Circular Array?

[Bruce Kieffer]

Is there a way using the circular array command to easily duplicate this triangle to follow the circle and so all the duplicated triangles touch each other? I',m trying to model a cupcake paper baking liner.

[Pat Stanford]

Unless you really need to have it be that exact circle and size, I would work it the other way and do the basic math of what the perimeter would by of a polygon with X sides equal to the base of your triangle and then figure the rotation angle to get 360° with that number of faces of a polygon (360/X).

 

Or start with a regular polygon with the number of sides you want and then make a triangle that matches the length of one face.

 

Trying to get a solution where the length of an arbitrary number of equal chords that will match the circumference of a circle won't be easy to do either the math or graphically.

 

To actually do the duplicates you can do either Duplicate Array with the Rotate Duplicates and Use Duplication Angle options set or use the Duplicate Along Path with the Tangent to Path and Keep Original Orientation options on and the Center Object on Path option off.

 

Or if you don't want to have to do math and you are going to do an Add Surface at the end to get a single polygon anyway. Make a regular polygon with the appropriate number of sides. Draw an overlapping circle with a radius equal to the points of the triangles and Send to Back. With the Snap to Object and Snap to Angle snaps on, use the Reshape Polygon tool in the Add Point mode to drag the center point of each face out to the circle. Use the Perpendicular and Object snaps to get it right.  For the ~30-60 sides you need it should not take more than about 2 minutes.

[mike m oz]

Bruce there is.  You need to adjust the size of your triangle first though because at the moment it is approximately 46.27 triangles around the circumference.  You need to have a whole number.

 

48 would give you an included angle of 7.5° for lines drawn from the centre of the circle to the circumference.  Adjust the base of the triangle so it matches that.  Then use the circular array tool with the following settings:

 

 

Result:

 

 

keiffer circular array.vwx

Edited January 24, 2020 by mike m oz
Add Vw 2020 file

[Bruce Kieffer]

Thanks Pat and Mike. I used a combination of both your suggestions. I drew a 48 sided "regular" polygon equal to the dia. of the center circle. Then I drew a tangent centerline from the circle counterpoint through the midpoint of one of the polygon segments. Then I drew an equal sided triangle touching the endpoints of one segment. Next will be to duplicate the triangle 47 times.

Edited January 24, 2020 by Bruce Kieffer