September 95 - The Basics of QuickDraw 3D Geometries
Nick Thompson and Pablo Fernicola
No
matter how realistic or sophisticated you want your 3D images to be, you must
always build objects with the primitive geometric shapes provided by the
graphics system. Our article in Issue 22 gave the basic information you need to
start developing applications with QuickDraw 3D. Here we delve deeper into the
primitive geometric shapes provided by QuickDraw 3D and show how to use them
effectively. We also give you some tips we've gained from working with
developers.
Geometric shapes -- or geometries -- form the foundation of any 3D scene.
QuickDraw 3D provides a rich set of primitive geometric types that you use to
define the shapes of things. You can apply attributes (such as colors) to
geometric objects, collect geometric objects into groups, and copy, illuminate,
texture, transform, or otherwise modify them to attain the visual effects you
want. In other words, everything that's drawn by QuickDraw 3D is either a
geometry or a modification of a geometry. So you need to know how to define
geometries (and usually also how to create and dispose of them) to work
effectively with QuickDraw 3D. This article describes the geometries available
in QuickDraw 3D version 1.0 and shows how they relate to other aspects of the
QuickDraw 3D architecture (such as the class hierarchy).
We're assuming that you're already familiar with the basic capabilities of
QuickDraw 3D. For a good introduction, see our article "QuickDraw 3D: A New
Dimension for Macintosh Graphics" in Issue 22 of develop (a copy is on this
issue's CD). In that article, we provided an overview of QuickDraw 3D's
architecture and capabilities. You can think of QuickDraw 3D as having three
main parts: graphics, I/O (the QuickDraw 3D metafile), and human interface
guidelines. Here, we provide more detail on the graphics portion of the
QuickDraw 3D API and highlight some parts of that API that could use
clarification as you try to implement geometries.
To help you get started using geometries, this issue's CD contains version 1.0
of the QuickDraw 3D shared library and programming interfaces, sample code, and
an electronic version of the book 3D Graphics Programming With QuickDraw 3D,
which provides complete documentation for the QuickDraw 3D programming
interfaces.
Our previous article included an introduction to rendering; we'll review a key
concept here -- retained vs. immediate rendering. We'll also elaborate on an
important point we glossed over in that article: submitting something to be
rendered rather than just rendering it. These concepts will help set the stage
for what you'll learn here about working with geometries.
A powerful feature of QuickDraw 3D is that it supports both retained and
immediate modes for rendering geometric data; you can even mix these modes
within the same rendering loop. In retained mode, the definition and storage of
the geometric data are kept internal to QuickDraw 3D -- as abstract geometric
objects. In immediate mode, the application keeps the only copy of the
geometric data; for efficiency, the application should use QuickDraw 3D data
structures to hold the data, but those structures can be embedded in
application-defined structures. Retained mode geometric objects and immediate
mode geometric data define the shapes of objects. You'll typically use one or
more primitive geometric types provided by QuickDraw 3D (such as triangles or
meshes) to build up a scene.
Whether you use retained or immediate mode to render geometries usually depends
on how much of a model changes from one rendering operation to the next. As
we'll illustrate with examples in this section, we prefer to use retained
geometries most of the time and to use immediate mode only for temporary
objects. Since our preference for retained mode is a departure from the
traditional QuickDraw way of drawing, we'll attempt to convince you that
retained mode is a much more efficient method of rendering geometries.
Immediate
mode. When you use immediate mode rendering, the data that defines a geometry
is stored and managed by your application. For example, to draw a triangle you
would write code similar to that in Listing 1. If you wanted to draw this
triangle many times, or from different camera angles, you would have to
maintain the data in your application's data structures.
Listing 1. Rendering a triangle in immediate mode
TQ3TriangleData myTriangle;
// Set up the triangle with appropriate data.
...
// Render the triangle.
Q3View_StartRendering(myView);
do {
Q3Triangle_Submit(&myTriangle, myView);
} while (Q3View_EndRendering(myView) == kQ3ViewStatusRetraverse);
Typically
when using immediate mode, you stick to a single type of geometry (triangles
are popular with developers accustomed to lower-level 3D graphics libraries).
If you use multiple geometric types, you need to define a data structure to
manage the order of the geometries. An example of rendering several geometries
in immediate mode is shown in Listing 2.
Listing 2. Rendering several geometries in immediate mode
typedef struct myGeometryStructure {
TQ3ObjectType type;
void *geom;
struct myGeometryStructure *next;
} myGeometryStructure;
myGeometryStructure *currentGeometry;
...
Q3View_StartRendering(myView);
do {
while (currentGeometry != NULL) {
switch (currentGeometry->type) {
case kQ3GeometryTypeTriangle:
Q3Triangle_Submit(
(TQ3TriangleData *) currentGeometry->geom, myView);
break;
case kQ3GeometryTypePolygon:
Q3Polygon_Submit(
(TQ3PolygonData *) currentGeometry->geom, myView);
break;
}
currentGeometry = currentGeometry->next;
}
} while (Q3View_EndRendering(myView) == kQ3ViewStatusRetraverse);
If
you wanted to apply transforms to a geometry as it's being drawn, you would
have to add a new case to the switch statement. This gets complicated pretty
quickly. As a result, many developers, when given a choice, will use immediate
mode only for models that have a fixed geometry and are not being altered.
Retained
mode. Creating geometric objects allows renderers to take advantage of
characteristics of particular geometries and thus optimize the drawing code.
The code in Listing 3 draws a triangle in retained mode.
Listing 3. Rendering a triangle in retained mode
TQ3TriangleData triangleData;
// Set up the triangle with appropriate data.
