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
$524.94
Apple Inc.
+5.93
MSFT
$40.01
Microsoft Corpora
-0.39
GOOG
$536.10
Google Inc.
-20.44

MacTech Search:
Community Search:

Software Updates via MacUpdate

VMware Fusion 6.0.3 - Run Windows apps a...
VMware Fusion allows you to create a Virtual Machine on your Mac and run Windows (including Windows 8.1) and Windows software on your Mac. Run your favorite Windows applications alongside Mac... Read more
Tweetbot 1.5.1 - Popular iOS twitter cli...
Tweetbot is a full-featured OS X Twitter client with a lot of personality. Whether it's the meticulously-crafted interface, sounds and animation, or features like multiple timelines and column views... Read more
Mac DVDRipper Pro 4.1.7 - Copy, backup,...
Mac DVDRipper Pro is the DVD backup solution that lets you protect your DVDs from scratches, save your batteries by reading your movies from your hard disk, manage your collection with just a few... Read more
PDFpenPro 6.2 - Advanced PDF toolkit for...
PDFpenPro allows users to edit PDF's easily. Add text, images and signatures. Fill out PDF forms. Merge or split PDF documents. Reorder and delete pages. Even correct text and edit graphics! Create... Read more
PDFpen 6.2 - Edit and annotate PDFs with...
PDFpen allows users to easily edit PDF's. Add text, images and signatures. Fill out PDF forms. Merge or split PDF documents. Reorder and delete pages. Even correct text and edit graphics! Features... Read more
Monolingual 1.5.9 - Remove unwanted OS X...
Monolingual is a program for removing unnecesary language resources from OS X, in order to reclaim several hundred megabytes of disk space. It requires a 64-bit capable Intel-based Mac and at least... Read more
Maya 2015 - Professional 3D modeling and...
Maya is an award-winning software and powerful, integrated 3D modeling, animation, visual effects, and rendering solution. Because Maya is based on an open architecture, all your work can be scripted... Read more
Starcraft II: Wings of Liberty 1.1.1.180...
Download the patch by launching the Starcraft II game and downloading it through the Battle.net connection within the app. Starcraft II: Wings of Liberty is a strategy game played in real-time. You... Read more
Sibelius 7.5.0 - Music notation solution...
Sibelius is the world's best-selling music notation software for Mac. It is as intuitive to use as a pen, yet so powerful that it does most things in less than the blink of an eye. The demo includes... Read more
Typinator 5.9 - Speedy and reliable text...
Typinator turbo-charges your typing productivity. Type a little. Typinator does the rest. We've all faced projects that require repetitive typing tasks. With Typinator, you can store commonly used... Read more

Latest Forum Discussions

See All

Have a Special Dead Trigger 2 Easter Bas...
Have a Special Dead Trigger 2 Easter Basket Full of Goodies, Courtesy of Madfinger Games Posted by Rob Rich on April 18th, 2014 [ permalink ] Dead Trigger 2 | Read more »
Almost All of Playdek’s Library is on Sa...
Almost All of Playdek’s Library is on Sale Right Now, and You Should Check it Out Posted by Rob Rich on April 18th, 2014 [ permalink ] Playdek has released quite a few great iOS ports of board and card games over the years, and now most of them... | Read more »
Zynga Launches Brand New Farmville Exper...
Zynga Launches Brand New Farmville Experience with Farmville 2: Country Escape Posted by Tre Lawrence on April 18th, 2014 [ permalink ] | Read more »
David. Review
David. Review By Cata Modorcea on April 18th, 2014 Our Rating: :: MINIMALISTIC IN A DIFFERENT WAYUniversal App - Designed for iPhone and iPad David is a minimalistic game wrapped inside of a soothing atmosphere in which the hero... | Read more »
Eyefi Unveils New Eyefi Cloud Service Th...
Eyefi Unveils New Eyefi Cloud Service That Allows Users to Share Media Across Personal Devices Posted by Tre Lawrence on April 18th, 2014 [ permalink ] | Read more »
Tales from the Dragon Mountain: The Lair...
Tales from the Dragon Mountain: The Lair Review By Jennifer Allen on April 18th, 2014 Our Rating: :: STEADY ADVENTURINGiPad Only App - Designed for the iPad Treading a safe path, Tales from the Dragon Mountain: The Lair is a... | Read more »
Yahoo Updates Flickr App with Advanced E...
Yahoo Updates Flickr App with Advanced Editing Features and More Posted by Tre Lawrence on April 18th, 2014 [ permalink ] | Read more »
My Incredible Body - A Kid's App to...
My Incredible Body - A Kid's App to Learn about the Human Body 1.1.00 Device: iOS Universal Category: Education Price: $2.99, Version: 1.1.00 (iTunes) Description: Wouldn’t it be cool to look inside yourself and see what was going on... | Read more »
Trials Frontier Review
Trials Frontier Review By Carter Dotson on April 18th, 2014 Our Rating: :: A ROUGH LANDINGUniversal App - Designed for iPhone and iPad Trials Frontier finally brings the famed stunt racing franchise to mobile, but how much does its... | Read more »
Evernote Business Notebook by Moleskin I...
Evernote Business Notebook by Moleskin Introduced – Support Available in Evernote for iOS Posted by Tre Lawrence on April 18th, 2014 [ permalink ] | Read more »

