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
$102.47
Apple Inc.
+2.71
MSFT
$44.88
Microsoft Corpora
+0.80
GOOG
$526.54
Google Inc.
+5.70

MacTech Search:
Community Search:

Software Updates via MacUpdate

EyeTV 3.6.6 - Watch and record TV on you...
EyeTV brings a rich TV experience to your Mac. Watch live TV on your Mac. Pause, rewind, and record whenever you want. EyeTV gives you powerful control over what you watch and how you watch it. Put... Read more
RapidWeaver 6.0 - Create template-based...
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
NTFS 12.0.39 - Provides full read and wr...
Paragon NTFS breaks down the barriers between Windows and OS X. Paragon NTFS effectively solves the communication problems between the Mac system and NTFS, providing full read and write access to... Read more
RestoreMeNot 2.0.3 - Disable window rest...
RestoreMeNot provides a simple way to disable the window restoration for individual applications so that you can fine-tune this behavior to suit your needs. Please note that RestoreMeNot is designed... Read more
Macgo Blu-ray Player 2.10.9.1750 - Blu-r...
Macgo Mac Blu-ray Player can bring you the most unforgettable Blu-ray experience on your Mac. Overview Macgo Mac Blu-ray Player can satisfy just about every need you could possibly have in a Blu-ray... Read more
Apple iOS 8.1 - The latest version of Ap...
The latest version of iOS can be downloaded through iTunes. Apple iOS 8 comes with big updates to apps you use every day, like Messages and Photos. A whole new way to share content with your family.... Read more
TechTool Pro 7.0.5 - Hard drive and syst...
TechTool Pro is now 7, and this is the most advanced version of the acclaimed Macintosh troubleshooting utility created in its 20-year history. Micromat has redeveloped TechTool Pro 7 to be fully 64... Read more
PDFKey Pro 4.0.2 - Edit and print passwo...
PDFKey Pro can unlock PDF documents protected for printing and copying when you've forgotten your password. It can now also protect your PDF files with a password to prevent unauthorized access and/... Read more
Yasu 2.9.1 - System maintenance app; per...
Yasu was originally created with System Administrators who service large groups of workstations in mind, Yasu (Yet Another System Utility) was made to do a specific group of maintenance tasks... Read more
Hazel 3.3 - Create rules for organizing...
Hazel is your personal housekeeper, organizing and cleaning folders based on rules you define. Hazel can also manage your trash and uninstall your applications. Organize your files using a... Read more

Latest Forum Discussions

See All

Infuse Pro (Photography)
Infuse Pro 3.0 Device: iOS Universal Category: Photography Price: $9.99, Version: 3.0 (iTunes) Description: ** All-new version 3 includes fully licensed and certified DTS® and DTS-HD® audio! ** | Read more »
Swap Heroes (Games)
Swap Heroes 1.0 Device: iOS Universal Category: Games Price: $.99, Version: 1.0 (iTunes) Description: **Half price for a limited time only** Swap Heroes is a casual turn-based strategy adventure. Form a group of heroes and guide them... | Read more »
Ghost Blade (Games)
Ghost Blade 1.1 Device: iOS Universal Category: Games Price: $4.99, Version: 1.1 (iTunes) Description: Get the most outstanding 3D Action Game from App Store NOW! For those who dare pursue dreams. Masterpiece of Yu Shi Game ---China... | Read more »
Fiete – A Day on a Farm Review
Fiete – A Day on a Farm Review By Amy Solomon on October 21st, 2014 Our Rating: :: A MEMORABLE EXPERIENCEUniversal App - Designed for iPhone and iPad Fiete – A day on a farm in an interactive app for young children full of... | Read more »
Tilt to Live: Gauntlet’s Revenge is Almo...
Tilt to Live: Gauntlet’s Revenge is Almost Here Posted by Jessica Fisher on October 21st, 2014 [ permalink ] One Man Left has announced the official release date of Tilt to Live: Gauntlet’s Re | Read more »
Sago Mini Monsters Celebrates Halloween...
Sago Mini Monsters Celebrates Halloween with Fun Costumes and Special Treats. Posted by Jessica Fisher on October 21st, 2014 [ permal | Read more »
Inferno 2 Review
Inferno 2 Review By Andrew Fisher on October 21st, 2014 Our Rating: :: TWIN STICK GOODNESSUniversal App - Designed for iPhone and iPad With tight controls and awesome, stark visuals, Inferno 2 is loads of fun.   | Read more »
Clips Review
Clips Review By Jennifer Allen on October 21st, 2014 Our Rating: :: CONVENIENT PASTINGUniversal App - Designed for iPhone and iPad Making copying and pasting more powerful than usual, Clips is a great way to move stuff around.   | Read more »
MonSense Review
MonSense Review By Jennifer Allen on October 21st, 2014 Our Rating: :: ORGANIZED FINANCESiPhone App - Designed for the iPhone, compatible with the iPad Organize your finances with the quick and easy to use, MonSense.   | Read more »
This Week at 148Apps: October 13-17, 201...
Expert App Reviewers   So little time and so very many apps. What’s a poor iPhone/iPad lover to do? Fortunately, 148Apps is here to give you the rundown on the latest and greatest releases. And we even have a tremendous back catalog of reviews; just... | Read more »