...
// Create the triangle.
triangleObject = Q3Triangle_New(&triangleData);
// Render the triangle.
Q3View_StartRendering(myView);
do {
Q3Object_Submit(triangleObject, myView);
} while (Q3View_EndRendering(myView) == kQ3ViewStatusRetraverse);
You'll notice that the routine to draw an object is Q3Object_Submit. This
probably seems a bit strange: why didn't we call it Q3Object_Draw? The reason
is that there are four occasions in which you need to specify a geometry --
when writing data to a file, when picking, when determining the bounds of a
geometry, and when rendering -- and QuickDraw 3D provides a single routine that
you use in all of these cases. To indicate which operation you want to perform,
you call the Submit routine inside a loop that begins and ends with the
appropriate calls. For instance, to render a model, you call Submit functions
inside a rendering loop, which begins with a call to Q3View_StartRendering and
ends with a call to Q3View_EndRendering (as shown in Listing 3). Similarly, to
write a model to a file, you call Submit functions inside a writing loop, which
begins with a call to Q3View_StartWriting and ends with a call to
Q3View_EndWriting.
We recommend that you put all your Submit calls together within a single
function (such as the one shown in Listing 4) that you can then call from your
rendering loop, picking loop, writing loop, or bounding loop. Organizing your
code in this fashion will prevent a common mistake: creating rendering loops
that are out of sync with picking or bounding loops. It also simplifies your
rendering and picking loops -- you just call your submitting function from
within the loop. Here's an example of calling the function in Listing 4 from
within a rendering loop:
Q3View_StartRendering((**theDocument).fView);
do {
theStatus = SubmitScene(theDocument);
} while (Q3View_EndRendering((**theDocument).fView)
== kQ3ViewStatusRetraverse);
Listing
4. A submitting function
// Submit the scene for rendering, file I/O, bounding, or picking.
TQ3Status SubmitScene(DocumentHdl theDocument)
{
TQ3Vector3D globalScale, globalTranslate;
globalScale.x = globalScale.y = globalScale.z =
(**theDocument).fGroupScale;
globalTranslate = *(TQ3Vector3D *)&(**theDocument).fGroupCenter;
Q3Vector3D_Scale(&globalTranslate, -1, &globalTranslate);
Q3Style_Submit((**theDocument).fInterpolation,
(**theDocument).fView);
Q3Style_Submit((**theDocument).fBackFacing, (**theDocument).fView);
Q3Style_Submit((**theDocument).fFillStyle, (**theDocument).fView);
Q3MatrixTransform_Submit(&(**theDocument).fRotation,
(**theDocument).fView);
Q3ScaleTransform_Submit(&globalScale, (**theDocument).fView);
Q3TranslateTransform_Submit(&globalTranslate,
(**theDocument).fView);
Q3DisplayGroup_Submit((**theDocument).fModel,
(**theDocument).fView);
return (kQ3Success);
}
Even if you perform all your rendering in immediate mode -- that is, without
creating any QuickDraw 3D geometric objects -- you still need to create some
QuickDraw 3D objects, such as a view, camera, and draw context, in order to
render any image at all. So working with geometries in QuickDraw 3D means
working with at least some objects. Before going into detail about how to
create and use QuickDraw 3D geometric objects, let's review the object system
and some of its basic classes.
QuickDraw 3D is an object-based system. We chose to implement the API with the
C language, which doesn't support objects directly; nevertheless QuickDraw 3D
is organized into a definite class hierarchy. Figure 1 shows part of this
hierarchy, emphasizing the classes that are discussed in this article. At the
top of the class hierarchy is the basic QuickDraw 3D Object class. Geometries,
such as the triangle, polygon, and mesh classes, are at the bottom of the
hierarchy.
The Object class is really named TQ3Object. This article uses shortened forms
of the QuickDraw 3D class names.*
1. Partial QuickDraw 3D class hierarchy
You can determine the class in which a function is defined simply by looking at
the function's name: function names have the form Q3class-name_method. For
example, the function Q3Shared_GetReference is defined in the Shared class and
returns a reference to the shared object that's passed as an argument. The
function Q3Object_Dispose is defined in the Object class; it accepts any
QuickDraw 3D object as an argument (since Object is the root class) and
disposes of it.
In the following sections, we'll talk more about the classes shown in Figure 1
and answer some questions developers have had about using them when working
with geometries. Then we'll (finally!) talk about the geometric objects
themselves and provide sample code for using many of them.
Generally speaking, drawing anything with QuickDraw 3D involves working with
objects that inherit from the Shared class. There can be multiple references to
shared objects (hence the name); the way QuickDraw 3D determines whether a
shared object is still referenced is by way of a reference count, initially 1.
Developers new to QuickDraw 3D are sometimes confused by reference counts, but
they're actually very straightforward. When you create a shared object, its
reference count is 1. For example:
myNewObject = Q3Mesh_New();
// myNewObject now has a reference count of 1.
When
you get a shared object as a result of a Get call, or pass one as an argument
in an Add or Set call, the object's reference count is incremented.
// The following calls increment the object's reference count.
Q3Group_GetPositionObject(myGroup, currentPosition,
&myExistingObject);
...
Q3Group_AddObject(myGroup, myObject);
...
Q3View_SetDrawContext(myView, myDrawContext);
Passing
a shared object as the argument to a Dispose call decrements its reference
count; only when the count goes to 0 does QuickDraw 3D actually dispose of the
memory occupied by the object. As a general rule, you should dispose of the
object before the scope of the variable expires. For example:
{ // Start of the block. Variables come into scope.
