1. Hierarchical and Object-Oriented Graphics
Chapter 8

2. Chapter 8 -- Hierarchical and Object-Oriented Graphics
Introduction:
In this chapter we explore multiple approaches to developing and working with models of geometric objects.
We extend the use of transformations from Chapter 4 to include hierarchical relationships among the objects.
The techniques that we develop are appropriate for applications, such as robotics and figure animation, where the dynamic behavior of the objects is characterized by relationships among the parts of the model.
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The notion of hierarchy is a powerful one and is an integral part of object oriented methodologies.
We extend our hierarchical model of objects to hierarchical models of whole scenes, including cameras, lights, and material properties.
Such models allow us to extend our graphics APIs to more objet-oriented systems and gives us insight in how to use graphics over networks and distributed environments, such as the Web.
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1. Symbols and Instances
Our first concern is how to store a model that may include many sophisticated objects.
There are two immediate issues:
How do we define a complex object
How do we represent a collection of these objects.
We can take a non hierarchical approach to modeling regarding these objects as symbols, and modeling our world as a collection of symbols
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Symbols are usually represented at a convenient size and orientation.
For example: a cylinder
In OpenGL we have to set up the appropriate transformation from the frame of the symbol to the world coordinate frame to apply it to the model-view matrix before we execute the code for the symbol.
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For example: the instance transformation
M = TRS
is a concatenation of a translation, a rotation, and a scale
And the OpenGL program often contains this code:
glMatrixMode(GL_MODELVIEW);
glLaodIdentity();
glTranslatef(...);
glRotatef(...);
glScalef(...);
glutSolidCylinder(...)’
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We can also think of such a model in the form of a table
The table shows no relationship among the objects. However, it does contain everything we need to draw the objects.
We could do a lot of things with this data structure, but its flatness limits us.
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2. Hierarchical Models
Suppose we wish to build an automobile that we can animate
We can build it from the chassis, and 4 wheels
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Two frames of our animation could look like this:
We could calculate how far the wheel moved, and have code that looks like
calculate(speed, distance);
draw_right_front_wheel(speed, dist);
draw_left_front_wheel(speed, dist);
draw_right_rear_wheel(speed, dist);
draw_left_rear_wheel(speed, dist);
draw_chassis(speed, dist);
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BUT this is the kind of code we do NOT want....
It is linear, and it shows none of the relationships between the 5 objects.
There are two types of relationships we wish to convey
First, we cannot separate the movement of the car from the movement of the wheels
If the car moves forward, the wheels must turn.
Second, we would like to note that all the wheels are identical and just located and oriented differently.
We typically do this with a graph.
Def: node, edge, root, leaf, ...
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Tree Representation:
DAG Representation:
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3. A Robot Arm
Robotics provides many opportunities for developing hierarchical models.
Consider this arm
It consists of 3 parts
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The mechanism has 3 degrees of freedom, each of which can be described by a joint angle between the components
In our model, each joint angle determines how to position a component with respect to the component to which it is attached
q - rotation of the base
f - rotation of first arm
y - rotation of second arm piece.
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We could write it as follows:
display() {
glRotatef(theta, 0.0, 1.0, 0.0);
base();
glTranslatef(0.0, h1, 0.0);
glRotatef(phi, 0.0, 0.0, 1.0);
lower_arm();
glTranslatef(0.0, h2, 0.0);
glRotatef(0.0, 0.0, 1.0);
upper_arm(); }
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Note that we have described the positioning of the arm independently of the details of the individual parts.
We have also put it into a tree structure
This makes it possible to write separate programs to describe the components and animate the robot.
Drawing an object stored in a tree requires performing a tree traversal (you must visit every node)
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4. Tree Traversal
Here we have a box-like representation of a human figure.
We can represent this figure as a tree
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If we put the matrices with each node we can specify exactly how to draw the robot
The issue is how to traverse the tree...
Typically you do a pre-order traversal.
This can be done in two ways:
with code and a stack
recursively (implicit stack)
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4.1 A Stack-Based Traversal
Consider the code necessary to draw the Robot.
This function might be called from the display callback
The Model-View matrix, M, in effect when the function is invoked determines the position of the robot relative to the rest of the scene.
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The function must manipulate the model-view matrix before each part of the robot is drawn.
In addition to the usual OpenGL functions for rotation, translation, and scaling, the functions glPushMatrix and glPopMatrix are particularly helpful for traversing our tree.
The first glPushMatrix duplicates the current model-view matrix
assuming that we have done a previous glMatrixMode(GL_MODELVIEW)
When we have finished with changes we can do a glPopMatrix to get back the original one saved
Note: we must do another glPushMatrix to leave a copy that we can later go back to.
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OpenGL also has the functions glPushAttrig and glPopAttrib that allow us to deal with attributes in a similar manner
OpenGL divides its state into groups, and allows a user to push any set of these groups on th attribute stack.
The user needs only to set the bits in a mask that is the parameter for glPushAttrib
Attribute groups include lighting, so we can push material properties and lights onto the stack.
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21. 5. Use of Tree Data Structures
The second approach is to use a standard tree data structure to represent our hierarchy and then to render it with a traversal algorithm that is independent of the mode of traversal.
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At each node we must store the information necessary to draw the object:
a function that defines the object
the homogeneous coordinate matrix that positions the object relative to the parent.
Typedef struct treenode{
Glfloat m[16];
void (*f)();
struct treenode *sibling;
struct treenode *child; }
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Traversing the tree in a preorder traversal can be accomplished
void traverse (treenode * root) {
if(root == NULL) return
glPushMatrix();
glMultMatrix(root->m);
root->f();
if(root->child!= NULL) traverse(root->child);
glPopMatrix();
if(root->sibling!= NULL) traverse(root->sibling); }
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6. Animation
Our robot example is articulated
consists of rigid parts connected by joints
We can make such models change their positions in time - animate them - by altering a small set of parameters.
Hierarchical models allow us to reflect correctly the compound motions incorporating the physical relationships among parts of the model.
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Of the many approaches to animation, a few basic techniques are of particular importance when we work with articulated figures.
Kinematics
describing the position of the parts of the model based on only their joint angles.
Inverse kinematics and inverse dynamics
given a desired state of the model, how can we adjust the angles so as to achieve this position?
key-frame animation
position the objects at a set of times.
Inbetweening
then fill in (interpolate).
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26. 5. Use of Tree Data Structures
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6. Animation
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7. Graphical Objects
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7.1 Methods, Attributes, and Messages
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7.2 A Cube Object
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7.3 Objects and Hierarchy
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7.4 Geometric Objects
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8. Scene Graphs
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9. Other Tree Structures
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9.1 CSG Trees
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9.2 BSP Trees
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9.3 Quadtrees and Octrees
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10. Graphics and the Web
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10.1 Networks and Protocols
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10.2 Hypermedia and HTML
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10.3 Databases and VRML
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10.4 JAVA and Applets
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11. Summary
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12. Suggested Readings
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65. Exercises -- Due next class
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