 ### Introduction to Quartz

Quartz is at the center of all graphics in Cocoa. It provides basic graphics data structures and drawing routines, as well Mac OS X's window server.

This beginner-level tutorial introduces basic Cocoa graphics concepts: rectangles, points, colors, and coordinate systems.

This tutorial is written and illustrated by Scott Stevenson

### Rectangles and Points

All drawing in Quartz involves rectangles. In Cocoa, you use the NSRect struct to describe a rectangle's location and dimensions:

(Rects don't automatically draw themselves. These are just diagrams to go with the examples.)

typedef struct { NSPoint origin; NSSize size; } NSRect; // make a rect at (0,0) which is 20x20 NSRect myRect; myRect.origin.x = 0; myRect.origin.y = 0; myRect.size.width = 20; myRect.size.height = 20; The origin field is the "anchor point" of the rect, where the drawing starts. A point is described by NSPoint, which has x and y coordinates:

typedef struct { float x; float y; } NSPoint; // make three points on the canvas NSPoint point1; point1.x = 4; point1.y = 11; NSPoint point2; point2.x = 12; point2.y = 21; NSPoint point3; point3.x = 19; point3.y = 8; The size field of a rect is an NSSize, which holds a width and a height. There's no way to depict an instance of NSSize, it has to be part of a rect to be useful.

typedef struct { float width; float height; } NSSize;
Much of 2D drawing in Cocoa is based on these three structs. Remember these are not Objective-C classes. You can't call methods on them directly, but there are functions that go with them.

All measurements in Quartz are float values, which gives you finer control of drawing than integer-based coordinates.

### Convenience Functions

Cocoa has a number of functions for creating geometry structs. Most of them are listed in Foundation's NSGeometry.h file.

// make a point at coordinate 20,20 NSPoint newPoint = NSMakePoint ( 20, 20 ); // make a size of 100 wide x 100 high NSSize newSize = NSMakeSize ( 100, 100 ); // use the previous point and size to make a rect NSRect newRect = NSMakeRect ( newPoint.x, newPoint.y, newSize.width, newSize.height ); // also can just do this NSRect newRect = NSMakeRect ( 20, 20, 100, 100 );
Using these functions instead of creating the structs manually makes the code a bit more obvious and makes searching easier.

### Coordinates in Quartz

The drawing area of a view in Cocoa is treated as a rect. Quartz calls this drawing area the "bounds." An NSPoint can represent any location in the view bounds.

The standard Quartz coordinate system is based on PDF model, which means drawing in a view starts in the bottom-left. This is what you see in geometry textbooks.

Sometimes it's easier to write drawing code if the origin is in the top-left. This is how things work in web page design, for example. Quartz calls this a flipped coordinate system. You can easily convert points between standard and flipped views using NSView's convertPoint:fromView: and convertPoint:toView: methods.

### Rects as Objects

Because they're not objects, you can't store the geometry structs in an NSArray, NSDictionary, or NSSet directly, but you can wrap them in an NSValue object:

NSRect newRect = NSMakeRect ( 20, 20, 100, 100 ); NSValue * rectObject = [NSValue valueWithRect: newRect]; NSMutableArray * myArray = [NSMutableArray array]; [myArray addObject: rectObject]; NSRect originalRect = [[myArray objectAtIndex: 0] rectValue];
NSValue has similar methods for NSPoint and NSSize. You can also log information about rects using the NSStringFromRect function:

NSRect newRect = NSMakeRect ( 20, 20, 100, 100 ); NSLog (@"%@", NSStringFromRect( newRect ));
Another function, NSRectFromString takes a properly-formatted rect description and returns an NSRect. Both sets of functions also exist for NSPoint and NSSize.

### Derived Rects

Cocoa provides functions to create new rects based on existing ones. Here's how to make a rect which has the same dimensions as the original, but is shifted down and to the right (offset).

// create a rect, then get the 5x5 offset NSRect rect1; rect1.origin.x = 0; rect1.origin.y = 0; rect1.size.width = 30; rect1.size.height = 25; NSRect rect2; rect2 = NSOffsetRect ( rect1, 5, 5 ); You can use negative values for the offset if you want to move in the opposite directions.

Here's how to get the intersection area of two rects:

// get the common area between two rects NSRect rect1; rect1.origin.x = 0; rect1.origin.y = 0; rect1.size.width = 30; rect1.size.height = 25; NSRect rect2; rect2 = NSOffsetRect ( rect1, 5, 5 ); NSRect rect3; rect3 = NSIntersectionRect ( rect1, rect2 ); Here's how to create a rect which encloses two other rects (a union).

