One common problem with drawing code in Cocoa (iOS and Mac OS X) is that people have trouble getting crisp, sharp lines. Often this problem ends up as a question like "How do I get a 1-pixel line from NSBezierPath" or "Why are my UIBezierPath lines fuzzy and transparent" or "Why are there little black dots at the corners of my NSRect".
The problem here is that coordinates in Quartz are not pixels. They are actually "virtual" coordinates that form a grid. At 1x resolution (i.e. non-Retina), these coordinates, using a unit commonly referred to as "points" to distinguish them from act pixels on a screen (or on a printer!), lie at the intersections between pixels. This is fine when filling a rectangle, because every pixel that lies inside the coordinates gets filled:
But lines are technically (mathematically!) invisible. To draw them, Quartz has to actually draw a rectangle with the given line width. This rectangle is centered over the coordinates:
So when you ask Quartz to stroke a rectangle with integral coordinates, it has the problem that it can only draw whole pixels. But here you see that we have half pixels. So what it does is it averages the color. For a 50% black (the line color) and 50% white (the background) line, it simply draws each pixel in 50% grey. For the corner pixels, which are 1/4th black and 3/4ths black, you get lighter/darker shades accordingly:
This is where your washed-out drawings, half-transparent and too-wide lines come from. The fix is now obvious: Don't draw between pixels, and you achieve that by moving your points by half a pixel, so your coordinate is centered over the desired pixel:
Now of course just offsetting may not be what you wanted. Because if you compare the filled variant to the stroked one, the stroke is one pixel larger towards the lower right. If you're e.g. clipping to the rectangle, this will cut off the lower right:
Since people usually expect the rectangle to stroke inside the specified rectangle, what you usually do is that you offset by 0.5 towards the center, so the lower right effectively moves up one pixel. Alternately, many drawing apps offset by 0.5 away from the center, to avoid overlap between the border and the fill (which can look odd when you're drawing with transparency).
Note that this only holds true for 1x screens. 2x Retina screens exhibit this problem differently, because each of the pixels below is actually drawn by 4 Retina pixels, which means they can actually draw the half-pixels needed for a 1 point wide line:
However, you still have this problem if you want to draw a line that is even thinner (e.g. 0.5 points or 1 device pixel). Also, since Apple may in the future introduce other Retina screens where e.g. every pixel could be made up of 9 Retina pixels (3x), you should really not rely on fixed numbers. Instead, there are now API calls to convert rectangles to "backing aligned", which do this for you, no matter whether you're running 1x, 2x, or a fictitious 3x. Otherwise, you may be moving things off pixels that would have displayed just fine:
And that's pretty much all there is to sharp drawing with Quartz.