TweetFollow Us on Twitter

September 96 - Graphical Truffles: A Library for Traversing Paths

Graphical Truffles: A Library for Traversing Paths

Daniel I. Lipton

The QuickDraw GX graphics system is based on shape objects that are used by reference. An application creates a shape object such as a path or a polygon by passing in data that represents the geometric points of the shape to be drawn or otherwise manipulated. The QuickDraw GX graphics system then stores this information in its internal database and returns to the application a reference to the shape object. This reference is then passed to the various QuickDraw GX routines that perform operations on the shape.

Since the QuickDraw GX graphics system is maintaining the original data in its database, the application often won't keep this data around. Also, an application may not even have created the geometric points in the first place, as in the case of converting text into a path.

It's often desirable, for a variety of purposes, for an application to retrieve the geometric information from a shape object. Given the richness of geometric information that these objects can contain, it can be a nontrivial task to read back the information. This column describes a C library that any application can incorporate for the purpose of traversing the geometric information in QuickDraw GX paths.

WHAT'S IN A QUICKDRAW GX PATH OBJECT

The QuickDraw GX graphics system provides several types of graphics primitives with which to create visual content: lines, curves, polygons, paths, typography, and bitmaps. In this system, curves are quadratic Béziers that can be defined by three control points, the middle point being off the curve and the other two being on. Figure 1 depicts a single quadratic curve segment.

Figure 1. A QuickDraw GX quadratic curve segment

A QuickDraw GX path object is just a conglomeration of curve and line segments, resulting from an array of points. The object can contain multiple contours, each contour being a group of connected segments.

The question arises, if we look at a specific point in a path structure, whether the point is part of a line segment or part of a curve segment. The answer is that in addition to the points themselves, a path contains an array of flags, one for each point, indicating whether the point is on or off the path. To represent a single contour for a path object, QuickDraw GX uses the gxPath data structure:

struct gxPath {
   long               vectors;
   long               controlBits[1];
   struct gxPoint      vector[1];
};
typedef struct gxPath gxPath;
The vectors field is an integer that specifies the number of points in the contour, the controlBits field is a bit array representing the on-curve/off-curve flags, and the vector field is an array of points for the contour.

To represent a path object, QuickDraw GX uses the gxPaths data structure:

struct gxPaths {
   long               contours;
   struct gxPath      contour[1];
};
typedef struct gxPaths gxPaths;
The contours field is an integer specifying the number of contours, and the contour field is an array of gxPath structures, one for each contour.

Hence we have enough information to figure out what the points mean. If we see two on-path points in a row, we know that represents a line. If we see an on-path point followed by an off-path point followed by an on-path point, we know that's a quadratic curve segment.

So to read the QuickDraw GX path object to determine the actual shape, all we have to do is get a point and then get the next point. According to the previous description, it would be safe to assume that the very first point in a contour is an on-path point. Then, if the next one were also on the path, we'd have a line; if it were off, we'd know that we'd have to read a third one (which by definition would have to be on) and we'd have a curve.

The only trouble is that those assumptions aren't necessarily true. The design of QuickDraw GX could have restricted applications to using only those patterns of on-path/off-path points, disallowing two consecutive off-path points and requiring the first point and the last point in a contour to be on the path; however, it didn't.

In the interest of saving memory, QuickDraw GX allows two consecutive off-path points to imply a middle on-path point -- known as an implicit point -- exactly halfway between the off-path points. An example of this is shown in Figure 2.

Figure 2. A QuickDraw GX quadratic path

For each implicit point there's a memory savings of 8 bytes in QuickDraw GX. This allows us to define geometries in less space than would be required in other popular graphics models that use cubic Bézier curves without implicit points, but it does complicate traversing the path.

QuickDraw GX also allows the first or the last point of a contour to be off the curve, in the case where the contour is closed. This further complicates path traversal.

THE SHAPEWALKER LIBRARY

You can use the ShapeWalker library (which is included on this issue's CD) to avoid having to write a huge blob of code to deal with all those points and flags discussed above. It allows an application to pass in a QuickDraw GX shape object and be sent back (via callbacks) each line and curve segment in the shape. All implicit points are resolved by the library, so the client sees only complete line or curve segments.

