset on the 8 pointed star:

and check its size (11.906)

Then select the group:

Scale it

Done

and rotate 22.5 degrees:

Done

Ungroup

Select the 8 short arcs and duplicate them in place twice:

Then rotate one set of the duplicates 45 degrees:

Done

Select the point for one star:

Join Vectors:

Yes

Select the circle for the center dowel:

and copy-paste it in place twice:

Select one of those circles and two arcs which describe a complete flower petal:

copy-paste them in place so as to duplicate, and use Trim Vectors to delete all but one petal:

OK

Use Join Vectors to close:

Yes

Repeat this for a petal which is overlaid by the two adjacent petals:

Note that it will be necessary to include copies of the two lines which describe the overlap.

Ok

Select the geometry for the overlaid petal:

Join Vectors:

Yes

At this point we should have closed versions of all the geometry necessary to describe the design — we can check this by selecting the open vectors:

and moving them to a hidden layer:

At which point the closed geometry can be duplicated and rotated as needed to arrive at:

and after a bit of cleaning up we arrive at:

which simply requires one additional piece of closed geometry which may be easily made by drawing a polyline to roughly define one example:

Ok

Join Vectors

Yes

which may then be duplicated as needed:

OK

At this point the geometry may be re-arranged and rotated so as to be cut out of the veneer for application to the round for the table.

… as requested on support …

[Zman (MICHAEL ZEMANEK)]

I am sorry for this comment.

As I was going through the info, I wanted to go up in the Attic and get my old Spirograph.

Great job Will

[WillAdams (William Adams (Carbide 3D))]

The Spirograph would be more for:

Guilloché: A History & Practical Manual