How to find points on the circumference of a arc knowing a start point, an end point and the radius?

Question

Please see the image below for a visual clue to my problem:

I have the coordinates for points 1 and 2. They were derived by a formula that uses the other information available (see question: How to calculate a point on a circle knowing the radius and center point).

What I need to do now (separately from the track construction) is plot the points in green between point 1 and 2.

What is the best way of doing so? My Maths skills are not the best I have to admit and I'm sure there's a really simple formula I just can't work out (from my research) which to use or how to implement.

Answer 1

In the notation of my answer to your linked question (i.e. x,y is the current location, fx,fy is the current 'forward vector', and lx,ly is the current 'left vector')

for (i=0; i<=10; i++)
{
  sub_angle=(i/10)*deg2rad(22.5);
  xi=x+285.206*(sin(sub_angle)*fx + (1-cos(sub_angle))*(-lx))
  yi=y+285.206*(sin(sub_angle)*fy + (1-cos(sub_angle))*(-ly))
  // now plot green point at (xi, yi)
}

would generate eleven green points equally spaced along the arc.

Answer 2

The equation of a circle with center (h,k) and radius r is

(x - h)² + (y - k)² = r² if that helps

check out this link for points http://www.analyzemath.com/Calculators/CircleInterCalc.html

The parametric equation for a circle is

x = cx + r * cos(a) y = cy + r * sin(a) Where r is the radius, cx,cy the origin, and a the angle from 0..2PI radians or 0..360 degrees.