TQ3Object myObject = Q3Mesh_New(); // The start of myObject's scope
// Do something that manipulates myObject.
...
// The scope of myObject is going to end at the next closing brace,
// so dispose of it before we go out of scope.
Q3Object_Dispose(myObject);
} // End of the block.
If
you were assigning an object reference to a global variable, you would dispose
of the object before calling Q3Exit and exiting your program.
Q: Why does my application crash when I call Q3Exit?
A: In the debugging version of QuickDraw 3D, Q3Exit generates a debugging
message for each remaining object. The default behavior is to display the
message with the DebugStr call; the message is displayed in MacsBug (or
whatever debugger you use). So your application isn't crashing; it's trying to
tell you to tidy up after yourself! To avoid this unscheduled trip into your
debugger, you can install your own error handler and log the message to a file.
And, of course, you should fix your application so that it doesn't leak
memory!*
Let's take a closer look at what happens to reference counts when you create
and dispose of a shared object. Figure 2 shows the typical lifetime of a group
of QuickDraw 3D objects (we'll talk more about groups later).
- An application creates a geometric object. Its reference count is 1.
- The application creates a group object. Its reference count is also 1.
- The application adds the geometry to the group (by calling the function
Q3Group_AddObject), which increments the reference count of the geometric
object (to 2).
- The application disposes of the geometric object (by calling the
function Q3Object_Dispose), which is safe to do once it's added to the group.
This decrements the reference count of the geometry back to 1. The application
can then operate on the group (which now contains the geometry).
- When it's finished with the group, the application can dispose of the
group object. This lowers the reference count of the group to 0, which causes
QuickDraw 3D to dispose of the group and of all the objects within the group.
As you can see, the geometry is disposed of as a side effect of disposing of
the group.
The view object ties together the elements required to draw a scene; it's the
central object that holds the state information for rendering a scene. A scene
consists of the geometry being drawn (hereafter referred to as the model),
together with the light, camera, draw context, and other objects. Our previous
article discussed how to set up a view; we'll expand on that discussion by
describing how to create and manage multiple scenes of a model.
To display a scene, you need at least one view object, and each view object
must have a camera associated with it. Each of your application's windows
usually has one view object attached to it. When you need to display multiple
scenes of the same model, you can create multiple windows, each with its own
view object. Then you simply submit the model to the desired view.
Alternatively, you can display multiple scenes using a single view object by
setting up several different cameras and draw contexts and switching between
them -- manipulating the view's camera to create each scene (see Figure 3).
You can have only one active draw context and camera for each view object, so
to update one of your windows, you need to manually set the active draw context
and camera for the appropriate scene. For this reason, the first option (one
view per window) is usually simpler to implement.
QuickDraw 3D provides a number of classes for grouping objects together. Groups
are useful because they provide a structure to your models, allowing you to
express the relationship between different geometric objects. Of course, if you
want to use your own data structures for storing your geometries, you can do
so, but generally it's more work. Using QuickDraw 3D's group classes, you can
create hierarchies of geometric data by nesting groups within other groups.
Figure 4 shows the group classes provided with QuickDraw 3D.
You can create a group object by calling Q3Group_New. This creates an object
belonging to the generic Group class. QuickDraw 3D provides the following
subgroups of the generic Group class, which are distinguished by the types of
objects you're allowed to place in them:
- A light group places the light objects for a scene in a group, which
simplifies lighting management. For example, you could provide an iterator
function to loop through the group and turn all the lights on or off.
- A display group manages objects that are drawable, including
geometries, styles, and transforms. You can use the function
Q3Object_IsDrawable to confirm whether an object is drawable.
- An information group stores informational strings, such as the author,
copyright, trademark, and other human-readable information within a
metafile.
Because we want to talk about geometries, which are drawable
objects, we'll concentrate on display group objects. In addition to "plain"
display groups, there are two specialized subclasses of the display group
class: ordered and I/O proxy. For a plain display group, the order in which
items are placed in the group is the order in which they're drawn when the
group is submitted, regardless of the class that the objects belong to. For an
ordered display group, objects in the group are sorted by object type and are
submitted (when you call Q3DisplayGroup_Submit) in the following order:
transforms, styles, attribute sets, shaders, geometric objects, groups.
Ordered display groups are most useful when you want to operate on a group of
objects as a single entity. For example, you know that transforms are always at
the start of the group, so you could manipulate the transform to alter the
orientation of the entire group. (If you were using a plain display group, you
would have to search for the transform, or otherwise store a reference to it,
which makes life more complicated.) Sometimes you'll want to nest a number of
ordered display groups within a plain display group. If you were animating a
robotic arm, for example, each component of the arm could be an ordered display
group that's nested within a plain display group.
You can use I/O proxy display groups to provide multiple representations of the
same data. This is useful when dealing with applications that aren't based on
QuickDraw 3D or that run on other platforms. For example, some applications
might be able to read only mesh objects; your application may want to use NURB
patches (another type of geometric object), but you want other applications to
be able to read your metafiles. In this case, you could write a NURB patch
representation of your data, followed by a mesh representation. To provide both
representations of the same data in a metafile, you would create an
I/O proxy group that contains the NURB patch object first and the mesh
object second, and write the group to the metafile. When you draw with
QuickDraw 3D, the objects that appear first in the group are preferred over
later objects in the group.
The Transform class enables you to change the position, orientation, or size of
geometries. When you specify the coordinates for the vertices that define a
geometry, the x, y, z values are expressed as floating-point values in local
coordinates. Rendering, however, and associated operations like backface
removal and lighting are performed in world coordinates. To transform a
geometry from one space to another, QuickDraw 3D multiplies the local
coordinates by a local-to-world matrix. The default value for this matrix is
the identity matrix, which leaves the original geometry unchanged. By changing
the value of the local-to-world matrix, you can transform geometries without
having to change the geometries' coordinates.
