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December 96 - QuickDraw GX Line Layout:

QuickDraw GX Line Layout: Bending the Rules

Daniel I. Lipton

Many high-end drawing applications provide the user with a way to draw text along an arbitrary path. Some of them even provide the means to edit this text in place. The methods discussed here will illustrate how to do both in a QuickDraw GX-based application. In fact, I'll show you how QuickDraw GX enables your application to provide better line layout capabilities than those currently available in mainstream graphics arts applications.

One of the things that makes QuickDraw GX interesting is its amazing typography -- whatever else has been said about GX, its type capabilities are universally acknowledged as the best. Besides aesthetics, a distinguishing attribute of QuickDraw GX typography is not what is graphically possible, but the ease with which visual content can be created. A user can create documents that are kerned or tracked or have swashes, ligatures, and so on without QuickDraw GX, but achieving these effects requires a great deal of manual labor, with lots of Shift-Option-Command key combinations and switching to special fonts -- assuming the developer has made the effort to provide such a level of functionality. With QuickDraw GX, these effects are features designed into the font itself, so all the user needs to do is type and the text comes out beautifully. For different effects, the user just picks font features from a dialog or palette. The time saved by the user can be 90% over a non-GX interface! It simply has to be experienced to be appreciated.

All of this great typography is easy for the user to use because it's easy for the developer to implement. How many pre-GX drawing and illustration packages support the same level of typographic quality as their pre-GX publishing package counterparts? Not many, and of those that do, how much more memory do those applications require than they would without the typography code? Thanks to QuickDraw GX, we're beginning to see drawing and illustration programs that incorporate high-end typographic features and page layout programs that incorporate high-end graphics features -- all with lower overall memory requirements (when compared with traditional non-GX applications) because the code is in the system and is shared between applications.

Let me get to the real topic of this article. A favorite feature in illustration and page layout programs is to enable the user to lay a line of text along an arbitrary path, be it straight or curved. My goal here is to provide the developer with a way to do this, using QuickDraw GX, that's familiar to those who have been using GX and enticing to those who haven't tried it yet. If you've written code to handle text on a path in a non-GX application, consider the amount of code needed to do the editing on the screen and the amount of code you had to write to make it print on a PostScript printer. Then compare it to what's presented here -- I think the QuickDraw GX advantage will be clear!

I'll assume you have some knowledge of typography and a working knowledge of QuickDraw GX throughout my discussion. If you need to brush up on GX, there are the Inside Macintosh: QuickDraw GX books; the Programmer's Overview and Typography volumes are most relevant here.

Accompanying this article on this issue's CD and develop's Web site is a library of code called CurveLayout which very closely parallels the QuickDraw GX line layout mechanism but with support for curved layouts. The functions of this library will be described later.


It turns out that QuickDraw GX provides an extremely simple method for drawing text along a curve, since it lets us make any shape a dash outline for any other shape -- to dash a shape means to draw another shape in a repeating pattern along the perimeter of the first shape (see Figure 1). The PostScript language, by comparison, allow only simple dashing.

Figure 1. Dashing a shape

Since QuickDraw GX text is a shape, you can draw text along a path by using dashing, as shown in Listing 1.

Listing 1. Drawing text on a curve using dashing

void PutTextOnCurve(gxShape myPath)
   gxDashRecord   aDash;
   gxShape         textShape = GXNewText(5, "Hello", nil);

   // Call primitive shape to convert text to glyph.
   GXPrimitiveShape(textShape);   // All dashes must be primitive.
   aDash.dash = textShape;
   aDash.attributes = gxBreakDash;// Dash each letter separately.
   aDash.advance = 0;             // 0 advance means single repeat.

   GXSetShapeDash(myPath, &aDash);
   GXDisposeShape(textShape);       // Dash is now sole owner of it.
   GXSetShapeFill(myPath, gxFrameFill);
                                    // Dash only for framed shapes.
}   // PutTextOnCurve

Listing 1 demonstrates just how simple it can be to put text on a path in QuickDraw GX. This method would also work with layout shapes in addition to text shapes (although there's a bug in GX 1.1.3 and earlier that may cause a crash if you do try to dash with a layout). While dashing may be a simple interface for drawing text along a curve, it isn't an efficient solution for editing because of the overhead incurred by constantly rebuilding the dash every time the text changes. Additionally, the dashing solution puts you at the mercy of the algorithms used for dashing -- they weren't specifically designed for text or layout manipulation.


