TweetFollow Us on Twitter

Bezier Curve
Volume Number:5
Issue Number:1
Column Tag:C Workshop

Related Info: Quickdraw

Bezier Curve Ahead!

By David W. Smith, Los Gatos, CA

Note: Source code files accompanying article are located on MacTech CD-ROM or source code disks.

David W. Smith (no known relation to the Editor) is a Sr. Software Engineer at ACM Research, Inc., in Los Gatos.

There comes a time in the development of some applications when arcs and wedges just don’t cut the mustard. You want to draw a pretty curve from point A to point B, and QuickDraw isn’t giving you any help. It seems like a good time to reach for a computer graphics text, blow the dust off of your college math, and try to decipher their explanation of splines. Stop. All is not lost. The Bezier curve may be just what you need.

Bezier Curves

Bezier curves (pronounced “bez-yeah”, after their inventor, a French mathematician) are well suited to graphics applications on the Macintosh for a number of reasons. First, they’re simple to describe. A curve is a function of four points. Second, the curve is efficient to calculate. From a precomputed table, the segments of the curve can be produced using only fixed-point multiplication. No trig, no messy quadratics, and no inSANEity. Third, and, to some, the most important, the Bezier curve is directly supported by the PostScript curve and curveto operators, and is one of the components of PostScript’s outlined fonts. The Bezier curve is also one of the principle drawing elements of Adobe Illustrator™. (Recently, they’ve shown up in a number of other places.)

Bezier curves have some interesting properties. Unlike some other classes of curves, they can fold over on themselves. They can also be joined together to form smooth (continuous) shapes. Figure 1 shows a few Bezier curves, including two that are joined to form a smooth shape.

The Gruesome Details

The description of Bezier curves below is going to get a bit technical. If you’re not comfortable with the math, you can trust that the algorithm works, and skip ahead to the implementation. However, if you’re curious about how the curves work and how to optimize their implementation, or just don’t trust using code that you don’t understand, read on.

The Bezier curve is a parametric function of four points; two endpoints and two “control” points. The curve connects the endpoints, but doesn’t necessarily touch the control points. The general form Bezier equation, which describes each point on the curve as a function of time, is:

where P1 and P4 are the endpoints, P2 and P3 are the control points, and the wn’s are weighting functions, which blend the four points to produce the curve. (The weights are applied to the h and v components of each point independently.) The single parameter t represents time, and varies from 0 to 1. The full form of the Bezier curve is:

We know that the curve touches each endpoint, so it isn’t too surprising that at t=0 the first weighting function is 1 and all others are 0 (i.e., the initial point on the curve is the first endpoint). Likewise, at t=1, the fourth weighting function is 1 and the rest are 0. However, it’s what happens between 0 and 1 that’s really interesting. A quick side-trip into calculus to take some first derivatives tells us that the second weighting function is maximized (has its greatest impact on the curve) at t=1/3, and the third weight is maximized at t=2/3. But the clever part--the bit that the graphics books don’t bother to mention--run the curve backwards by solving the equation for 1-t, and you find that w1(t)=w4(1-t) and w2(t)=w3(1-t). As we’ll see below, this symmetry halves the effort needed to compute values for the weights.

Figure 1. Some Beizer Curves and Shapes

Implementing Bezier Curves

One strategy for implementing Bezier curves is to divide the curve into a fixed number of segments and then to pre-compute the values of the weighting functions for each of the segments. The greater the number of segments, the smoother the curve. (I’ve found that 16 works well for display purposes, but 32 is better for hardcopy.) Computing any given curve becomes a simple matter of using the four points and the precomputed weights to produce the end-points of the curve segments. Fixed-point math yields reasonable accuracy, and is a hands down winner over SANE on the older (pre-Mac II) Macs, so we’ll use it.

We can optimize the process a bit. The curve touches each endpoint, so we can assume weights of 0 or 1 and needn’t compute weights for these points. Another optimization saves both time and space. By taking advantage of the symmetric nature of the Bezier equation, we can compute arrays of values for the first two of the weighting functions, and obtain values for the other two weights by indexing backwards into the arrays.

Drawing the curve, given the endpoints of the segments, is the duty of QuickDraw (or of PostScript, if you’re really hacking).

The listing below shows a reasonably efficient implementation of Bezier curves in Lightspeed C™. A few reminders about fixed-point math: an integer times a fixed-point number yields a fixed-point number, and a fixed by fixed multiplication uses a trap. The storage requirement for the algorithm, assuming 16 segments, (32 fixed-point values), is around 32*4*4, or 512 bytes. The algorithm computes all of the segments before drawing them so that the drawing can be done at full speed. (Having all of the segments around at one time can be useful for other reasons.)