Using an example from our previous article, let's say that you have a model
that contains several boxes (see Figure 5). We could enter the coordinates for
the points that make up each of the four boxes, but that's a lot of work (and
if you're creating an object for each box, it's a waste of memory). Instead, we
define one box at a certain location and call it the reference box. To get the
effect of four boxes in different locations, we draw the reference box four
times -- changing the local-to-world matrix each time before drawing.
If you look in the file QD3DTransform.h, you'll notice that there are several
different types of transforms. The most general type is the matrix transform,
which is a 4 x 4 matrix. To use this transform, you supply the translation,
rotation, and scale values in the appropriate entries of the matrix, as shown
in Figure 6. You can do any type of transform that can be expressed as a 4 x 4
matrix. In the figure, you can see that the upper 3 x 3 submatrix is a rotation
matrix, with the entries in the main diagonal containing the scale factors for
x, y, and z. The lower row contains the translation factors.
If you know which type of transform you'll be applying, however, it's better to
use one of the more specific types. In this way, QuickDraw 3D renderers and
shaders will be able to take advantage of the information contained in the
transform; for example, if your local-to-world matrix is just a translate
transform, the renderer doesn't have to transform normals before performing the
backface removal operation (because directions are not affected by
translations). Also, using the more specific types provides a better
abstraction and tends to make the logic of your code easier to understand (and
you don't have to deal with all those pesky matrices).
When you change the local-to-world matrix by applying transforms, each
transform is concatenated as it's applied through a Submit call. For example,
if before drawing a point object, we submit a translate transform, a rotate
transform, a scale transform, and then a point, the point will be transformed
as follows:
p' = p * S * R * T
p' is the resulting transformed point and p is the original point. T is the
matrix containing the translate operation, R is the matrix containing the
rotate operation, and S is the matrix containing the scale operation.
You can apply transforms either by using immediate mode calls or by creating
transform objects -- just as you do for geometries. Note that transforms
accumulate; that is, if you apply a translation, any objects drawn after that
will be translated by the same amount. If you want a transform to apply to a
certain object only, you can use the Q3Push_Submit and Q3Pop_Submit calls
around it or place the object in a group, since groups perform an implicit push
and pop (you can change this behavior if you want).
So, let's build on what we've learned so far. We want to draw the model shown
in Figure 5. Let's first do it by submitting new transforms in immediate mode,
before each box is drawn, as shown in Listing 5.
Listing 5. Using translate transforms in immediate mode
Q3View_StartRendering(viewObject);
do {
TQ3Vector3D translationX = {2.0, 0.0, 0.0},
translationY = {0.0, -2.0, 0.0};
Q3View_Push(viewObject);
// Note how we are using a retained mode geometry with immediate
// mode transforms. As we execute each of the calls, the boxes
// are drawn.
Q3Object_Submit(referenceBox, viewObject);
// Move to the right.
Q3TranslateTransform_Submit(&translationX, viewObject);
Q3Object_Submit(referenceBox, viewObject);
// The Pop will move back to the left.
Q3View_Pop(viewObject);
// Move down.
Q3TranslateTransform_Submit(&translationY, viewObject);
Q3Object_Submit(referenceBox, viewObject);
// Move to the right.
Q3TranslateTransform_Submit(&translationX, viewObject);
Q3Object_Submit(referenceBox, viewObject);
} while (Q3View_EndRendering(viewObject) == kQ3ViewStatusRetraverse);
Alternatively,
we could create the model of the four boxes as a group, as shown in Listing 6.
Listing 6. Creating translate transform objects
TQ3GroupObject myModel;
TQ3Vector3D translationX = {2.0, 0.0, 0.0},
translationYAndNegativeX = {-2.0, -2.0, 0.0};
TQ3TransformObject xform_x, xform_yx;
// Note that as we execute these calls, nothing is drawn.
myModel = Q3Group_New();
xform_x = Q3TranslateTransform_New(&translationX);
xform_yx = Q3TranslateTransform_New(&translationYAndNegativeX);
Q3Group_AddObject(myModel, referenceBox);
Q3Group_AddObject(myModel, xform_x);
Q3Group_AddObject(myModel, referenceBox);
Q3Group_AddObject(myModel, xform_yx);
Q3Group_AddObject(myModel, referenceBox);
Q3Group_AddObject(myModel, xform_x);
Q3Group_AddObject(myModel, referenceBox);
// To draw the boxes, you would call Q3Object_Submit(myModel, myView)
// within a submitting loop.
Attributes affect the way an object is rendered in QuickDraw 3D. A view has a
default set of attributes, defined in the QD3DView.h file, that can be modified
to suit a particular application. If no attributes are supplied for the objects
being rendered within a view, the default view attributes are applied.
Attributes can be applied in a number of ways: by submitting them to a view
object; by adding them to a group; or by attaching them to a geometry, to a
geometry's face, or to each vertex of a geometry.
The order in which attribute sets are applied during rendering is based on a
fixed hierarchy, as illustrated in Figure 7. Attributes of the same type (such
as diffuse color) can override one another; they use the following preference
hierarchy, from highest to lowest precedence: vertex, face, geometry, group,
view. For example, a specular color attribute at the vertex level does not
override a diffuse color attribute at the geometry level, whereas a specular
color attribute at the vertex level does override a specular color attribute at
the geometry level (because they are attributes of the same type). If
attributes at any level are not supplied, the parent's attributes apply. If
there are no attributes supplied anywhere in the hierarchy, the default
attribute set for the view will be used.