The CurveLayout library discussed here provides the illusion of a new shape type for QuickDraw GX which I affectionately call the "curve layout." I wanted to continue the object-oriented philosophy of GX by providing an API for drawing and editing text along a curved path. The idea is to provide an efficient mechanism for adding curve layouts to your application without forcing you to learn too much new stuff. While the article will go into great detail concerning the algorithms used, you need not understand them to incorporate curve layouts into your application using the CurveLayout library.


Before we go too much further, it's worth discussing some things about our friend the glyph shape. There are three different kinds of shapes for drawing text: the text shape, the glyph shape, and the layout shape. Text shapes are the most familiar to those of us who have used QuickDraw or PostScript. When a text shape is drawn, its appearance is the same as the result of the DrawString call in QuickDraw or the show operator in PostScript: simply the text itself.

The relationship between glyph and layout shapes can be compared to programming. The layout shape is like a high-level language such as LISP -- a very high-level, powerful way of drawing text that produces beautiful results, but it makes specific manipulations difficult. The glyph shape is more like assembly language -- you can control every aspect of how the text draws, but even simple things require a good deal of programming effort. Nevertheless, it's the direct control possible with the glyph shape that enabled me to write CurveLayout.

A glyph shape allows the specification of individual positions and tangent vectors (and even typographic style) of every typographic element drawn in a shape.

Figure 2 illustrates the power of the glyph shape for our purposes. At left is a typical straight piece of text. The arrows represent the tangent vectors stored in the glyph shape and the dots at the ends of the arrow lines show the positions. (Note that both here and in Figure 3, the tangent vectors are drawn as normals -- rotated 90 degrees counterclockwise from their actual positions -- since otherwise they would run together and make a mess of the figures.) Beside that is the same text with different tangents and positions showing how these attributes might be manipulated to draw text along a path. The tangent vector specifies the scale and rotation of the glyph and is stored in the glyph shape as a point. The x and y values of this point are used to construct the mapping shown at the right in the figure. This mapping is applied to the glyph to reposition it as desired.

Figure 2. Glyph shape tangents, positions, and mapping matrix

But wait -- while glyph shapes give us the control we need to flow our glyphs along a path (by setting positions and tangents for each glyph in the shape), they're still like assembly language, and we don't want to position every glyph ourselves if we don't need to. The good news is that QuickDraw GX provides a "compiler" to convert layout shapes to glyph shapes, so we can use the high-level language (layout shape) instead. Our compiler is the routine GXPrimitiveShape, which allows us to deal mostly in the beautiful world of layouts and then convert them into glyph shapes that can have their positions and tangents modified to flow along a path. Layout shapes also provide us with the high-level abilities required for interactive editing (more on this later).

Now we've seen how we can convert a line layout shape into a glyph shape, and how the glyph shape can have its positions and tangents modified so that the glyphs draw along a path, but how do we generate those positions and tangents?


QuickDraw GX can evaluate points along paths. GXShapeLengthToPoint accepts a distance and a polygon or path and returns the point along that polygon or path that's the specified distance along its perimeter. In addition to the point, the tangent vector at that point (slope of the path or polygon) is returned, which is exactly what we need! With this information, we can lay glyph shapes along a path by simply modifying the tangents and positions appropriately.

The x coordinate of each glyph's position represents the current linear offset of the glyph in the layout (as if it were along a straight line). A glyph's position can be determined with the GXGetGlyphMetrics function and can be used as the length along the path for GXShapeLengthToPoint. The returned point and tangent can then be inserted into the glyph shape. The results of this technique are almost what we want, but consider the example shown in Figure 3.

Figure 3. Glyphs positioned on a curve using x position as length along curve

In Figure 3, the arrows show the positions and tangents of glyphs that have been rotated around their positions, which are typically on the bottom left (at least for Roman fonts) rather than around their centers. Because of this, the text doesn't look quite right -- some of the wider glyphs even seem to leap off the curve! We can do better than this. We can use the horizontal centers of the glyphs (that is, the center of the glyph along its baseline) as the input rather than their positions. Unfortunately, the point we put back in the glyph shape must be for the position of the glyph, not its center, so we have a little work to do translating back and forth.

