Curve text on existing circle

Question

For an application I am building I have drawn 2 circles. One a bit bigger than the other. I want to curve text between those lines, for a circular menu I am building.

I read most stuff about curving a text that you have to split up your text in characters and draw each character on it's own with the right angle in mind (by rotating the context you are drawing on).

I just can't wrap my head around on how to get the right angles and positions for my characters.

I included a screenshot on what the menu, at the moment, look like. Only the texts I added by are loaded from an image in an UIImageView.

I hope someone can get me some starting points on how I can draw the text in the white circle, at certain points.

EDIT: Ok, I am currently at this point:

I accomplish by using the following code:

- (UIImage*) createMenuRingWithFrame:(CGRect)frame
{
    CGRect imageSize = CGRectMake(0,0,300,300);
    float perSectionDegrees = 360 / [sections count];
    float totalRotation = 90;
    char* fontName = (char*)[self.menuItemsFont.fontName cStringUsingEncoding:NSASCIIStringEncoding];

    CGColorSpaceRef colorSpace = CGColorSpaceCreateDeviceRGB();
    CGContextRef context = CGBitmapContextCreate(NULL, imageSize.size.width, imageSize.size.height, 8, 4 * imageSize.size.width, colorSpace, kCGImageAlphaPremultipliedFirst);

    CGContextSetTextMatrix(context, CGAffineTransformIdentity);
    CGContextSelectFont(context, fontName, 18, kCGEncodingMacRoman);

    CGContextSetRGBFillColor(context, 0, 0, 0, 1);

    CGPoint centerPoint = CGPointMake(imageSize.size.width / 2, imageSize.size.height / 2);
    double radius = (frame.size.width / 2);

    CGContextStrokeEllipseInRect(context, CGRectMake(centerPoint.x - (frame.size.width / 2), centerPoint.y - (frame.size.height / 2), frame.size.width, frame.size.height));

    for (int index = 0; index < [sections count]; index++)
    {
        NSString* menuItemText = [sections objectAtIndex:index];
        CGSize textSize = [menuItemText sizeWithFont:self.menuItemsFont];
        char* menuItemTextChar = (char*)[menuItemText cStringUsingEncoding:NSASCIIStringEncoding];

        float x = centerPoint.x + radius * cos(degreesToRadians(totalRotation));
        float y = centerPoint.y + radius * sin(degreesToRadians(totalRotation));

        CGContextSaveGState(context);

        CGContextTranslateCTM(context, x, y);
        CGContextRotateCTM(context, degreesToRadians(totalRotation - 90));
        CGContextShowTextAtPoint(context, 0 - (textSize.width / 2), 0 - (textSize.height / 2), menuItemTextChar, strlen(menuItemTextChar));

        CGContextRestoreGState(context);

        totalRotation += perSectionDegrees;
    }

    CGImageRef contextImage = CGBitmapContextCreateImage(context);

    CGContextRelease(context);
    CGColorSpaceRelease(colorSpace);

    return [UIImage imageWithCGImage:contextImage];
}

These are the variables I use in there:

NSArray* sections = [[NSArray alloc] initWithObjects:@"settings", @"test", @"stats", @"nog iets", @"woei", @"woei2", nil];
self.menuItemsFont = [UIFont fontWithName:@"VAGRounded-Bold" size:18];

The rotation of the words seem correct, the placement also. Now I need somehow figure out at which rotation the letters (and their coordinates) should be. I could use some help with that.

Edit: Fixed! Check out the following code!