Here are the six most commonly used predefined attribute types that you can
specify (there are 12 in all):
- The diffuse color is the actual color of the object.
- The specular color is the color of the light reflected by the object,
which may or may not be the same as the diffuse color.
- The specular control determines how much light of the specular color is
reflected.
- The ambient coefficient determines how much the ambient lighting
affects the object.
- The surface UV attribute specifies how a texture is mapped to a
geometry's vertex.
- A texture shader can be applied to a surface that has UV
parameterization applied (more on this later).
You can also define your own
custom attributes. Later, in the geometry code samples, we'll create attribute
sets to affect the way the geometries are drawn.
Now we're ready to look at the specific geometries and show how to build them.
QuickDraw 3D version 1.0 supports 12 geometries (illustrated in Figure 8). In
the code examples later in this article, we'll cover the most commonly used
geometries.
- A marker object is a bitmap that's displayed face-on at any orientation --
similar to a sprite. It's useful for denoting the position of objects and for
providing annotations, such as labels on objects in a 3D chart.
- A point object is the most basic object in QuickDraw 3D; it specifies
discrete points in a scene.
- A line object is a line between two points.
- A polyline object is a line that consists of multiple segments.
- A triangle object is a closed planar geometry defined by three
intersecting lines. It's the simplest form of a polygon.
- A simple polygon object is a planar geometry described by a list of
vertices; it's a figure formed by a closed chain of intersecting straight
lines. A simple polygon consists of a single convex contour and may not contain
holes.
- A general polygon object is a planar geometry that may contain holes,
be concave, and consist of one or more contours.
- A trigrid object is a grid whose surface consists of multiple triangles
that share edges and vertices.
- A box object is a three-dimensional rectangular object.
- A mesh object is a collection of vertices, faces, and edges that
represent a topological polyhedron. It's sometimes referred to as a winged-edge
structure.
- A NURB curve object is a curve described by a NURB equation.
- A NURB patch object is a three-dimensional surface described by a NURB
equation.
NURB stands for nonuniform rational B-spline. A B-spline is a
parametric curve (a curve defined by coordinates derived from functions sharing
a common parameter) whose shape is determined by a series of control points
whose influence is described by basis functions.*
Let's start with some simple geometries first: lines, polylines, triangles,
simple polygons, and general polygons. In essence, these are the building
blocks for QuickDraw 3D. You can use combinations of these to construct your
model, or you can use some of the composite geometries, such as meshes and
trigrids (described later).
Line
and polyline objects. Lines are defined by two noncoincident points. If you
want to have multiple line segments, you can use polylines (see Listing 7). In
polylines, every vertex after the first one defines a new line. You can attach
attributes at the geometry level or at the vertex level (which is useful for
having multicolored lines, but remember that you need to use per-vertex
interpolation when rendering in order for the multiple colors to apply).
Listing 7. Creating a polyline
TQ3ColorRGB polyLineColor;
TQ3PolyLineData polyLineData;
TQ3GeometryObject polyLineObject;
static TQ3Vertex3D
points[4] = { { { -1.0, -0.5, -0.25 }, NULL }, // first vertex
{ { -0.5, 1.5, 0.45 }, NULL }, // second vertex
{ { 0.0, 0.0, 0.0 }, NULL }, // third vertex
{ { 1.5, 1.5, 1.0 }, NULL } // fourth vertex
};
// The polyline has four vertices.
polyLineData.numVertices = 4;
polyLineData.vertices = points;
// Add a color to the line as a whole.
polyLineData.polyLineAttributeSet = Q3AttributeSet_New();
Q3ColorRGB_Set(&polyLineColor, 0.4, 0.2, 0.9);
AttributeSet_AddDiffuseColor(polyLineData.polyLineAttributeSet,
&polyLineColor);
// Create the polyline.
polyLineObject = Q3PolyLine_New(&polyLineData);
Q3Object_Dispose(polyLineData.polyLineAttributeSet);
Triangle
objects. Triangles are the most basic of the planar geometries in QuickDraw 3D.
Triangles are defined by three noncolinear, noncoincident vertices. In Listing
8, we set a color attribute for the entire geometry and for the individual
vertices. When you draw the triangle with flat interpolation, the geometry
color is used; when you draw it with per-vertex interpolation, however, the
vertex attributes take precedence and you can see a color ramp on the triangle
(see Figure 8, where the color ramp is approximated in grayscale).
Listing 8. Creating a triangle in a group
TQ3ColorRGB triangleColor;
TQ3GroupObject model;
TQ3TriangleData triangleData;
TQ3GeometryObject triangleObject;
static TQ3Vertex3D
vertices[3] = { { { -1.0, -0.5, -0.25 }, NULL },
{ { 0.0, 0.0, 0.0 }, NULL },
{ { -0.5, 1.5, 0.45 }, NULL } };
triangleData.vertices[0] = vertices[0];
triangleData.vertices[1] = vertices[1];
triangleData.vertices[2] = vertices[2];
triangleData.triangleAttributeSet = Q3AttributeSet_New();
Q3ColorRGB_Set(&triangleColor, 0.8, 0.5, 0.2);
AttributeSet_AddDiffuseColor(triangleData.triangleAttributeSet,
&triangleColor);
triangleData.vertices[0].attributeSet = Q3AttributeSet_New();
triangleData.vertices[1].attributeSet = Q3AttributeSet_New();
triangleData.vertices[2].attributeSet = Q3AttributeSet_New();
Q3ColorRGB_Set(&triangleColor, 1.0, 0.0, 0.0);
AttributeSet_AddDiffuseColor(triangleData.vertices[0].attributeSet,
&triangleColor);
Q3ColorRGB_Set(&triangleColor, 0.0, 1.0, 0.0);
AttributeSet_AddDiffuseColor(triangleData.vertices[1].attributeSet,
&triangleColor);
Q3ColorRGB_Set(&triangleColor, 0.0, 0.0, 1.0);
AttributeSet_AddDiffuseColor(triangleData.vertices[2].attributeSet,
&triangleColor);
// Create the triangle and group.