The header file to be used with the library defines types for four callbacks and a prototype for the ShapeWalker function:

// Function is called to move to a new point
// (start new contour).
typedef Boolean (*TpwMovetoProc)(gxPoint *p,
                  void* refcon);

// Function is called to draw a line from
// current point to p.
typedef Boolean (*TpwLinetoProc)(gxPoint *p,
                  void* refcon);

// Function is called to draw a curve from
// current point (which will be p[0]) through 
// p[1] to p[2].
typedef Boolean (*TpwCurvetoProc)(gxPoint p[3],
                  void* refcon);

// Function is called to close a contour.
typedef Boolean (*TpwClosepathProc)
                  (void* refcon);

// Return result will be true if path walking
// was terminated by one of the callbacks.
Boolean ShapeWalker(gxShape theShape,
                     TpwMovetoProc DoMoveto,
                     TpwLinetoProc DoLineto,
                     TpwCurvetoProc DoCurveto, 
                     TpwClosepathProc DoClosepath,
                     void* refcon);
When using the library, you provide four callbacks and a refcon. Each callback will get passed the refcon and possibly point information. It's suggested that the client maintain whatever state information is necessary for the purpose at hand. The refcon can be a pointer to a structure containing the state information. One typical component of such information that most clients would need is the notion of the current point. The current point is the piece of the path we've looked at most recently, representative of the state of processing the shape. This current point should be updated as segments come through the callbacks. (We'll see this in a moment in our sample application.)

Each callback must also return a result of type Boolean, giving the client a mechanism for causing the library to terminate traversal of the shape before completion. Return false and the shape walker will continue on to the next segment; return true and it will terminate early. This can be used to catch errors in processing the points, or to terminate processing if you've finished with the shape before the last point is reached.

The four callbacks are as follows:

  • DoMoveto -- This procedure is called at the start of each new contour in the shape. It gets passed a single point and the refcon. The point identifies the location of the beginning of the contour. If the client is maintaining a current point via the refcon, it should be updated to the point passed in.

  • DoLineto -- This procedure is called for each line segment in the contour. It gets passed a single point and the refcon. The point represents the end point of the line segment. The start point of the line segment is whatever point we last saw; that will be the current point if one is being maintained. If the client is maintaining a current point via the refcon, it should be updated to the point passed in.

  • DoCurveto -- This procedure is called for each quadratic curve segment in the contour. It gets passed an array of three points and the refcon. The three points correspond to the control points of the curve. The first point in the array will be the current point if one is being maintained. The current point should then be updated to reflect the third point in the array.

  • DoClosepath -- This procedure is called at the end of every contour if the QuickDraw GX shape is closed (has the gxClosedFrameFill shape fill attribute). Closing a contour implies connecting the last point in the contour (whatever the current point is when this function is called) with the first point in the contour (the point passed into the DoMoveto function).
The code shown in Listing 1 is a sample application (SamplePathWalker.c) that converts a piece of text to a path and then uses the ShapeWalker library to read the points from the result. In this example the callback procedures are used only to print out the points in the segments, but of course they can be used to do a lot of other things as well.



Listing 1. Sample application using the ShapeWalker library
// The following structure is used to maintain a state while
// walking a shape. 
typedef struct {
   gxPoint         currentPoint;      // current point
   gxPoint         firstPoint;        // first point in contour
} TestWalkRec;

#define fix2float(x) ((double)x / 65536.0)

Boolean   TestMoveto(gxPoint *p, TestWalkRec* pWalk);
Boolean   TestMoveto(gxPoint *p, TestWalkRec* pWalk)
{
   printf("Begin new contour: %f, %f\r\n", fix2float(p->x),
            fix2float(p->y));
   pWalk->currentPoint.x = p->x;
   pWalk->currentPoint.y = p->y;
   pWalk->firstPoint.x = p->x;
   pWalk->firstPoint.y = p->y;
   return (false);
}