More Fun With Curves

Given an implementation for Bezier curves, there are some neat things that fall out for almost free. Drawing a set of joined curves within an OpenPoly/ClosePoly or an OpenRgn/CloseRgn envelope yields an object that can be filled with a pattern. (Shades of popular illustration packages?) For that matter, lines, arcs, wedges, and Bezier curves can be joined to produce complicated shapes, such as outlined fonts. Given the direct mapping to PostScript’s curve and curveto operators, Bezier curves are a natural for taking better advantage of the LaserWriter.

As mentioned above, Bezier curves can be joined smoothly to produce more complicated shapes (see figure 1). The catch is that the point at which two curves are joined, and the adjacent control points, must be colinear (i.e., the three points must lay on a line). If you take a close look at Adobe Illustrator’s drawing tool, you’ll see what this means.

One nonobvious use of Bezier curves is in animation. The endpoints of the segments can be used as anchor-points for redrawing an object, giving it the effect of moving smoothly along the curve. One backgammon program that I’ve seen moves the tiles along invisible Bezier curves, and the effect is very impressive. For animation, you would probably want to vary the number of segments. Fortunately, the algorithm below is easily rewritten to produce the nth segment of an m segment curve given the the end and control points.

Further Optimizations

If you’re really tight on space or pressed for speed, there are a few things that you can do to tighten up the algorithm. A bit of code space (and a negligible amount of time) can be preserved by eliminating the setup code in favor of statically initializing the weight arrays with precomputed constant values. Drawing can be optimized by using GetTrapAddress to find the address in ROM of lineto, and then by calling it directly from inline assembly language, bypassing the trap mechanism. I’ve found that neither optimization is necessary for reasonable performance.

/*
**  Bezier  --  Support for Bezier curves
** Herein reside support routines for drawing Bezier curves.
**  Copyright (C) 1987, 1988 David W. Smith
**  Submitted to MacTutor for their source-disk.
*/

#include <MacTypes.h>
/*
   The greater the number of curve segments, the smoother the curve, 
and the longer it takes to generate and draw.  The number below was pulled 
out of a hat, and seems to work o.k.
 */
#define SEGMENTS 16

static Fixedweight1[SEGMENTS + 1];
static Fixedweight2[SEGMENTS + 1];

#define w1(s)  weight1[s]
#define w2(s)  weight2[s]
#define w3(s)  weight2[SEGMENTS - s]
#define w4(s)  weight1[SEGMENTS - s]

/*
 *  SetupBezier  --  one-time setup code.
 * Compute the weights for the Bezier function.
 *  For the those concerned with space, the tables can be precomputed. 
Setup is done here for purposes of illustration.
 */
void
SetupBezier()
{
 Fixed  t, zero, one;
 int    s;

 zero  = FixRatio(0, 1);
 one   = FixRatio(1, 1);
 weight1[0] = one;
 weight2[0] = zero;
 for ( s = 1 ; s < SEGMENTS ; ++s ) {
 t = FixRatio(s, SEGMENTS);
 weight1[s] = FixMul(one - t, FixMul(one - t, one - t));
 weight2[s] = 3 * FixMul(t, FixMul(t - one, t - one));
 }
 weight1[SEGMENTS] = zero;
 weight2[SEGMENTS] = zero;
}

/*
 *  computeSegments  --  compute segments for the Bezier curve
 * Compute the segments along the curve.
 *  The curve touches the endpoints, so don’t bother to compute them.
 */
static void
computeSegments(p1, p2, p3, p4, segment)
 Point  p1, p2, p3, p4;
 Point  segment[];
{
 int    s;
 
 segment[0] = p1;
 for ( s = 1 ; s < SEGMENTS ; ++s ) {
 segment[s].v = FixRound(w1(s) * p1.v + w2(s) * p2.v +
 w3(s) * p3.v + w4(s) * p4.v);
 segment[s].h = FixRound(w1(s) * p1.h + w2(s) * p2.h +
 w3(s) * p3.h + w4(s) * p4.h);
 }
 segment[SEGMENTS] = p4;
}

/*
 *  BezierCurve  --  Draw a Bezier Curve
 * Draw a curve with the given endpoints (p1, p4), and the given 
 * control points (p2, p3).
 *  Note that we make no assumptions about pen or pen mode.
 */
void
BezierCurve(p1, p2, p3, p4)
 Point  p1, p2, p3, p4;
{
 int    s;
 Point  segment[SEGMENTS + 1];

 computeSegments(p1, p2, p3, p4, segment);
 MoveTo(segment[0].h, segment[0].v);

 for ( s = 1 ; s <= SEGMENTS ; ++s ) {
 if ( segment[s].h != segment[s - 1].h ||
  segment[s].v != segment[s - 1].v ) {
 LineTo(segment[s].h, segment[s].v);
 }
 }
}