triangleObject = Q3Triangle_New(&triangleData);
model = Q3OrderedDisplayGroup_New();
if (triangleObject != NULL) {
Q3Group_AddObject(model, triangleObject);
Q3Object_Dispose(triangleObject);
}
Q3Object_Dispose(triangleData.vertices[0].attributeSet);
Q3Object_Dispose(triangleData.vertices[1].attributeSet);
Q3Object_Dispose(triangleData.vertices[2].attributeSet);
Q3Object_Dispose(triangleData.triangleAttributeSet);
Simple
polygon and general polygon objects. Simple polygons and general polygons are
planar objects with multiple vertices. Simple polygons must be convex, but
general polygons can be either convex or concave. In addition, general polygons
can be self-intersecting and have multiple contours.
As was shown in Figure 8, a general polygon can have a "hole" in it, but a
simple polygon never does. This is the primary difference between the two
geometries. Processing general polygons takes more time than processing simple
polygons, so we advise you to use simple polygons whenever possible.
If the geometry you're creating is convex, you should use simple polygons to
achieve better performance. If your polygons always have three vertices,
however, you should opt for triangles. If you don't know what your geometry
looks like (for example, it's being built by the user on the fly and you don't
want to check the points), use general polygons and set the complexity flag to
kQ3GeneralPolygonShapeHintComplex (see Listing 9). Renderers look at this flag
as a hint on how to process the general polygon.
Listing 9. Creating polygons
TQ3PolygonData polygonData;
TQ3GeneralPolygonData genPolyData;
TQ3GeometryObject polygonObject, generalPolygonObject;
TQ3GeneralPolygonContourData contours[2];
TQ3ColorRGB color;
static TQ3Vertex3D polyVertices[4] = {
{ { -1.0, 1.0, 0.0 }, NULL },
{ { -1.0, -1.0, 0.0 }, NULL },
{ { 1.0, -1.0, 0.0 }, NULL },
{ { 1.0, 1.0, 0.0 }, NULL }
},
genPolyHoleVertices[4] = {
{ { -0.5, 0.5, 0.0 }, NULL },
{ { -0.5, -0.5, 0.0 }, NULL },
{ { 0.5, -0.5, 0.0 }, NULL },
{ { 0.5, 0.5, 0.0 }, NULL }
};
polygonData.numVertices = 4; polygonData.vertices = polyVertices;
polygonData.polygonAttributeSet = NULL;
polygonObject = Q3Polygon_New(&polygonData);
contours[0].numVertices = 4; contours[0].vertices = polyVertices;
contours[1].numVertices = 4;
contours[1].vertices = genPolyHoleVertices;
genPolyData.numContours = 2; genPolyData.contours = contours;
genPolyData.shapeHint = kQ3GeneralPolygonShapeHintComplex;
genPolyData.generalPolygonAttributeSet = Q3AttributeSet_New();
Q3ColorRGB_Set(&color, 1.0, 1.0, 1.0);
AttributeSet_AddDiffuseColor(genPolyData.generalPolygonAttributeSet,
&color);
polyVertices[1].attributeSet = Q3AttributeSet_New();
polyVertices[2].attributeSet = Q3AttributeSet_New();
Q3ColorRGB_Set(&color, 0.0, 0.0, 1.0);
AttributeSet_AddDiffuseColor(polyVertices[1].attributeSet, &color);
Q3ColorRGB_Set(&color, 0.0, 1.0, 1.0);
AttributeSet_AddDiffuseColor(polyVertices[2].attributeSet, &color);
genPolyHoleVertices[0].attributeSet = Q3AttributeSet_New();
genPolyHoleVertices[2].attributeSet = Q3AttributeSet_New();
Q3ColorRGB_Set(&color, 1.0, 0.0, 1.0);
AttributeSet_AddDiffuseColor(genPolyHoleVertices[0].attributeSet,
&color);
Q3ColorRGB_Set(&color, 1.0, 1.0, 0.0);
AttributeSet_AddDiffuseColor(genPolyHoleVertices[2].attributeSet,
&color);
generalPolygonObject = Q3GeneralPolygon_New(&genPolyData);
Q3Object_Dispose(genPolyData.generalPolygonAttributeSet);
Q3Object_Dispose(polyVertices[1].attributeSet);
Q3Object_Dispose(polyVertices[2].attributeSet);
Q3Object_Dispose(genPolyHoleVertices[0].attributeSet);
Q3Object_Dispose(genPolyHoleVertices[2].attributeSet);
There's nothing wrong with using only simple geometries, as described above.
You can build any complex object just with triangles, but from a performance
point of view that's not always the best thing to do. When your object is made
up of faces that share vertices, it's a good idea to use a representation that
allows the graphics system to reuse the vertex information (such as lighting
calculations) for the shared vertices.
With a box, for example, each vertex is shared by three faces, where each face
is made up of two triangles. If we draw the box as a bunch of triangles,
QuickDraw 3D would have to perform the same lighting calculations on each
vertex up to six times. If, on the other hand, we represent the box as a box
primitive or mesh object, the lighting calculations are performed only once per
vertex. (However, if you attach vertex colors or face attributes, such as
normals or colors, the calculations need to be performed more often.)