Boolean   TestLineto(gxPoint *p, TestWalkRec* pWalk);
Boolean   TestLineto(gxPoint *p, TestWalkRec* pWalk)
{
   printf("Line from %f, %f to %f, %f\r\n",
            fix2float(pWalk->currentPoint.x),
            fix2float(pWalk->currentPoint.y),
            fix2float(p->x), fix2float(p->y));
   pWalk->currentPoint.x = p->x;
   pWalk->currentPoint.y = p->y;
   return (false);
}
Boolean   TestCurveto(gxPoint p[3], TestWalkRec* pWalk);
Boolean   TestCurveto(gxPoint p[3], TestWalkRec* pWalk)
{
   printf("Curve from %f, %f through %f, %f, to %f, %f\r\n",
            fix2float(p[0].x), fix2float(p[0].y),
            fix2float(p[1].x), fix2float(p[1].y),
            fix2float(p[2].x), fix2float(p[2].y));
   pWalk->currentPoint.x = p[2].x;
   pWalk->currentPoint.y = p[2].y;
   return (false);
}

Boolean TestClosepath(TestWalkRec* pWalk);
Boolean TestClosepath(TestWalkRec* pWalk)
{
   printf("Closing the contour\r\n\r\n");
   pWalk->currentPoint.x = pWalk->firstPoint.x;
   pWalk->currentPoint.y = pWalk->firstPoint.y;
   return (false);
}

main()
{
   gxShape         theShape;
   gxPoint         location = {ff(100), ff(100)};
   TestWalkRec      walker;
   Boolean         result;
   
   theShape = GXNewText(5, "Hello", &location);
   GXSetShapeTextSize(theShape, ff(50));
   GXSetShapeType(theShape, gxPathType);
   GXSetShapeFill(theShape, gxClosedFrameFill);

   result = ShapeWalker(theShape, TestMoveto, TestLineto,
                         TestCurveto, TestClosepath, &walker);
   GXDisposeShape(theShape);
}

WALKING THE PATH

The files PathWalking.h and PathWalking.c are all that are required to use the ShapeWalker library in your application (for the sake of brevity, PathWalking.c isn't shown in this column). This library should make it easy for your application to process QuickDraw GX path objects. For completeness, the library will also process curve objects, line objects, rectangle objects, and polygon objects in a similar manner. All other shape types will result in the posting of the "illegal_type_for_shape" graphics error. (Graphics errors can be polled with the GXGetGraphicsError function.) The ShapeWalker library is actually based on the same code used by QuickDraw GX in its built-in GX-to-PostScript translator for printing. The library's versatility means that its uses in your application are limited only by your imagination, so get creative and try it out!

DANIEL I. LIPTON (daniel_lipton@powertalk.apple.com) has worked at Apple for seven years and is one of the original QuickDraw GX team members. In his spare time, Dan runs a small business repairing perpetual motion machines.*

Thanks to Dave Hersey, Ingrid Kelly, and Dave Polaschek for reviewing this column.*

 
AAPL
$118.93
Apple Inc.
-0.07
MSFT
$47.81
Microsoft Corpora
+0.06
GOOG
$541.83
Google Inc.
+1.46

MacTech Search:
Community Search:

