How to draw stars using Quartz Core?

Question

I'm trying to adapt an example provided by Apple in order to programmatically draw stars in line, the code is the following:

CGContextRef context = UIGraphicsGetCurrentContext();
CGContextSetLineWidth(context, aSize);

    for (NSUInteger i=0; i<stars; i++) 
    {

       CGContextSetFillColorWithColor(context, aColor);
       CGContextSetStrokeColorWithColor(context, aColor);

       float w = item.size.width;
       double r = w / 2;
       double theta = 2 * M_PI * (2.0 / 5.0); // 144 degrees

       CGContextMoveToPoint(context, 0, r);

       for (NSUInteger k=1; k<5; k++) 
       {
          float x = r * sin(k * theta);
          float y = r * cos(k * theta);
          CGContextAddLineToPoint(context, x, y);
       }

       CGContextClosePath(context);
       CGContextFillPath(context);
    }

The code above draws a perfect star, but is 1. displayed upside down 2. is black and without border. What I want to achive is to draw many stars on the same line and with the given style. I understand that I'm actually drawing the same path 5 times in the same position and that I have somehow to flip the context vertically, but after several tests I gave up! (I lack the necessary math and geometry skills :P)... could you please help me?

UPDATE:

Ok, thanks to CocoaFu, this is my refactored and working draw utility:

- (void)drawStars:(NSUInteger)count inContext:(CGContextRef)context;
{
    // constants
    const float w = self.itemSize.width;
    const float r = w/2;
    const double theta = 2 * M_PI * (2.0 / 5.0);
    const float flip = -1.0f; // flip vertically (default star representation)

    // drawing center for the star
    float xCenter = r;

    for (NSUInteger i=0; i<count; i++) 
    {
        // get star style based on the index
        CGContextSetFillColorWithColor(context, [self fillColorForItemAtIndex:i]);
        CGContextSetStrokeColorWithColor(context, [self strokeColorForItemAtIndex:i]);

        // update position
        CGContextMoveToPoint(context, xCenter, r * flip + r);

        // draw the necessary star lines
        for (NSUInteger k=1; k<5; k++) 
        {
            float x = r * sin(k * theta);
            float y = r * cos(k * theta);
            CGContextAddLineToPoint(context, x + xCenter, y * flip + r);
        }

        // update horizontal center for the next star
        xCenter += w + self.itemMargin; 

        // draw current star
        CGContextClosePath(context);
        CGContextFillPath(context);
        CGContextStrokePath(context);
    }
}

Answer 1

Here is code that will draw 3 stars in a horizontal line, it's is not pretty but it may help:

-(void)drawRect:(CGRect)rect
{
    int aSize = 100.0;
    const CGFloat color[4] = { 0.0, 0.0, 1.0, 1.0 }; // Blue
    CGColorRef aColor = CGColorCreate(CGColorSpaceCreateDeviceRGB(), color);
    CGContextRef context = UIGraphicsGetCurrentContext();
    CGContextSetLineWidth(context, aSize);
    CGFloat xCenter = 100.0;
    CGFloat yCenter = 100.0;

    float  w = 100.0;
    double r = w / 2.0;
    float flip = -1.0;

    for (NSUInteger i=0; i<3; i++) 
    {
        CGContextSetFillColorWithColor(context, aColor);
        CGContextSetStrokeColorWithColor(context, aColor);

        double theta = 2.0 * M_PI * (2.0 / 5.0); // 144 degrees

        CGContextMoveToPoint(context, xCenter, r*flip+yCenter);

        for (NSUInteger k=1; k<5; k++) 
        {
            float x = r * sin(k * theta);
            float y = r * cos(k * theta);
            CGContextAddLineToPoint(context, x+xCenter, y*flip+yCenter);
        }
        xCenter += 150.0;
    }
    CGContextClosePath(context);
    CGContextFillPath(context);
}

Answer 2

Here's an algorithm to implement what buddhabrot implied:

- (void)drawStarInContext:(CGContextRef)context withNumberOfPoints:(NSInteger)points center:(CGPoint)center innerRadius:(CGFloat)innerRadius outerRadius:(CGFloat)outerRadius fillColor:(UIColor *)fill strokeColor:(UIColor *)stroke strokeWidth:(CGFloat)strokeWidth {
    CGFloat arcPerPoint = 2.0f * M_PI / points;
    CGFloat theta = M_PI / 2.0f;

    // Move to starting point (tip at 90 degrees on outside of star)
    CGPoint pt = CGPointMake(center.x - (outerRadius * cosf(theta)), center.y - (outerRadius * sinf(theta)));
    CGContextMoveToPoint(context, pt.x, pt.y);

    for (int i = 0; i < points; i = i + 1) {
        // Calculate next inner point (moving clockwise), accounting for crossing of 0 degrees
        theta = theta - (arcPerPoint / 2.0f);
        if (theta < 0.0f) {
            theta = theta + (2 * M_PI);
        }
        pt = CGPointMake(center.x - (innerRadius * cosf(theta)), center.y - (innerRadius * sinf(theta)));
        CGContextAddLineToPoint(context, pt.x, pt.y);

        // Calculate next outer point (moving clockwise), accounting for crossing of 0 degrees
        theta = theta - (arcPerPoint / 2.0f);
        if (theta < 0.0f) {
            theta = theta + (2 * M_PI);
        }
        pt = CGPointMake(center.x - (outerRadius * cosf(theta)), center.y - (outerRadius * sinf(theta)));
        CGContextAddLineToPoint(context, pt.x, pt.y);
    }
    CGContextClosePath(context);
    CGContextSetLineWidth(context, strokeWidth);
    [fill setFill];
    [stroke setStroke];
    CGContextDrawPath(context, kCGPathFillStroke);
}

Works for me for most basic stars. Tested from 2 points (makes a good diamond!) up to 9 stars.

If you want a star with point down, change the subtraction to addition.

To draw multiples, create a loop and call this method multiple times, passing a new center each time. That should line them up nicely!