Here we show how to use two composite geometries -- trigrid and mesh objects --
as well as UV parameterization, which you may need to supply if you want to
apply a texture to a trigrid or mesh.
Trigrid
objects. Trigrids are a collection of triangles that share vertices. We create
a trigid in Listing 10.
Listing 10. Creating a trigrid
TQ3ColorRGB triGridColor;
TQ3GroupObject model;
TQ3TriGridData triGridData;
TQ3GeometryObject triGridObject;
unsigned long numFacets, i;
static TQ3Vertex3D
vertices[12] = { { { -1.0, -1.0, 0.0 }, NULL },
... // 10 more lines of vertex data
{ { 0.7, 1.0, 0.5 }, NULL }};
triGridData.numRows = 3; triGridData.numColumns = 4;
triGridData.vertices = vertices;
triGridData.triGridAttributeSet = Q3AttributeSet_New();
Q3ColorRGB_Set(&triGridColor, 0.8, 0.7, 0.3);
AttributeSet_AddDiffuseColor(triGridData.triGridAttributeSet,
&triGridColor);
numFacets = (triGridData.numRows - 1) * (triGridData.numColumns - 1)
* 2;
triGridData.facetAttributeSet =
malloc(numFacets * sizeof(TQ3AttributeSet));
for (i = 0; i < numFacets; i++) {
triGridData.facetAttributeSet[i] = NULL;
}
Q3ColorRGB_Set(&triGridColor, 1.0, 0.0, 0.5);
triGridData.facetAttributeSet[5] = Q3AttributeSet_New();
AttributeSet_AddDiffuseColor(triGridData.facetAttributeSet[5],
&triGridColor);
triGridObject = Q3TriGrid_New(&triGridData);
UV
parameterization. Texturing allows you to have more realistic looking models.
For texturing to work, the geometry must have UV parameters on its vertices,
which may have to be supplied by you. The UV parameters are two floating-point
values (U and V) that correlate a location on the geometry to a point in the
picture of the texture (see Figure 9).
The convention for QuickDraw 3D is to start the UV parameters at 0.0,0.0 at the
bottom left, with U increasing toward the right and V increasing upward. You
supply the UV parameterization as a collection of vertex attributes.
Once a UV parameterization has been applied to a surface's vertices, the
surface can be texture mapped. There are several steps to texturing surfaces
with QuickDraw 3D. In general, you'll already have a texture stored in a pixel
map somewhere. What you need to do is create a texture shader (of type
TQ3TextureObject) and add it into your display group before you add the
geometry you want to shade.
Listing 11 is a general-purpose routine for adding a texture shader to a group.
It's interesting for a number of reasons: it shows how to search a group for
particular objects (in this case, an existing shader that it will replace), how
to edit items within a group, and how to add new items.
Listing 11. Routine to texture-map an object
TQ3Status AddTextureToGroup(TQ3GroupObject theGroup,
TQ3StoragePixmap *textureImage)
{
TQ3TextureObject textureObject;
TQ3GroupPosition position;
TQ3Object firstObject;
// Create a texture object.
textureObject = Q3PixmapTexture_New(textureImage);
if (textureObject) {
if (Q3Object_IsType(theGroup, kQ3GroupTypeDisplay) == kQ3True) {
// If the group is a display group...
Q3Group_GetFirstPosition(theGroup, &position);
Q3Group_GetPositionObject(theGroup, position, &firstObject);
if (Q3Object_IsType(firstObject, kQ3SurfaceShaderTypeTexture)
== kQ3True) {
TQ3TextureObject oldTextureObject;
TQ3StoragePixmap oldTextureImage;
// Replace existing texture by new one.
Q3TextureShader_GetTexture(firstObject, &oldTextureObject);
Q3PixmapTexture_GetPixmap(oldTextureObject,
&oldTextureImage);
Q3Object_Dispose(oldTextureObject);
Q3TextureShader_SetTexture(firstObject, textureObject);
Q3Object_Dispose(textureObject);
} else {
TQ3ShaderObject textureShader;
// Create texture shader and add it to group.
textureShader = Q3TextureShader_New(textureObject);
if (textureShader) {
Q3Object_Dispose(textureObject);
Q3Group_AddObjectBefore(theGroup, position,
textureShader);
Q3Object_Dispose(textureShader);
} else
return (kQ3Failure);
}
Q3Object_Dispose(firstObject);
} else if (Q3Object_IsType(theGroup, kQ3DisplayGroupTypeOrdered)
== kQ3True) {
// If the group is an ordered display group...
TQ3ShaderObject textureShader;
Q3Group_GetFirstPositionOfType(theGroup, kQ3ShapeTypeShader,
&position);
if (position) {
Q3Group_GetPositionObject(theGroup, position,
&firstObject);
if (Q3Object_IsType(firstObject,
kQ3SurfaceShaderTypeTexture) == kQ3True) {
TQ3TextureObject oldTextureObject;
TQ3StoragePixmap oldTextureImage;
// Replace existing texture by new one.