Software Updates via MacUpdate

Adobe Photoshop Elements 13.0 - Consumer...
Adobe Photoshop Elements 12--the #1 selling consumer photo editing software--helps you edit pictures with powerful, easy-to-use options and share them via print, the web, Facebook, and more.Version... Read more
Skype 7.2.0.412 - Voice-over-internet ph...
Skype allows you to talk to friends, family and co-workers across the Internet without the inconvenience of long distance telephone charges. Using peer-to-peer data transmission technology, Skype... Read more
HoudahSpot 3.9.6 - Advanced file search...
HoudahSpot is a powerful file search tool built upon MacOS X Spotlight. Spotlight unleashed Create detailed queries to locate the exact file you need Narrow down searches. Zero in on files Save... Read more
RapidWeaver 6.0.3 - Create template-base...
RapidWeaver is a next-generation Web design application to help you easily create professional-looking Web sites in minutes. No knowledge of complex code is required, RapidWeaver will take care of... Read more
iPhoto Library Manager 4.1.10 - Manage m...
iPhoto Library Manager lets you organize your photos into multiple iPhoto libraries. Separate your high school and college photos from your latest summer vacation pictures. Or keep some photo... Read more
iExplorer 3.5.1.9 - View and transfer al...
iExplorer is an iPhone browser for Mac lets you view the files on your iOS device. By using a drag and drop interface, you can quickly copy files and folders between your Mac and your iPhone or... Read more
MacUpdate Desktop 6.0.3 - Discover and i...
MacUpdate Desktop 6 brings seamless 1-click installs and version updates to your Mac. With a free MacUpdate account and MacUpdate Desktop 6, Mac users can now install almost any Mac app on macupdate.... Read more
SteerMouse 4.2.2 - Powerful third-party...
SteerMouse is an advanced driver for USB and Bluetooth mice. It also supports Apple Mighty Mouse very well. SteerMouse can assign various functions to buttons that Apple's software does not allow,... Read more
iMazing 1.1 - Complete iOS device manage...
iMazing (was DiskAid) is the ultimate iOS device manager with capabilities far beyond what iTunes offers. With iMazing and your iOS device (iPhone, iPad, or iPod), you can: Copy music to and from... Read more
PopChar X 7.0 - Floating window shows av...
PopChar X helps you get the most out of your font collection. With its crystal-clear interface, PopChar X provides a frustration-free way to access any font's special characters. Expanded... Read more

Latest Forum Discussions

See All

Mystery Case Files: Dire Grove, Sacred G...
Mystery Case Files: Dire Grove, Sacred Grove HD Review By Jennifer Allen on November 28th, 2014 Our Rating: iPad Only App - Designed for the iPad A decent new installment for the popular Mystery Case Files series.   | Read more »
Castaway Paradise – Tips, Tricks, and St...
Ahoy there, castaways: Were you curious about our own thoughts regarding this pristine shipwreck? Check out our Castaway Paradise review! Castaway Paradise is out for iOS, finally giving mobile gamers the opportunity to enjoy the idyllic lifestyle... | Read more »
Castaway Paradise VIP Subs are on Sale f...
Castaway Paradise VIP Subs are on Sale for a Limited Time, and a Special Holiday Update is Coming Soon Posted by Rob Rich on November 28th, 2014 [ | Read more »
Primitive Review
Primitive Review By Jordan Minor on November 28th, 2014 Our Rating: :: FOLK ARTUniversal App - Designed for iPhone and iPad True to its name, Primitive is about as straightforward as runners get.   | Read more »
7 tips to get ahead of the competition i...
7 tips to get ahead of the competition in Dynasty of Dungeons Posted by Simon Reed on November 28th, 2014 [ permalink ] Playcrab has launched their action-packed new dungeon crawler, Dynasty of Dungeons, today. | Read more »
Master of Tea Kung Fu Review
Master of Tea Kung Fu Review By Jordan Minor on November 28th, 2014 Our Rating: :: ONE DROP RULESUniversal App - Designed for iPhone and iPad Master of Tea Kung Fu is a creative and complex caffeinated brawler.   | Read more »
Monster Strike Review
Monster Strike Review By Campbell Bird on November 28th, 2014 Our Rating: :: BILLIARD STRATEGYUniversal App - Designed for iPhone and iPad Collect monsters and battle by flinging them across the battlefield in this strangely... | Read more »
Proun+ Review
Proun+ Review By Jennifer Allen on November 28th, 2014 Our Rating: :: TWITCHY RACINGUniversal App - Designed for iPhone and iPad Twitchy racing aplenty in Proun+, an enjoyably tricky title.   | Read more »
Lucha Amigos (Games)
Lucha Amigos 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: Forget Ninja Turtles, and meet Wrestlers Turtles! Crazier, Spicier and…Bouncier! Sling carapaces of 7 Luchadores to knock all... | Read more »
Record of Agarest War Zero (Games)
Record of Agarest War Zero 1.0 Device: iOS Universal Category: Games Price: $7.99, Version: 1.0 (iTunes) Description: HyperDevbox Holiday Turkey Black Friday Special Pricing! To celebrate the opening of the holiday season HyperDevbox... | Read more »