/*
**  CurveLayer.c  
** These routines provide a layer of support between my bare-  
 bones application skeleton and the Bezier curve code.   
  There’s little here of interest outside of the mouse 
  tracking and the curve drawing.
**  David W. Smith
*/

#include “QuickDraw.h”
#include “MacTypes.h”
#include “FontMgr.h”
#include “WindowMgr.h”
#include “MenuMgr.h”
#include “TextEdit.h”
#include “DialogMgr.h”
#include “EventMgr.h”
#include “DeskMgr.h”
#include “FileMgr.h”
#include “ToolboxUtil.h”
#include “ControlMgr.h”

/*
 *  Tracker objects.  Similar to MacAPP trackers, but much,
 much simpler.
 */
struct Tracker
{
 void (*track)();
 int    thePoint;
};

static struct Tracker aTracker;
static struct Tracker bTracker;

/*
 *  The Bezier curve control points.
 */
Point   control[4] = {{144,72}, {72,144}, {216,144}, {144,216}};


/*
 *  Draw
 *  Called from the skeleton to update the window.  Draw the   
 initial curve.
 */
Draw()
{
 PenMode(patXor);
 DrawTheCurve(control, true);
}

/*
 *  DrawTheCurve
 * Draw the given Bezier curve in the current pen mode.Draw 
   the control points if requested.
 */
DrawTheCurve(c, drawPoints)
 Point  c[];
{
 if ( drawPoints )
 DrawThePoints(c);
 BezierCurve(c[0], c[1], c[2], c[3]);
}

/*
 *  DrawThePoints
 *  Draw all of the control points.
 */
DrawThePoints(c)
 Point  c[];
{
 int    n;
 
 for ( n = 0 ; n < 4 ; ++n ) {
 DrawPoint(c, n);
 }
}

/*
 *  DrawPoint
 *  Draw a single control point
 */
DrawPoint(c, n)
 Point  c[];
 int    n;
{
 PenSize(3, 3);
 MoveTo(c[n].h - 1, c[n].v - 1);
 LineTo(c[n].h - 1, c[n].v - 1);
 PenSize(1, 1);
}

/*
 * GetTracker
 * Produce a tracker object
 * Called by the skeleton to handle mouse-down events.
 * If the mouse touches a control point, return a tracker for
 that point. Otherwise, return a tracker that drags a gray 
 rectangle.
 */
struct Tracker *
GetTracker(point)
 Point  point;
{
 void   TrackPoint(), TrackSelect();
 int    i;

 aTracker.track = TrackPoint;

 for ( i = 0 ; i < 4 ; ++i ) {
 if ( TouchPoint(control[i], point) ) {
 aTracker.thePoint = i;
 return (&aTracker);
 }
 }
 bTracker.track = TrackSelect;
 return (&bTracker);
}

/*
 *  TouchPoint
 *  Do the points touch?
 */
#define abs(a) (a < 0 ? -(a) : (a))

TouchPoint(target, point)
 Point  target;
 Point  point;
{
 SubPt(point, &target);
 if ( abs(target.h) < 3 && abs(target.v) < 3 )
 return (1);
 return (0);
}

/*
 *  TrackPoint
 *  Called while dragging a control point.
 */
void
TrackPoint(tracker, point, phase)
 struct Tracker  *tracker;
 Point  point;
 int    phase;
{
 Point  savePoint;

 switch ( phase ) {
 case 1:
 /* initial click - XOR out the control point */
 DrawPoint(control, tracker->thePoint);
 break;
 case 2:
 /* drag - undraw the original curve and draw the new one */
 DrawTheCurve(control, false);
 control[tracker->thePoint] = point;
 DrawTheCurve(control, false);
 break;
 case 3:
 /* release - redraw the control point */
 DrawPoint(control, tracker->thePoint);
 break;
 }
}

/*
 *  TrackSelect
 *  Track a gray selection rectangle
 */
static Pointfirst;
static Rect r;

void
TrackSelect(tracker, point, phase)
 struct Tracker  *tracker;
 Point  point;
 int    phase;
{
 switch ( phase ) {
 case 1:
 PenPat(gray);
 first = point;
 SetupRect(&r, first, point);
 FrameRect(&r);
 break;
 case 2:
 FrameRect(&r);
 SetupRect(&r, first, point);
 FrameRect(&r);
 break;
 case 3:
 FrameRect(&r);
 PenPat(black);
 break;
 }
}

/*
 *  SetupRect
 *  Setup the rectangle for tracking.
 */
#define min(x, y) (((x) < (y)) ? (x) : (y))
#define max(x, y) (((x) > (y)) ? (x) : (y))

SetupRect(rect, point1, point2)
 Rect   *rect;
 Point  point1;
 Point  point2;
{
 SetRect(rect,
 min(point1.h, point2.h),
 min(point1.v, point2.v),
 max(point1.h, point2.h),
 max(point1.v, point2.v));
}