Q3TextureShader_GetTexture(firstObject,
&oldTextureObject);
Q3PixmapTexture_GetPixmap(oldTextureObject,
&oldTextureImage);
Q3Object_Dispose(oldTextureObject);
Q3TextureShader_SetTexture(firstObject, textureObject);
Q3Object_Dispose(textureObject);
} else {
// Create texture shader and add it to group.
textureShader = Q3TextureShader_New(textureObject);
if (textureShader) {
Q3Object_Dispose(textureObject);
Q3Group_SetPositionObject(theGroup, position,
textureShader);
Q3Object_Dispose(textureShader);
} else
return (kQ3Failure);
}
} else {
// Create texture shader and add it to group.
textureShader = Q3TextureShader_New(textureObject);
if (textureShader) {
Q3Object_Dispose(textureObject);
Q3Group_AddObject(theGroup, textureShader);
Q3Object_Dispose(textureShader);
} else
return (kQ3Failure);
}
}
return (kQ3Success);
} else // If pixmap shader not created...
return (kQ3Failure);
}
Mesh
objects. Listing 12 shows the key components needed to create a simple mesh
geometry. We create a mesh consisting of two faces, with one of them having a
hole. We also add UV parameters to the vertices so that we can texture-map the
mesh. Figure 10 shows the texture map and the resulting textured mesh.
Listing 12. Creating a mesh
TQ3GroupObject BuildMesh(void)
{
TQ3ColorRGB meshColor;
TQ3GroupObject model;
TQ3Vertex3D vertices[9] = {
{ { -0.5, 0.5, 0.0 }, NULL },
{ { -0.5, -0.5, 0.0 }, NULL },
{ { 0.0, -0.5, 0.3 }, NULL },
{ { 0.5, -0.5, 0.0 }, NULL },
{ { 0.5, 0.5, 0.0 }, NULL },
{ { 0.0, 0.5, 0.3 }, NULL },
{ { -0.4, 0.2, 0.0 }, NULL },
{ { 0.0, 0.0, 0.0 }, NULL }
};
TQ3Param2D verticesUV[9] = {
{ 0.0, 1.0 }, { 0.0, 0.0 }, { 0.5, 0.0 },
{ 1.0, 0.0 }, { 1.0, 1.0 }, { 0.5, 1.0 },
{ 0.1, 0.8 }, { 0.5, 0.5 }, { 0.1, 0.4 }
};
TQ3MeshVertex meshVertices[9];
TQ3GeometryObject meshObject;
TQ3MeshFace meshFace;
TQ3AttributeSet faceAttributes;
unsigned long i;
meshObject = Q3Mesh_New();
Q3Mesh_DelayUpdates(meshObject);
for (i = 0; i < 9; i++) {
TQ3AttributeSet vertexASet;
meshVertices[i] = Q3Mesh_VertexNew(meshObject, &vertices[i]);
vertexASet = Q3AttributeSet_New();
AttributeSet_AddSurfaceUV(vertexASet, &verticesUV[i]);
Q3Mesh_SetVertexAttributeSet(meshObject, meshVertices[i],
vertexASet);
Q3Object_Dispose(vertexASet);
}
faceAttributes = Q3AttributeSet_New();
Q3ColorRGB_Set(&meshColor, 0.3, 0.9, 0.5);
AttributeSet_AddDiffuseColor(faceAttributes, &meshColor);
meshFace = Q3Mesh_FaceNew(meshObject, 6, meshVertices,
faceAttributes);
Q3Mesh_FaceToContour(meshObject, meshFace,
Q3Mesh_FaceNew(meshObject, 3, &meshVertices[6], NULL));
Q3Mesh_ResumeUpdates(meshObject);
model = Q3OrderedDisplayGroup_New();
Q3Group_AddObject(model, meshObject);
Q3Object_Dispose(faceAttributes);
Q3Object_Dispose(meshObject);
return (model);
}
Q3Mesh_DelayUpdates and Q3Mesh_ResumeUpdates, used in Listing 12, are two very
important routines. Mesh objects can often contain hundreds and even thousands
of vertices. When you're building a complex model, we advise that you turn off
updates to the internal ordering of the mesh data, so that building the mesh
takes as little time as possible. The difference between doing this and not
doing this can be, in the case of a complex model containing 3000 polygons,
several minutes when Q3Mesh_DelayUpdates is not called, compared with 3 seconds
when it is called (on a mid-level computer).
We hope that the hints in this article will save you some time and help you in
your development process. We've been pleasantly surprised by some of the
applications in which developers have been putting QuickDraw 3D to use; for
example, a European developer used QuickDraw 3D to prproduce 3D representations of his code profiler application's data. Learning the basics of QuickDraw 3D's geometries is the first step toward mining the rich seam of functionality that QuickDraw 3D offers.
NICK THOMPSON (AppleLink NICKT) from Apple's Developer Technical Support group took a trip to Las Vegas this year in a rented Cadillac. He was impressed by some of the ancient architecture on show in this fine city, such as the Pyramid of Luxor, Excalibur's Castle, and Caesar's Palace (he was surprised that the ancient Egyptians, King Arthur, and the Roman emperor had all made it that far west). He was also impressed by the free food and drinks -- all he had to do was sit at a table and buy small plastic disks with green scraps of paper that the got from a hole in the wall. Having rented a Cadillac for this trip, Nick now has his heart set on a 1968 Eldorado convertible.*
PABLO FERNICOLA (AppleLink PFF, eWorld EscherDude), the short one in the picture, is the brains behind the operation. His hobbies include traveling to exotic places (such as the local supermarket), eating fine cuisine, and talking to his dog (who is almost as big as Nick, and probably a lot smarter). He's hard at work on the next generation of QuickDraw 3D, which--like Pablo--is bound to be even smarter. Pablo says, "You can use QuickDraw 3D's metafile format everywhere, even for defining virtual environments on the net. So get those applications ready, won't you?"*
Thanks to our technical reviewers Tom Dowdy, Tim Monroe, and Philip Schneider.*