Price Scanner via MacPrices.net

Deal Alert! 13-inch MacBook Pro on sale for $...
Best Buy has the 13″ 2.5GHz MacBook Pro on sale for $999.99 on their online store. Choose free shipping or free instant local store pickup (if available). Their price is $200 off MSRP. Price is valid... Read more
Free HopTo 2.2 Helps Enhance Your Productivit...
The HopTo app helps you do more on your iPad by providing more and easier adaccess to files and documents. Version 2.2 adds Egnyte and HopTo’s Mac OSX File Connector. If you already have the hopTo... Read more
National Distracted Driving Awareness Month:...
As the country recognizes National Distracted Driving Awareness Month, Sprint is reminding wireless consumers to focus on driving while behind the wheel, to not text or email while driving, and to... Read more
13-inch 2.4GHz Retina MacBook Pro available f...
Abt has the 13″ 2.4GHz 128GB Retina MacBook Pro available for $1229 including free shipping. Their price is $70 off MSRP. Read more
iMacs on sale for up to $160 off MSRP this we...
Best Buy has iMacs on sale for up to $160 off MSRP for a limited time. Choose free home shipping or free instant local store pickup (if available). Prices are valid for online orders only, in-store... Read more
iPad Airs on sale this weekend for up to $100...
Best Buy has WiFi iPad Airs on sale for $50 off MSRP and WiFi + Cellular iPad Airs on sale for $100 off MSRP on their online store for a limited time, with prices now starting at $449. Choose free... Read more
Apple restocks refurbished Mac minis starting...
The Apple Store has restocked Apple Certified Refurbished Mac minis for up to $150 off the cost of new models. Apple’s one-year warranty is included with each mini, and shipping is free: - 2.5GHz Mac... Read more
Hyundai Brings Apple CarPlay To The 2015 Sona...
Hyundai Motor America has announced it will bring Apple CarPlay functionality to the 2015 Sonata. CarPlay is pitched as a smarter, safer and easier way to use iPhone in the car and gives iPhone users... Read more
Updated iPads Coming Sooner Than We Had Thoug...
MacRumors, cites KGI securities analyst Ming Chi Kuo, well-respected as an Apple product prognisticator, saying that Apple will introduce an upgraded iPad Air and iPad mini in 2014/Q3, meaning the... Read more
Toshiba Unveils New High And Low End Laptop M...
Toshiba has announced new laptop models covering both the high-end and low-end of the notebook computer spectrum. Toshiba 4K Ultra HD Laptop Toshiba’s new Satellite P55t features one of the world’s... Read more

Jobs Board

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
*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* Inc. Research Data Specialist - Appl...
…of Worldwide Market Research & Intelligence. The team is responsible for conducting Apple branded consumer market research. It is also responsible for analyzing data Read more
*Apple* Automotive Parts Department position...
Apple Automotive is one of the fastest growing dealer…and it shows. Consider making the switch to the Apple Automotive Group today! At Apple Automotive, we 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.