Given a glyph shape, the function GXGetGlyphMetrics gave us the position information that we needed to compute the points and tangents for our first attempt. This function can also be used to obtain the bounding box of a glyph, and from the bounding box we can determine the horizontal center points of each glyph.

In Figure 4, we see the glyphs for the word "Pig." The dots represent the glyph positions obtained from GXGetGlyphMetrics and the starbursts represent the horizontal center of each glyph along the x axis, determined by the bounding boxes, which I've bisected for clarity. (Note that the position of a glyph doesn't necessarily fall on the left edge of the glyph's bounding box.)

Figure 4. Glyph shape positions and horizontal centers

Listing 2 shows the loop for repositioning glyphs from CurveLayout. It illustrates how to compute the new glyph position given the location and tangent returned from GXShapeLengthToPoint, using the horizontal center to adjust the input length rather than merely using the glyph's x position. Before looping through the glyphs, we get some necessary information about the glyph shapes: the tangents (the glyph shape may have rotated glyphs to begin with, and we'd like to preserve them), the positions, and the bounding boxes. Then, for each glyph we do the following:

  1. Compute the horizontal center of the glyph's bounding box.

  2. Compute a vector that describes the glyph's position relative to the horizontal center of the bounding box (we'll use this in step 4).

  3. Find out the position and tangent on the curve using the horizontal center of the glyph as the length along the curve.

  4. Compute the new glyph position. Since earlier we described the glyph position as a vector relative to the horizontal bounding box center, and the point returned from GXShapeLengthToPoint is on the curve at the place where we want the horizontal bounding box center, we can compute the new glyph position as the vector we saved translated to the new position and rotated by the angle described by the tangent.

  5. Compute the new tangent. This is the composition of the glyph's original tangent vector and the one from the path.

Listing 2. The CurveLayout glyph loop

// Get the positions, tangents, and bounding boxes of all glyphs.
GXGetGlyphs(theGlyphs, nil, nil, nil, nil, tangents, nil, nil, nil);
GXGetGlyphMetrics(theGlyphs, positions, glyphBoxes, nil);

// For each glyph, move its position to the correct place on the
// curve.
for (idx = 0; idx < glyphCount; ++idx) {
   // Compute glyph's horizontal center.
   pointToMapOnCurve.x = glyphBoxes[idx].left + 
      (glyphBoxes[idx].right - glyphBoxes[idx].left) / 2;
   pointToMapOnCurve.y = 0;
   // Compute new glyph position relative to horizontal center.
   relativePosition.x = positions[idx].x - pointToMapOnCurve.x;
   relativePosition.y = positions[idx].y - pointToMapOnCurve.y;

   // Find the new location and tangent for horizontal center.
   GXShapeLengthToPoint(thePath, 0, pointToMapOnCurve.x, &newPoint,

   // New position will be the glyph's position relative to the 
   // horizontal center rotated by the tangent. First rotate.
   ResetMapping(&aMapping);[0][0] = newTangent.x;[1][0] = -newTangent.y;[0][1] = newTangent.y;[1][1] = newTangent.x;
   MapPoints(&aMapping, 1, &relativePosition);
   // Now position this relative to the new point.
   positions[idx].x = newPoint.x + relativePosition.x;
   positions[idx].y = newPoint.y + relativePosition.y;

   // Concatenate the new tangent with the old.
   oldTangent.x = tangents[idx].x;
   oldTangent.y = tangents[idx].y;
   tangents[idx].x = FixedMultiply(oldTangent.x, newTangent.x) -
      FixedMultiply(oldTangent.y, newTangent.y);
   tangents[idx].y = FixedMultiply(oldTangent.x, newTangent.y) +
      FixedMultiply(oldTangent.y, newTangent.x);
}   // end for

The results of applying this algorithm are seen in Figure 5, where the round end of the line denotes the horizontal center of the bounding box and the square end of the line denotes the glyph position. On the left is a glyph with a line illustrating the relative location of the glyph's position and its horizontal bounding box center before wrapping. On the right is that same glyph positioned on a curve using our algorithm. You can see how the glyph here is positioned more naturally on the curve than was the case in Figure 3.

