Is point inside a circle sector

Question

I need help on how to determine if a point "D" is inside a circle sector of 180°, known radius & center "B". As for the direction of the sector I don't know how to explain it with words so I made a sketch but basically it depends on another point "A".

sketch

An explanation would be good enough but I'm not very good at maths so if you could give me a pseudocode it would be perfect!

Thanks !

It is called a sector, not a cone. Here's an answer maybe could help https://stackoverflow.com/a/13675772/3807365 — IT goldman, Jun 24 '22 at 18:00
Thanks, this is what I was looking for. And do you have any additional information to give for the sectorStart/sectorEnd ? — Dromd, Jun 24 '22 at 18:13
see [Generate a "pieslice" in C without using the pieslice() of graphics.h](https://stackoverflow.com/a/58246614/2521214) — Spektre, Jun 26 '22 at 07:30

John Alexiou · Accepted Answer · 2022-06-26T14:48:54.543

0

What you are looking for is the angle ψ below, to test if it is within certain limits (like +/- 90°)

fig1

This can be done by finding the angle ψ between the vectors B-A and D-B.

The angle between them is found using the following dot and cross product rules

fig2 fig3

and the pseudocode using the atan2(dy,dx) function that must programming environments have

v_1.x = B.x-A.x
v_1.y = B.y-A.y
v_2.x = D.x-B.x
v_2.y = D.y-B.y

ψ = atan2( (v_1.x*v_2.y - v_1.y*v_2.x), (v_1.x*v_2.x + v_1.y*v_2.y) )

Note that the result is within -π and +π covering all 4 quadrants

Now just check if abs(ψ) <= π/2.

_{Take a note of the definition of atan2 since some environments define it as atan2(dx,dy) and some as atan2(dy,dx), where the angle is measured such that dx=r*cos(ψ) and dy=r*sin(ψ).}

And don't forget to check also the distance BD if it's within the radius of the circle.

edited Jun 26 '22 at 14:48

answered Jun 24 '22 at 18:59

John Alexiou

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That looks like a solved question, thanks! – Dromd Jun 24 '22 at 19:14
Other answers might come also, but in my opinion the above is the simplest and it avoids taking any square roots and the complexities that arise from complementary angles. – John Alexiou Jun 24 '22 at 19:17
goniometrics is not needed for this at all ... – Spektre Jun 26 '22 at 07:31

Is point inside a circle sector

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