Question

Background:

I was recently playing around with GDI+ to draw a “Disc” displaying a sweeping color change through 360 degrees. (I dug up some HSL to RGB code to loop through HSL(1,1,1) -> HSL(360,1,1))

Regarding the disc, I first drew a full solid circle using the above, and then a second circle in Grey over the center to give the following

So this is all fine… but I realised that GDI+ is insulating us from a lot of the tricky match that’s going on here by way of the FillPie method. Also, FillPie requires you to supply a bounding rectangle for the pie as opposed to a Radius Length. It also does a full segment fill and doesnt allow you to specify a part of that segment only.

Question:

Can anyone point me in the direction of some Math functions or give any explanation on what forumla I would need to calculate the area & plot points of the following “Green Filled Area” given:

Point `c` - an x,y co-ordinate
Angle `A` - an angle from horizontal
Angle `B  - an angle from horizontal where `B` - `A` == the sweep angle
Length `r` - a distance from `c`
Length `r2` - a distance from `c` where `r2` - `r` == the `height` of the segment to be filled.

Links to Math sources are fine but I’ve had a quick google & look at Wolfram Math and could find what I was looking for. Also, if there was some way to generate a sequence of bounding (x,y) co-or’s that could be passed as a Point[] to Graphics.FillPolygon, that’d be cool too.

Answer 1

The area is the difference of the outer and inner disc parts. The area of a disc part is proportional to the angle sweep:

area = (b-a)*((r+r2)^2-r^2)/2

a and b must be expressed in radians.
For b-a = 2*Pi, area = Pi*(r+r2)^2 - Pi*r^2 is the difference of the areas of the outer and inner discs.

You can generate points on the inner / outer circle using

x = cx + r * cos(t)     /     x = cx + (r+r2) * cos(t)
y = cy + r * sin(t)     /     y = cy + (r+r2) * sin(t)

Where t varies from a to b.