Figure 5. CurveLayout repositioning of a glyph

I've hand-drawn all the pictures so far using a QuickDraw GX-savvy draw program (LightningDraw GX) to illustrate the development of CurveLayout. Figure 6 is a picture generated with CurveLayout itself (see the test application that accompanies this article). The baseline curve is shown for clarity. Notice that the "te" ligature -- a particularly wide glyph -- in the word "pasteboard" is naturally tangent to the curve. Also, since this is QuickDraw GX, we can apply a number of transforms to the wrapped layout, such as the one shown in Figure 7.

Figure 6. Output of the CurveLayout routine

Figure 7. CurveLayout output with perspective transform applied


QuickDraw GX's ability to draw high-quality typographic content is only half of what's interesting about its line layout capabilities -- GX also provides a number of routines to facilitate writing code to do editing of these beautiful lines of text, as follows:
  • GXHitTestLayout for hit testing, to find out which character a given location is nearest. It's typically used for converting mouse clicks during editing. A point is converted to a character index.

  • GXGetLayoutCaret for computing the caret shape for a position between two characters. This is used for drawing the insertion point caret. A character index is converted into the caret shape.

  • GXGetLayoutHighlight to compute the highlight shape for a run of characters, used for selecting text. A starting index and ending index are converted into a shape describing the highlight for the characters in the run.
CurveLayout wouldn't be complete if we couldn't provide these abilities. It's important for the user to be able to edit a layout on a curve in true WYSIWYG fashion. These three functions implement much of what's needed for a basic line editor. Editing whole blocks of text is left as an exercise for the programmer and is not a subject for this article!


The first part of editing involves being able to convert a mouse click into a character index. Since the function GXHitTestLayout does this for a normal line layout, we'd like to use as much of it as possible. The input to that function is a point relative to the layout. The important value of the point is the horizontal component. Provided that the position is within the layout, the horizontal component determines which character is nearest that value.

So, given a point on the curve, we want to undo the curvature to determine a value to pass to GXHitTestLayout. If GXShapeLengthToPoint converts a distance into a location, we need an inverse function that converts a location back to a distance. Unfortunately, QuickDraw GX has no such function. Additionally, the location of the mouse click may not be exactly on the shape.

Given a point, we can find the closest point on a curve. Knowing a point on a curve, we can determine the distance that point falls along the curve by doing a binary search of GXShapeLengthToPoint:

  1. Find the length of the shape (GXGetShapeLength).

  2. Do a binary search for the point on the curve closest to the hit point by calling GXShapeLengthToPoint, passing in lengths between 0 and the total length of the curve, and systematically reducing the distance to the point you seek until it's as close as you choose.
The length determined by this method can then be passed into GXHitTestLayout.

It's important to note that the algorithm above is simplified for the sake of brevity: it works on a single quadratic curve or line segment. The code included in the CurveLayout library implements the full functionality using the ShapeWalker library described in my Graphical Truffles column in develop Issue 27. The ShapeWalker library is used to determine each individual line or curve segment of a shape; the distance from a hit point to each segment is determined and the smallest of them is chosen (code comments illustrate the method more completely).


To compute the caret of a line layout, we call GXGetLayoutCaret. This returns a shape describing the insertion position. If we take the resulting shape and use it to dash the curve (with only one repetition), the result is the curve layout caret. It's that simple (see Listing 3).

Listing 3. Computing the curve layout caret

theFill = GXGetShapeFill(thePath);
realCaret = GXGetLayoutCaret(layout, offset, highlightType,
   caretType, nil);

// Copy into caret passed in (if it's nil, the right thing happens).
result = GXCopyToShape(caret, thePath);

GXSetShapePen(result, ff(1))      // We don't want dashes to scale.
theDash.attributes = gxBreakDash;
theDash.dash = realCaret;
theDash.advance = 0               // We want only one repeat.
theDash.phase = ff(0);
theDash.scale = ff(1);
GXSetShapeDash(result, &theDash);

// Make sure we have a framed shape for the path.
if ((theFill != gxFrameFill) && (theFill != gxClosedFrameFill))
   GXSetShapeFill(result, gxClosedFrameFill);

// Now apply the dash to get the caret on the path.
GXSetShapeDash(result, nil);


We can also use QuickDraw GX's dashing ability to highlight the individual characters in a curve layout. If we call GXGetLayoutHighlight for each individual character in a specified range, each resulting shape can be used to build up a dash shape. The dash shape built will have one contour per character, each contour representing the highlight of that character. If we then dash the curve with these contours, we get the desired effect.

