Coordinates on the circumference of cirlce/ellipse?

Question

Given the angle and the radius, How do I determine the coordinates of the ends of the arc (i.e. the (x,y) of the ends of the arc in the circumference)

This can be thought of a pie chart where for each pie I would want to calculate the x,y of the ends of each pie on the circumference.

Thanks,

Jenni

Answer 1

For a circle
x=r*cos(theta)
y=r*sin(theta)

For an ellipse
x=a*cos(theta)
y=b*sin(theta)
where a=length along x-axis and b=length along y-axis

Answer 2

Depends on how complicated you want to make this.

You have an equation for the circle. From it, you can find the centre (X0, Y0).

Each radius is part of a line that goes through the centre (X0, Y0) and has a slope relative to the angle. For example, if your first line is horizontal (parallel to the x axis), then it has a slope of 0. It will cross the circle at (X0+R, Y0).

The second line is, let us say, at an angle w from the first (w is the angle at the centre of the circle). Then the slope of the second line is Tan(w), and you know that this line also goes through the centre of the circle (X0, Y0). From that, you can find the equation of the line, in the form y = mx + b, where m is the slope Tan(w), and b can be found by replacing x and y by X0 and Y0.

Now you have two unknowns and two equations (the line and the circle). Solve as a simultaneous system and the solution is the intersection (there will be two as the equation is for an infinite line in both directions -- pick the correct intersection).

PS: of course, if you prefer an easy way, use polar coordinates as the other two have said.

Answer 3

Essentially what you want to do is to convert from polar coordinates to rectangular coordinates.

The formulas for this are:

x = r cosθ
y = r sinθ