Price Scanner via MacPrices.net

Up To 75% Off Infovole Text Apps Over Black F...
Infovole’s entire range of apps, including the Textkraft family of word processors for iPads and iPhones, is being offered at 50-75% off over the Black Friday and Cyber Monday weekend. The five-day... Read more
Black Friday: Up to $60 off Mac minis, NY tax...
 B&H Photo has new 2014 Mac minis on sale for up to $60 off MSRP as part of their Black Friday sale. Shipping is free, and B&H charges NY sales tax only: - 1.4GHz Mac mini: $449.99 $50 off... Read more
Black Friday: 27-inch 5K iMac for $2299, save...
 B&H Photo continues to offer Black Friday sale prices on the 27″ 3.5GHz 5K iMac, in stock today and on sale for $2299 including free shipping plus NY sales tax only. Their price is $200 off MSRP... Read more
Karalux Announces 24K Gold-Plated iPhone 6
Karalux, a Vietnam-based jewellery firm, has launched a unique 24 karat gold-plated iPhone 6 version with gold-cast monolithic dragon on its back panel. The real 24 karat gold plated enclosure doesn’... Read more
Black Friday: 13-inch 2.6GHz Retina MacBook P...
 B&H Photo has lowered their price for the 13″ 2.6GHz/128GB Retina MacBook Pro to $1159 for Black Friday. That’s $140 off MSRP, and it’s the lowest price for this model (except for Apple’s $1099... Read more
View all the Black Friday sales on our Mac Pr...
We’ve updated our Mac Price Trackers with the latest information on prices, bundles, and availability on systems from Apple’s authorized internet/catalog resellers. View Black Friday sale prices at a... Read more
Black Friday: 11-inch MacBook Air for $779, s...
 Best Buy has lowered their price for the 2014 11″ 1.4GHz/128GB MacBook Air to $779.99 for Black Friday. That’s $120 off MSRP. Choose free shipping or free local store pickup (if available). Sale... Read more
Apple Store Black Friday sale for 2014: $100...
BLACK FRIDAY The Apple Store has posted their Black Friday deals for 2014. Receive a $100 PRODUCT(RED) branded iTunes gift card with the purchase of select Macs, $50 with iPads, and $25 with iPods,... Read more
Black Friday: 15% off iTunes Gift Cards
Staples is offering 15% off $50 and $100 iTunes Gift Cards on their online store as part of their Black Friday sale. Click here for more information. Shipping is free. Best Buy is offering $100... Read more
BEVL Releases Dock Tailored for iPhone 6 and...
Seattle based BEVL has released their first product: an iPhone dock that is divergent in build quality, rock-solid function and visual simplicity to complement the iPhone. BEVL is now accepting... Read more

Jobs Board

*Apple* Solutions Consultant (ASC) - Apple (...
**Job Summary** The ASC is an Apple employee who serves as an Apple brand ambassador and influencer in a Reseller's store. The ASC's role is to grow Apple Read more
Senior Event Manager, *Apple* Retail Market...
…This senior level position is responsible for leading and imagining the Apple Retail Team's global event strategy. Delivering an overarching brand story; in-store, Read more
*Apple* Retail - Multiple Positions (US) - A...
Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, you're also the Read more
*Apple* Solutions Consultant (ASC) - Apple (...
**Job Summary** The ASC is an Apple employee who serves as an Apple brand ambassador and influencer in a Reseller's store. The ASC's role is to grow Apple Read more
*Apple* Solutions Consultant (ASC) - Apple (...
**Job Summary** The ASC is an Apple employee who serves as an Apple brand ambassador and influencer in a Reseller's store. The ASC's role is to grow Apple Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.