76 msdn magazine
If you’re well-versed in 2D graphics,
you might assume that 3D is similar ex-
cept for the extra dimension. Not quite!
Anyone who’s dabbled in 3D graphics
programming knows how diffi cult it is.
3D graphics programming requires you to
master new and exotic concepts beyond
anything encountered in the conventional
2D world. A lot of preliminaries are
required to get just a little 3D on the
screen, and even then a slight miscalcula-
tion can render it invisible. Consequently,
the visual feedback so important to learn-
ing graphics programming is delayed
until all the programming pieces are in
place and working in harmony.
DirectX acknowledges the profound
difference between 2D and 3D graphics programming with the
division between Direct2D and Direct3D. Although you can mix
2D and 3D content on the same output device, these are very dis-
tinct and diff erent programming interfaces, and there’s no middle
ground. DirectX doesn’t allow you to be a little bit country, a
little bit rock-and-roll.
Or does it?
Interestingly, Direct2D includes some concepts and facilities that
originated in the 3D programming universe. Th rough features such
as geometry tessellation (the decomposition of complex geome-
tries into triangles) and 2D eff ects using shaders (which consist of
special code that runs on the graphics processing unit, or GPU),
it’s possible to exploit some powerful 3D concepts while still
remaining within the context of Direct2D.
Moreover, these 3D concepts can be encountered and explored
gradually, and you get the satisfaction of actually seeing the
results on the screen. You can get your 3D feet wet in Direct2D so
a later plunge into Direct3D programming is a little less shocking.
I guess it shouldn’t be all that surprising that Direct2D incor-
porates some 3D features. Architecturally, Direct2D is built on
top of Direct3D, which allows Direct2D to also take advantage of
the hardware acceleration of the GPU. Th is relationship between
Direct2D and Direct3D becomes more apparent as you begin
exploring the nether regions of Direct2D.
I’ll commence this exploration with
a review of 3D coordinates and coordi-
nate systems.
The Big Leap Outward
If you’ve been following this column
in recent months, you know it’s possi-
ble to call the GetGlyphRunOutline
method of an object that implements
the IDWriteFontFace interface to obtain
an ID2D1PathGeometry instance that
describes the outlines of text characters in
terms of straight lines and Bézier curves.
You can then manipulate the coordinates
of these lines and curves to distort the
text characters in various ways.
It’s also possible to convert the 2D
coordinates of a path geometry into 3D coordinates, and then manip-
ulate these 3D coordinates before converting them back into 2D to
display the path geometry normally. Does that sound like fun?
Coordinates in two-dimensional space are expressed as number
pairs (X, Y), which correspond to a location on the screen; 3D
coordinates are in the form (X, Y, Z) and, conceptually, the Z axis is
orthogonal to the screen. Unless you’re dealing with a holographic
display or a 3D printer, these Z coordinates aren’t nearly as real as
X and Y coordinates.
There are other differences between 2D and 3D coordinate
systems. Conventionally the 2D origin—the point (0, 0)—is the
upper-left corner of the display device. Th e X coordinates increase
to the right and Y coordinates increase going down. In 3D, very
oft en the origin is in the center of the screen, and it’s more akin to
a standard Cartesian coordinate system: Th e X coordinates still
increase going to the right, but the Y coordinates increase going up,
and there are negative coordinates as well. (Of course, the origin,
scale, and orientation of these axes can be altered with matrix
transforms, and usually are.)
Conceptually, the positive Z axis can either point out of the
screen or point into the screen. Th ese two conventions are known
as “right-hand” and “left-hand” coordinate systems, referring to
a technique to distinguish them: With a right-hand coordinate
system, if you point the index finger of your right hand in the
direction of the positive X axis, and the middle finger in the
direction of positive Y, your thumb points to positive Z. Also, if you
curve the fi ngers of your right hand from the positive X axis to the
A 2D Portal into a 3D World
DIRECTX FACTOR CHARLES PETZOLD
Code download available at msdn.microsoft.com/magazine/msdnmag0214.Figure 1 The Coordinate System Used
for the Programs in This Article