Drawing sectors

[Chakie]

Is there some easy way to draw sectors? I now do it by drawing two arcs and then fiddling with the curve until it looks somewhat right. Drawing arcs I do by drawing a line and adding an extra node at the approximate mid point and the fiddle that mid point sideways to get the arc. The two straight lines for the side and join it all. It's... horribly cumbersome not an ideal way to draw sectors. But my searching hasn't revealed any better way. I use this to create printed patterns for leather craft, so I need the curves and the straight edges to have exact lengths.

[walt.farrell]

Try the Donut Shape Tool.

[GarryP]

8 minutes ago, walt.farrell said:

Try the Donut Shape Tool.

I was going to suggest that but the OP wants to be able to set the exact lengths of the curves and straight lines, and the Donut Tool only does percentages and degrees.

There’s probably some basic maths that will convert to percentages and angles from the lengths but I can’t think of it at the moment.

[Chakie]

I had missed the donut tool. It does the shape I want, but not the exact size. It's possible to calculate the sector angle and needed overall size, but it gets a bit messy. It's basic geometry, but I have a computer drawing tool so that I don't need to sit with paper, pen and a calculator. I guess my best bet is still to draw my patterns by hand or guesstimate my curves.

[GarryP]

Do you only need to draw shapes that would have arcs which would both be parts of a (different, but with the same centre point) circle, as would be drawn by the Donut Tool when height and width proportions are constrained, or do things get more difficult?

[Chakie]

They always have the same center point. What I'm exactly doing is a pattern for a bracelet. A wider bracelet is a sector when "opened". I measure a hand where the bracelet will be and get, say, 19 cm and 21 cm for the inner and outer circumferences and, say, 6 cm between those. So I need to construct a sector that has 21 cm as the outer arc length and 19 cm as the inner arc length. The distance between those is 6 cm. These constraints define the only possible sector angle and the angle defines the curvature.

[v_kyr]

Try the Cog Tool ...

 

... and if needed, convert to curves and adjust the curve sides further with the Node Tool.

[GarryP]

I’ve read the given information more than once and think I’ve managed to figure out what’s wanted, up to a point, conceptually, but I’m still struggling to understand the full requirements or how to get the result.

It sounds to me like you want to make what’s in my attached example A, but curved as in my example B (example is just a mock-up and not accurate).
Unfortunately I don’t know how the three given dimensions can be retained, while curving the design, without knowing the amount by which the design needs to be ‘curved’, while also keeping everything in proportion and the correct lengths.
Whenever I try to make one thing the right length, the act of doing so changes the lengths of the other things.

Maybe someone else will know, but I suspect that you have come up against a limitation of generalised software which simply wasn’t designed to do this very specific sort of thing.

(I believe the thing you are trying to calculate is: “The ‘amount of bend’ by which the ‘sides’ stay straight, while the arcs are ‘concentric’ and ‘perpendicular’, while everything remains at the specific lengths, and the proportions are still correct”, which is beyond my meagre maths knowledge.)

[Chakie]

@GarryP The 3D shape here is really a standard cone without a bottom and with most of the top cut off. When you "slice open" such a cone you end up with a perfectly flat surface, just as in your B drawing.

But it seems that what I'm looking for puts too many constraints on the drawing, constraints that a normal vector program isn't meant to handle. I guess something like FreeCAD could do this and I think that's what I'll look at next. I'm anyway learning FreeCAD for my 3D printing adventures.

 

[Chakie]

19 hours ago, v_kyr said:

Try the Cog Tool ...

 

... and if needed, convert to curves and adjust the curve sides further with the Node Tool.

This tool also only gives percentages, not absolute values.

[GarryP]

36 minutes ago, Chakie said:

The 3D shape here is really a standard cone without a bottom and with most of the top cut off. When you "slice open" such a cone you end up with a perfectly flat surface

Ah, that explains it.

I found these which might be of some use: 
https://www.cmrp.com/cone-calculator
https://craig-russell.co.uk/cone-calculator/

You will need to convert your circumferences into diameters/radii before doing the calculation.

Then you should be able to create two circles – for the arcs – and a Pie shape – for the sides – and use the Shape Builder Tool to get the shape you want.

(There are probably other things out there on the web which will also help.)

[v_kyr]

1 hour ago, Chakie said:

This tool also only gives percentages, not absolute values.

Most of the Affinity tools which draw arc based shapes are defined that percentage way. That's a common way for plain drawing apps and the like ...

• Draw a circular sector with SVG

In order to get absolute values use some other more appropriate tools and/or draw things in SVG instead for reuse.

• Annulus Sector Calculator <--- ***
  
  
   
• SVG donut slice as path element (annular sector)
• svg-arc

Or use some SVG Path Editor for working and trying out direct values ...

 

Or create the needed sector element out of geometric subtract operations from other shapes ...

[Chakie]

I never got a notification about this last reply by @v_kyr...

The annulus calculator you linked to is great as it gives the used math. Unfortunately it calculates the opposite of what I wanted, i.e. I have to enter my unknowns and it will calculate what I already know. The other links have the same issue where they paint the annulus (nice new word!) based on the sector angle and the radii, but these are the values I don't have.

But as you say it seems that there could be other SVG related tools out there that could help. Or if I get the math correct I'll just create a small Python tool to do it for me.

[v_kyr]

2 hours ago, Chakie said:

Or if I get the math correct I'll just create a small Python tool to do it for me.

Should be a no-brainer to build a little Py script which converts a formula accordingly to the values you are looking for instead.

[LionelD]

Test - posts disappearing…

[LionelD]

Ok, looks like my posts are not disappearing anymore.

@Chakie Hi, how far did you get?  I ask because I made a toy for you several days ago, not sure if it might still be of interest..

Edited December 1, 2023 by LionelD
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