Price Scanner via MacPrices.net

Select MacBook Airs $100 off MSRP, free shipp...
B&H Photo has 2014 a couple of MacBook Airs on sale for $100 off MSRP. Shipping is free, and B&H charges NY sales tax only. They also include free copies of Parallels Desktop and LoJack for... Read more
13-inch 2.5GHz MacBook Pro on sale for $100 o...
B&H Photo has the 13″ 2.5GHz MacBook Pro on sale for $999.99 including free shipping plus NY sales tax only. Their price is $100 off MSRP. Read more
Strong iPhone, Mac And App Store Sales Drive...
Apple on Monday announced financial results for its fiscal 2014 fourth quarter ended September 27, 2014. The Company posted quarterly revenue of $42.1 billion and quarterly net profit of $8.5 billion... Read more
Apple Posts How-To For OS X Recovery
OS X 10.7 Lion and later include OS X Recovery. This feature includes all of the tools you need to reinstall OS X, repair your disk, and even restore from a Time Machine backup. OS X Recovery... Read more
Mac OS X Versions (Builds) Supported By Vario...
Apple Support has posted a handy resource explaining which Mac OS X versions (builds) originally shipped with or are available for your computer via retail discs, downloads, or Software Update. Apple... Read more
Deals on 2011 13-inch MacBook Airs, from $649
Daily Steals has the Mid-2011 13″ 1.7GHz i5 MacBook Air (4GB/128GB) available for $699 with a 90 day warranty. The Mid-2011 13″ 1.7GHz i5 MacBook Air (4GB/128GB SSD) is available for $649 at Other... Read more
2013 15-inch 2.0GHz Retina MacBook Pro availa...
B&H Photo has leftover previous-generation 15″ 2.0GHz Retina MacBook Pros now available for $1599 including free shipping plus NY sales tax only. Their price is $400 off original MSRP. B&H... Read more
Updated iPad Prices
We’ve updated our iPad Air Price Tracker and our iPad mini Price Tracker with the latest information on prices and availability from Apple and other resellers, including the new iPad Air 2 and the... Read more
Apple Pay Available to Millions of Visa Cardh...
Visa Inc. brings secure, convenient payments to iPad Air 2 and iPad mini 3as well as iPhone 6 and 6 Plus. Starting October 20th, eligible Visa cardholders in the U.S. will be able to use Apple Pay,... Read more
Textkraft Pocket – the missing TextEdit for i...
infovole GmbH has announced the release and immediate availability of Textkraft Pocket 1.0, a professional text editor and note taking app for Apple’s iPhone. In March 2014 rumors were all about... Read more

Jobs Board

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* 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
Project Manager / Business Analyst, WW *Appl...
…a senior project manager / business analyst to work within our Worldwide Apple Fulfillment Operations and the Business Process Re-engineering team. This role will work Read more
*Apple* Retail - Multiple Positions (US) - A...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
Position Opening at *Apple* - Apple (United...
…customers purchase our products, you're the one who helps them get more out of their new Apple technology. Your day in the Apple Store is filled with a range of Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.