- (void) drawStringAtContext:(CGContextRef) context string:(NSString*) text atAngle:(float) angle withRadius:(float) radius
{
    CGSize textSize = [text sizeWithFont:self.menuItemsFont];

    float perimeter = 2 * M_PI * radius;
    float textAngle = textSize.width / perimeter * 2 * M_PI;

    angle += textAngle / 2;

    for (int index = 0; index < [text length]; index++)
    {
        NSRange range = {index, 1};
        NSString* letter = [text substringWithRange:range];     
        char* c = (char*)[letter cStringUsingEncoding:NSASCIIStringEncoding];
        CGSize charSize = [letter sizeWithFont:self.menuItemsFont];

        NSLog(@"Char %@ with size: %f x %f", letter, charSize.width, charSize.height);

        float x = radius * cos(angle);
        float y = radius * sin(angle);

        float letterAngle = (charSize.width / perimeter * -2 * M_PI);

        CGContextSaveGState(context);
        CGContextTranslateCTM(context, x, y);
        CGContextRotateCTM(context, (angle - 0.5 * M_PI));
        CGContextShowTextAtPoint(context, 0, 0, c, strlen(c));
        CGContextRestoreGState(context);

        angle += letterAngle;
    }
}

- (UIImage*) createMenuRingWithFrame:(CGRect)frame
{
    CGPoint centerPoint = CGPointMake(frame.size.width / 2, frame.size.height / 2);
    char* fontName = (char*)[self.menuItemsFont.fontName cStringUsingEncoding:NSASCIIStringEncoding];

    CGFloat* ringColorComponents = (float*)CGColorGetComponents(ringColor.CGColor);
    CGFloat* textColorComponents = (float*)CGColorGetComponents(textColor.CGColor);

    CGColorSpaceRef colorSpace = CGColorSpaceCreateDeviceRGB();
    CGContextRef context = CGBitmapContextCreate(NULL, frame.size.width, frame.size.height, 8, 4 * frame.size.width, colorSpace, kCGImageAlphaPremultipliedFirst);

    CGContextSetTextMatrix(context, CGAffineTransformIdentity);

    CGContextSelectFont(context, fontName, 18, kCGEncodingMacRoman);
    CGContextSetRGBStrokeColor(context, ringColorComponents[0], ringColorComponents[1], ringColorComponents[2], ringAlpha);
    CGContextSetLineWidth(context, ringWidth);  

    CGContextStrokeEllipseInRect(context, CGRectMake(ringWidth, ringWidth, frame.size.width - (ringWidth * 2), frame.size.height - (ringWidth * 2)));
    CGContextSetRGBFillColor(context, textColorComponents[0], textColorComponents[1], textColorComponents[2], textAlpha);

    CGContextSaveGState(context);
    CGContextTranslateCTM(context, centerPoint.x, centerPoint.y);

    float angleStep = 2 * M_PI / [sections count];
    float angle = degreesToRadians(90);

    textRadius = textRadius - 12;

    for (NSString* text in sections)
    {
        [self drawStringAtContext:context string:text atAngle:angle withRadius:textRadius];
        angle -= angleStep;
    }

    CGContextRestoreGState(context);

    CGImageRef contextImage = CGBitmapContextCreateImage(context);

    CGContextRelease(context);
    CGColorSpaceRelease(colorSpace);

    [self saveImage:[UIImage imageWithCGImage:contextImage] withName:@"test.png"];
    return [UIImage imageWithCGImage:contextImage];

}

Answer 1

I tried to work it out quickly on paper, so i may be wrong :)

Convert the length of the string into units on the UnitCircle. Thus (string.lenght/ circle perimeter)*2Pi. You now have the angle in radians for the whole string. (That is the angle between start and end of the string)

For the separate letters you could do the same to get the angle (in radians) for individual letters (using letter widths)

Once you have the angle in radians you can work out the x and y position (and rotation) of the letters.

Bonus: for even spacing you could even work out the ratio between the total length of all strings and the whole perimeter. And divide the remaining space equally between the string.

Update I made a proof of concept using html5/canvas, so view it with a decent browser :) You should be able to port it. (mind you, the code isn't commented)
wtf: the code runs fine with the chrome debug console open, and fails when it is closed. (workaround: open chrome console: ctrl-shift-j and reload the page: f5); FF3.6.8 seems to do fine, but the letters 'dance'.