Maths question regarding curved bay window

I have been using Archimesh to create floor plans for a representation of my house. Generally, this is OK but it really is not very flexible with curved walls and cannot reflect my bay window at all.

All curved walls so far have not been smooth enough to add the 4 bay equal size window panels that I have.

I have finally decided that I will succumb to splitting the bay into 4 straight walls.

As it is not an exact representation, but I do want it to look right, I realise I have a maths problem to solve to identify the angles and lengths of these 4 walls.

The width of the bay on my plan is 240cm. At the centre of the bay, it should reflect a protrusion of 70cm and the curve of the bay is consistent with an arc on a perfect circle although I cannot be sure how many degrees of circumference this would be. It looks roughly 75 degrees to me. I expect with the width of the bay and the distance the window protrudes, this can all be calculated.

If anyone could provide me with wall lengths and angles to create this, I would be grateful.

Also, in case I have to change scale but with the same ratios, I would be grateful for the working to calculate this in the future.

Width of bay 240cm

Maximum protusion at centre of window 70cm

No of sections to split curve 4

Cheers

• Hi. I understand you would be using these measurements in Blender, but I think asking a question which just requires maths for the answer would be more on topic for somewhere like math.stackexchange.com (but you would have to check what is on-topic for their site). Thanks. Jun 24 '20 at 23:46
• I’m voting to close this question because it is not about using Blender. Jun 24 '20 at 23:46
• Jun 25 '20 at 4:17
• @RobinBetts Not entirely sure. The question seems like a general maths problem, which isn't on-topic. If the solution is related to blender that seems separate to whether the question is related, which tends to be the important part that determines if the question is on or off-topic. Maybe it's a border case. But I definitely think you could have a question on a separate StackExchange site that uses Blender as a solution, but that doesn't mean the question itself would be on topic here. Jun 25 '20 at 7:55
• FWIW: I flip flopped on the fence n fell off, ie voted to close then retracted. Question could be edited to "What is the (quickest or easiest or best or ... ) way to do this in blender" which often get thru. Jun 25 '20 at 11:46

1 Answer

@batFINGER's or something like it, is clearly the most accurate way, but if eyeballing is enough, you can use the Spin tool to create an arc between 3 points.

If the 2 end vertices are not aligned to a convenient set of axes, you may have to make a Custom Orientation from them.

Select the 2 end vertices, and ShiftS Cursor to selected. ShiftD duplicate one of the end vertices, and call up the Spin tool. Adjust the spin center in the perpendicular to the two ends to pass the arc of the spun vertex through the third point, and its angle to span the end points.

• I think all answers helped and allowed me to work out using planes, circles and vertices to work it out. Cheers Jun 27 '20 at 15:31