/*
**  Skeleton.c  --  A bare-bones skeleton.
** This has been hacked up to demonstrate Bezier curves.  
    Other than the tracking technique, there’s little here of 
    interest.
**  David W. Smith
*/

#include “QuickDraw.h”
#include “MacTypes.h”
#include “FontMgr.h”
#include “WindowMgr.h”
#include “MenuMgr.h”
#include “TextEdit.h”
#include “DialogMgr.h”
#include “EventMgr.h”
#include “DeskMgr.h”
#include “FileMgr.h”
#include “ToolboxUtil.h”
#include “ControlMgr.h”

WindowRecordwRecord;
WindowPtr myWindow;

/*
 *  main
 *  Initialize the world, then handle events until told to quit.
 */
main() 
{
 InitGraf(&thePort);
 InitFonts();
 FlushEvents(everyEvent, 0);
 InitWindows();
 InitMenus();
 InitDialogs(0L);
 InitCursor();
 MaxApplZone();

 SetupMenus();
 SetupWindow();
 SetupBezier();

 while ( DoEvent(everyEvent) )
 ;
}

/*
 *  SetupMenus
 *  For the purpose of this demo, we get somewhat non-standard and use 
no menus.  Closing the window quits.
 */
SetupMenus()
{
 DrawMenuBar();
}

/*
 *  SetupWindow
 *  Setup the window for the Bezier demo.
 */
SetupWindow()
{
 Rect   bounds;

 bounds = WMgrPort->portBits.bounds;
 bounds.top += 36;
 InsetRect(&bounds, 5, 5);

 myWindow = NewWindow(&wRecord, &bounds, “\pBezier Sampler - Click and 
Drag”, 1, noGrowDocProc, 0L, 1, 0L);
 
 SetPort(myWindow);
}

/*
 *  DoEvent
 *  Generic event handling.
 */
DoEvent(eventMask)
 int    eventMask;
{
 EventRecordmyEvent;
 WindowPtrwhichWindow;
 Rect   r;
 
 SystemTask();
 if ( GetNextEvent(eventMask, &myEvent) )
 {
 switch ( myEvent.what )
 {
 case mouseDown:
 switch ( FindWindow( myEvent.where, &whichWindow ) )
 {
 case inDesk: 
 break;
 case inGoAway:
 if ( TrackGoAway(myWindow, myEvent.where) )
 {
 HideWindow(myWindow);
 return (0);
 }
 break;
 case inMenuBar:
 return (DoCommand(MenuSelect(myEvent.where)));
 case inSysWindow:
 SystemClick(&myEvent, whichWindow);
 break;
 case inDrag:
 break;
 case inGrow:
 break;
 case inContent:
 DoContent(&myEvent);
 break;
 default:
 break;;
 }
 break;
 case keyDown:
 case autoKey: 
 break;
 case activateEvt:
 break;
 case updateEvt:
 DoUpdate();
 break;
 default:
 break;
 }
 }
 return(1);
}

/*
 *  DoCommand
 *  Command handling would normally go here.
 */
DoCommand(mResult)
 long   mResult;
{
 int    theItem, temp;
 Str255 name;
 WindowPeek wPtr;
 
 theItem = LoWord(mResult);

 switch ( HiWord(mResult) )
 {
 }

 HiliteMenu(0);
 return(1);
}

/*
 *  DoUpdate
 *  Generic update handler.
 */
DoUpdate()
{
 BeginUpdate(myWindow);
 Draw();
 EndUpdate(myWindow);
}

/*
 *  DoContent
 *  Handle mouse-downs in the content area by asking the application 
to produce a tracker object.  We then call the tracker repeatedly to 
track the mouse. This technique came originally (as nearly as I can tell) 
from Xerox, and is used in a modified form in MacApp.
 */
struct Tracker
{
 int    (*Track)();
};

int
DoContent(pEvent)
 EventRecord*pEvent;
{
 struct Tracker  *GetTracker();
 struct Tracker  *t;
 Point  point, newPoint;
 
 point = pEvent->where;
 GlobalToLocal(&point);
 t = GetTracker(point);
 if ( t ) {
 (*t->Track)(t, point, 1);
 while ( StillDown() ) {
 GetMouse(&newPoint);
 if ( newPoint.h != point.h || newPoint.v != point.v ) {
 point = newPoint;
 (*t->Track)(t, point, 2);
 }
 }
 (*t->Track)(t, point, 3);
 }
}

 
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

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 »
Angry Birds Transformers Review
Angry Birds Transformers Review By Jennifer Allen on October 20th, 2014 Our Rating: :: TRANSFORMED BIRDSUniversal App - Designed for iPhone and iPad Transformed in a way you wouldn’t expect, Angry Birds Transformers is a quite... | 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.