Is it worth using gothic geometry to make gothic arches/ windows and other gothic elements in studio?

Just as an example of the use of gothic geometry/ tracing

Im looking to possibly make a gothic structure and want to make sure its all geometrically harmonious, so would the best route simply be to use these forms of geometry- such as in the formation of these gothic window elements. I’d rather not eyeball this in studio.

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I took a quick try at that last shape with only using curve cutter and rotating in about 15 mins. I’m sure the other way would produce extremely detailed product so it comes down to really do you want to spend a lot of time or not. (Also please excuse that horrendous color choice :grimacing: )

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Ended up testing some of the geometry used to create the simplest shape out of them: the trefoil.

All the geometry involved:

This was all done at the origin of the baseplate to simplify positioning.

I had to use a circle generation plugin as well to ensure exact stud radii

Legend and explanation

Grey circles: The finished product.

Green dots: Centers of each needed circle: Being either the origin or a needed point in the intersection that would become the center of the corresponding circle.

Blue circles: I moved the center blue circle up by the radius of the gray, with then using the intersections of the center blue circle with the gray to find the centers of the 2 side blue circles. The outer circle had to be equatable to 8 in sections to ensure that there were parts equal in orientation to 0,90,180, and 270. The inner grey circles are half the amount segments.

Red lines: Imagine the circle in a square: the top red line is simply to top of the box, so its the top segment of the outer grey circle at 0 orientation. I needed to find its intersections with the side blue circles to verify the side circles’ center position was correct as well as create a triangle that meets at the origin. Orientations are -120 and 120.

Purple lines: The center purple line is simply the radius of the outer grey circle, which is needed for finding the intersection of the angle of the 2 other purple lines; their angles are half of 30, so in this case simply -120 and 120 plus and minus 15 degrees respectively. This was done at the green dots of each red line. The reasoning for this is that the top section of the radius line of the outer circle, past where the c-framed purple lines intersect, will become the radius of the inner circles.

Lime green lines: The distance between the intersection of the purple lines for the the bottom section of the large grey circle’s radius. I used the exact distance and copied for the bottom 2 intersection points to be the same without having to repeat the purple line procedure.

After configuring the width of each circle and negating the clipping parts of the inner circles to create the convex shape:

This is just for the basic shape without further detail. It took me about 1 hour to figure it all out, so is it worth it in the end to use this much math theory to ensure it’s basically geometrically harmonious? It’ll be much more involved for more complex gothic shapes and take me longer.