Well, we almost get the desired effect -- while the result does highlight the curved layout's text, the highlight has gaps. Achieving a contiguous highlight is a more difficult problem. In fact, popular PostScript-based drawing applications highlight text on a path with noncontiguous regions. Figure 8 compares noncontiguous highlighting similar to that of many popular non-GX-based applications with the contiguous highlighting obtainable by QuickDraw GX using CurveLayout. The library supports both methods.

Figure 8. Two ways to highlight

The code in Listing 4 achieves the noncontiguous highlight of a curve layout. But we can do better: the CurveLayout library implements contiguous highlighting using QuickDraw GX's ability to do hairline dashing or bend dashing. Rather than going on and on, I'll let the code in the library speak for itself.

Listing 4. Creating the highlight with dashing

oneCharHighlight = nil;
newHighlight = GXNewShape(gxEmptyType);

for (idx = startOffset; idx < endOffset; ++idx) {
   oneCharHighlight = GXGetLayoutHighlight(theLayout, idx, idx + 1,
      hilightType, oneCharHighlight);
   if (oneCharHighlight != nil) {
      // Add highlight for individual character to highlight shape.
      GXSetShapeParts(newHighlight, 0, 0, oneCharHighlight,
   }  // end if         
}   // end for

theShape = GXCopyToShape(highlight, thePath);
GXSetShapePen(theShape, ff(1));    // We don't want dashes to scale.
GXSetShapeFill(theShape, gxFrameFill);      
theDash.attributes = gxBreakDash;
theDash.dash = newHighlight;
theDash.advance = 0;                  // We want only one repeat.
theDash.phase = ff(0);
theDash.scale = ff(1);
GXSetShapeDash(theShape, &theDash);
GXSetShapeDash(theShape, nil);

// Change the fill of the result to winding. Since when bent around,
// contours can overlap, we want the overlaps to fill, too. With 
// even-odd, they wouldn't be filled and the highlight would look
// funny.
GXSetShapeFill(theShape, gxWindingFill);


CurveLayout is designed to look very much like the line layout functions you're used to -- we want a curve layout to look as if it really were a new QuickDraw GX shape type. All of the editing routines take the same parameters as the corresponding line layout routines, so I won't spend too much time describing those. See Inside Macintosh: QuickDraw GX Typography for more information. The most important functions in the CurveLayout library are as follows:
gxShape ClNewCurveLayout(gxShape theText, gxShape theShape);
void ClDisposeCurveLayout(gxShape curveLayout);
The ClNewCurveLayout function creates the curve layout shape. The input is a normal line layout shape and a curve. Actually, the second parameter can be any kind of shape: a line, a polygon, or a path. The resulting curve layout shape is the one that will be passed to the other library functions for editing. It's also the shape you'd draw and to which you can attach transforms for achieving rotation or other effects. The ClDisposeCurveLayout function destroys the shape.

Modification of the text in the layout (such as for editing) should be done on the layout shape passed in. The path can be changed as well. If either of the two input shapes is modified, you should call the ClChangedCurveLayout function before redrawing. For example, this function should be called for each character inserted or deleted from the original line layout shape.

The code accompanying this article also includes an application that demonstrates using the CurveLayout library. While I'll certify the actual CurveLayout library as ready for prime time, the test application is just a test application -- not a model of coding perfection! Also, as an extra bonus I've included the CurveLayoutGX control panel. This control panel adds the basic curve layout feature to all of your existing drawing applications by defining a key combination to activate it. (This is a bit of a hack; use it at your own risk.)

All of the functions of the library are documented (as is the CurveLayout code itself) in the header file, CurveLayout.h, so I won't go further into the API. See "Curve Measurement" for a few other details about the implementation.