// get a combination of two rects NSRect rect1; rect1.origin.x = 0; rect1.origin.y = 0; rect1.size.width = 30; rect1.size.height = 25; NSRect rect2; rect2 = NSOffsetRect ( rect1, 5, 5 ); NSRect rect3; rect3 = NSUnionRect ( rect1, rect2 ); An inset rect is helpful if you want to create a outer boundry, then create a rect for the content inside:

// get a contracted version of a rect NSRect rect1; rect1.origin.x = 0; rect1.origin.y = 0; rect1.size.width = 30; rect1.size.height = 25; NSRect rect2; rect2 = NSInsetRect ( rect1, 5, 5 ); ### Comparing Rects and Points

Foundation provides a group of functions to check the equality of points and rects, as well as functions to see if points and rects are inside in other rects.

NSRect rect1; rect1.origin.x = 0; rect1.origin.y = 0; rect1.size.width = 30; rect1.size.height = 25; NSPoint point1 = NSMakePoint ( 8,21 ); BOOL isInRect; isInRect = NSPointInRect ( point1, rect1 ); Below is a table of the most useful comparison functions. All of these functions return a YES or NO value.

Comparison Functions
NSEqualRects Are rects identical?
NSEqualPoints Are points identical?
NSEqualSizes Are sizes identical?
NSContainsRect Does the first rect contain the other?
NSIntersectsRect Do the rects at least partially overlap?
NSPointInRect Is the point inside the rect?
NSMouseInRect Is the mouse cursor in this rect?
NSIsEmptyRect Is the rect empty (no area)?

These functions are listed in Foundation's NSGeometry.h file.

### Drawing

NSRects and NSPoints only describe geometry, they don't actually do drawing. Let's look at some primitive drawing functions in Cocoa's NSGraphics.h file.

NSColor * gray = [NSColor grayColor]; NSColor * white = [NSColor whiteColor]; // fill background [gray set]; NSRectFill ( [self bounds] ); // fill target rect NSRect rect1 = NSMakeRect ( 21,21,210,210 ); [white set]; NSRectFill ( rect1 ); The example above uses NSColor. When you call the -set method on a color object, Quartz uses it for all drawing until you set a new one.

Here's how to draw a border around a rect:

NSColor * gray = [NSColor grayColor]; NSColor * white = [NSColor whiteColor]; // fill background [gray set]; NSRectFill ( [self bounds] ); // draw a border around target rect NSRect rect1 = NSMakeRect ( 21,21,210,210 ); [white set]; NSFrameRectWithWidth ( rect1, 1 ); You can also call NSFrameRect if you just want to use the default line width.

### Drawing Groups

It's often faster to draw an array of rects all at once instead of calling NSRectFill for each one individually.

Below is a more involved example which builds C-style arrays of NSRects and NSColors, then passes both to NSRectFillListWithColors.

// setup basics [[NSColor grayColor] set]; NSRectFill ( [self bounds] ); int count = 12; NSRect startingRect = NSMakeRect ( 21,21,50,50 ); // create arrays of rects and colors NSRect rectArray [count]; NSColor * colorArray[count]; rectArray  = startingRect; colorArray = [NSColor redColor]; // populate arrays int i; NSRect oneRect = rectArray; for ( i = 1; i < count; i++ ) { // move 100 pixels to the right oneRect.origin.x += 100; // if the right edge doesn't fit, move down 100 pixels if ( NSMaxX (oneRect) > NSMaxX ([self bounds]) ) { oneRect.origin.x = startingRect.origin.x; oneRect.origin.y += 100; } rectArray [i] = oneRect; // increment color colorArray[i] = [NSColor colorWithCalibratedHue: (i*0.04) saturation: 1 brightness: 0.9 alpha: 1]; } // use rect and color arrays to fill NSRectFillListWithColors ( rectArray, colorArray, count ); // draw a 2 pixel border around each rect [[NSColor whiteColor] set]; for ( i = 0; i < count; i++) { NSFrameRectWithWidth ( rectArray[i], 2 ); } This example also uses the function NSMaxX to get the maximum x-axis value of the rect (right edge). If it's outside of the view bounds, we move down to the next row.

### Wrap Up

We've covered basic Quartz concepts here. The next tutorial will dig into intermediate topics. You can download the final example here:

IntroToQuartz Xcode 2.4 Project (52k)

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For further reading, check out Cocoa Graphics Part II