Question

iPhone SDK and Objective-C

Goal:

I’m trying to calculate the ‘x’ and ‘y’ coordinates of 2 circles. I have the inner circle dimensions and want to calculate what the ‘x’ and ‘y’ coordinates of the larger outer circle circumference would be to match the same width (distance) along the edge of the larger circle as it does with the inner circle.

In the end, I just need to figure out what the edge x/y points would be for the large circles edge. So that it matches the same as the inner smaller circle. If the width is 10 high on the inner circle, I need to know the x/y points to make it 10 high to the larger circle. To make a rectangle that will extend. Perpendicular lines.

Example:

I’m using the following to calculate the first 2 sets of x/y for the arc on the inner circle to plot points:

- (CGPoint)coordinatePoints:(CGFloat)radius angleDegrees:(CGFloat)degrees xAxis:(CGFloat)x yAxis:(CGFloat)y {
    CGFloat pointX = (CGFloat) ((radius * cos((degrees * M_PI) / 180.0f)) + x);
    CGFloat pointY = (CGFloat) ((radius * sin((degrees * M_PI) / 180.0f)) + y);
    CGPoint points = CGPointMake(pointX, pointY);

    return points;
}

I call it for the first 2 positions on the inner circle. I need to figure out how to make it have the distance on the outer circle as well.

CGPoint innerPoints1 = [self coordinatePoints:innerRadius angleDegrees:startingPoint xAxis:x yAxis:y];
CGPoint innerPoints2 = [self coordinatePoints:innerRadius angleDegrees:endingPoint xAxis:x yAxis:y];

If the inner circle radius is 200, and the outer circle radius is 500, I want it to still be the same thickness from the inner circle to the larger outer circle when I plot the points.

// I have these calculated.
CGContextMoveToPoint(context, innerPoints1.x, innerPoints1.y);
CGContextAddLineToPoint(context, innerPoints2.x, innerPoints2.y);

// I need to find the solution for making innerPoints3 and innerPoints4 correctly.
CGContextAddLineToPoint(context, innerPoints3.x, innerPoints3.y);
CGContextAddLineToPoint(context, innerPoints4.x, innerPoints4.y);

I have the coordinates for the inner circle lines for spaced out x/y points. I need to find the proper way to get the same width plotted for the larger circle locations. Circle sizes will always change. Lengths of the lines will be dynamic. As I’m trying to create a polygon, I need to find 2 coordinates on the larger circles, for each segment.

Any help with this would be greatly appreciated.

Information graphics: a comprehensive illustrated reference
Page 74: In the section “Circular Column Graph”, my end goal is to be able to produce the same result as displayed in the 3 images.

Answer 1

If the spokes are not too thick, then the arc length is a good approximation of the spoke width:

So first you construct your 2 inner points, with 2 angles (a1 and a2) centered around a main spoke angle (a).
Then you calculate the distance D between these points (or you approximate it by R1*(a2-a1))

Then you take the points on the outer circle with angle values centered around the same main spoke angle: a-0.5*D/R2 and a+0.5*D/R2. These points will be D apart (measured on the arc)