    The current version of QuickDraw GX uses a numerical approximation for certain functions that are relevant here. The particular functions relate to the measurement of quadratic BÈzier curve segments and are used by GXShapeLengthToPoint, by GXGetShapeLength, and for dashing as invoked by either GXDrawShape or GXPrimitiveShape. The implementation of these was done as a numerical approximation to ensure sufficient performance on 680x0 machines, where the use of a closed mathematical equation would have been too slow. The bad news is that while this method is accurate enough for the original use intended (primarily dashing), its not accurate enough to produce good-looking text along a curve.

    As you've seen in this article, the functions mentioned above are heavily used in the CurveLayout library. The inaccuracies will manifest themselves as characters being spaced a little too far apart. To ensure high-quality text layout, a library has been included with this article that reimplements the low-level quadratic segment measurement functions using a floating-point closed equation. On top of that code, Ive built my own versions of GXShapeLengthToPoint, GXGetShapeLength, and GXPrimitiveShape, called AccurateShapeLengthToPoint, AccurateGetShapeLength, and AccuratePrimitiveShape. Within AccuratePrimitiveShape is an implementation of all cases of dashing that the CurveLayout library requires. All other cases of PrimitiveShape are dispatched to GXPrimitiveShape; hence this call isnt a complete replacement for GXPrimitiveShape. The CurveLayout.c file contains a compile-time conditional that can be defined to use the library code instead of the built-in QuickDraw GX code.

    The low-level math used by my library was written by Joseph Maurer. He wrote measurement routines that operate on individual quadratic curve segments. I built the shape measurement and dashing functions by using the ShapeWalker library described in my Graphical Truffles column in develop Issue 27 to extract individual segments from QuickDraw GX shapes.


The library provided with this article should enable anybody writing a QuickDraw GX application to add high-quality typography drawn along an arbitrary curve. If you've already written code to edit QuickDraw GX line layouts, you'll find the API in this library very familiar. For those of you who haven't thought about writing a GX-based application, perhaps the simplicity of using CurveLayout as well as the quality demonstrated by the output of this code will make you give GX another look. Without QuickDraw GX, an application would have to include code similar to what's in the CurveLayout library in addition to the code the application would need to do ordinary line layout, not to mention all of the additional code that would be required in the application to print something like a curve layout shape.

CurveLayout provides developers with a way to provide distinctly superior user value in their applications, while reducing code size and complexity at the same time -- what could be easier?


    • "Graphical Truffles: A Library for Traversing Paths" by Daniel Lipton, develop Issue 27.

    • Inside Macintosh: QuickDraw GX Programmer's Overview and Inside Macintosh: QuickDraw GX Typography by Apple Computer, Inc. (Addison-Wesley, 1994).

Although he's a member of the QuickDraw GX team, Daniel has been secretly developing a next-generation PostScript printer (based on the latest in artificial intelligence technology) that will achieve sentience on August 29, 1997. When not sleeping, Daniel can be found lost in San Francisco traffic or buying critters at his local aquarium shop.*

Thanks to our technical reviewers Alex Beaman, Brian Chrisman, Dave Hersey, and Ingrid Kelly. Special thanks to Joseph Maurer for the low-level curve measurement routines that made accurate text layout on curves possible.*


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*Apple* Site Security Manager - Apple (Unite...
# Apple Site Security Manager Job Number: 42975010 Culver City, Califo ia, United States Posted: Oct. 2, 2015 Weekly Hours: 40.00 **Job Summary** The Apple Site Read more
WiSE *Apple* Pay Quality Engineer - Apple (...
# WiSE Apple Pay Quality Engineer Job Number: 44313381 Santa Clara Valley, Califo ia, United States Posted: Nov. 13, 2015 Weekly Hours: 40.00 **Job Summary** Join our Read more
Holiday Retail Associate with *Apple* Knowl...
…and assertive.Someone who can troubleshoot iOS devices (iPhone and iPad) and Apple Mail issues.Someone who can offer solutions.Someone who can work weekends.Someone with Read more
*Apple* Systems Engineer (Mclean, VA and NYC...
Summary:Assist in providing strategic direction and technical leadership within the Apple portfolio, including desktops, laptops, and printing environment. This person Read more
Simply Mac *Apple* Specialist- Service Repa...
Simply Mac is the largest premier retailer of Apple products in the nation. In order to support our growing customer base, we are currently looking for a driven Read more
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