1. CSE 381 – Advanced Game Programming Basic 3D Graphics
A nice simple OpenGL triangle

2. Today’s Important Terms
projection transform
render
right-handed coordinate system
scene
screen coordinates
surface
transformed coordinates
transforms
untransformed coordinates
vertex buffer
view frustum
world space
world transform
aspect ratio
back face culling
camera
double buffering
face
field of view
frame buffer
GPU
index buffer
left-handed coordinate system
model space

3. Coordinate Systems
3D Graphics is about transforming data from one coordinate system (space) to another
Model
Space
World
Space
Screen
Space

4. Drawing Using Screen Coordinates
What is screen space?
drawing on a flat, 2D space (the monitor)
draw objects at x, y locations
0, 0 is top-left-hand corner of screen
(0, 0)
(width, height)

5. 2D Games naturally use screen coordinatesx y
Shift Flash Game:

6. You change the frame buffer pixel data
What is a frame buffer?
A 2D array of colors
what dimensions?
Represents the pixels we view on the monitor (screen space)
GPU
Often represented using a single 1D array
How?
You change the frame buffer pixel data
It ends up on the screen

7. What is double buffering?
A GPU has 2 (or more) frame buffers
Why?
one for filling in
one for current display
So?
when we’re done filling one in, we swap them
this prevents flickering
why would flickering happen?

8. So what else will the GPU do for us?
Has efficient implementations of OpenGL & DirectX functions
matrix math
model transformations
for rendering & animating
texturing
storing data
shading
etc.

9. But 3D Graphics have 3Ds (duh)
A game world is a cube
It has an origin (0,0,0)
We place objects at locations inside this world volume (x, y, z)
camera (s)
models (artwork)
terrain
particle systems
light sources
We project objects onto the camera’s “screen”

10. What is world space? A coordinate system for placing all game objects
Every model has coordinates (x,y,z)
Refers to either the coordinates of:
the model’s bounding box’s center
one of the model’s corners
A 3D game world is in a box or sphere
called its bounding volume

11. A game world’s bounding volume
Keeps all objects inside world
when objects move, test to make sure they don’t leave
An additional BV provides art for out of reach background
sky box or sky sphere
You’ll make both for HW 2

12. How do we project 3D objects onto a 2D screen?
Linear algebra
We’ll let OpenGL & the GPU do this for us
We could alternatively do this in software
What are pros & cons?
More on this in a minute

13. Which objects should we project?
That’s the trick
Projecting models is computationally expensive
even with a fast GPU
detailed models have lots & lots of data
We don’t want to have to try to project all objects in the game world
So, when rendering a world, the procedure is:
Calculate which objects should be drawn
Render only those objects
This will be a big issue all semester

14. What are models? Data describing 3D game assets (artwork)
also called meshes
What data might a model have?
vertices
triangles
adjacencies
materials
textures
bone hierarchy
animations
mipmaps
billboards
and more

15. Models are created using modeling software
Like Maya, Blender, 3ds max, etc.

16. Modeling Software uses Model Space
Each model has its own origin (0, 0, 0)
So how do they end up in world space?
Linear algebra matrix transformations

17. What’s a matrix?
A 2D array of numbers
used to position a vertex in 3D space
also used to project a vertex in 3D space onto a 2D screen
NOTE: If you want to be a game programmer you must know Matrix Math
Identity Matrix
What will this do?

18. Different Transformation Matrices
scaleX
scaleY 0 0
scaleZ 0
moveX moveY moveZ 1
Also rotation matrices, depending on axis of rotation

19. Matrices can be combined
Multiply matrices for combined effects
Result is transformation matrix for a given object
This is used to position all vertices of that object in world space
How?
by performing matrix math on x,y,z values of vertices

20. Model Vertices Conversions
Note: models are created in tools using their own coordinate system (model space)
During rendering of a model, for each vertex:
Perform necessary transformations to convert from model to world coordinates
translate (move to xyz location in world), rotate, scale
Convert to view coordinates (view transform)
Convert to screen coordinates (projection transform)
You’ll learn all about this in CSE 328

21. Scene
An assembly of objects presented on the screen at once

22. Rendering
The process of producing a pixel by pixel image of the scene for the screen
What is this thing?

23. The volume of the game world to be projected onto the screen
View Frustum
The volume of the game world to be projected onto the screen

24. A point for viewing the objects in world space
What is the camera?
A point for viewing the objects in world space
the camera is placed in world space
the camera looks in a specific direction in world space
based on where the camera is, where it’s looking, and some other conditions (ex: z-plane, culling), we can draw the appropriate graphics on the screen
How do we define the camera?
2 matrices (linear algebra), a.k.a. transforms
view transform
projection transform

25. Tells the computer three things:
View Transform
Defined by a 4 X 4 matrix
Tells the computer three things:
the camera position in world space (xc, yc, zc)
the direction in which the camera is pointed
defined as a 3D vector (xvc, yvc, zvc)
the orientation of the camera
the direction that is “up” for the camera
also defined as a 3D vector

26. Projection Transform Defined by a 4 X 4 matrix
Tells the computer how the scene should be projected onto the monitor
does so by defining the viewing frustum
only those elements inside the viewing frustum are rendered to the screen
Defines 4 things:
front clipping plane (z near plane)
back clipping plane (z far plane)
aspect ratio
y field of view

27. Field of View?
Z far
plane
Z near plane
Camera
Position
fov Z
If you have the y fov, the x fov can be calculated using the aspect ratio
fov defined using radians

28. 3 connected points (vertices)
Model’s Vertices
What is a triangle?
3 connected points (vertices)
if we combine 3 vertices, we can easily draw lines to connect them
Transformation Matrix
View Transform Matrix
Projection Transform Matrix
A bunch of vertices on screen
Note: this data then feeds texture mapping process

29. A wireframe model of a table
Models
face
the area between lines (sides) of a polygon
typically triangles or quadrilaterals
surface
a face or many faces together
A wireframe model of a table

30. Textures
Textures are 2D images
We can wrap the wireframe in a texture

31. How is texturing done? We have triangle data (3 vertices)
We specify for each triangle, texture mapping in U,V coordinates
refers to pixel region of an image
After vertices are transformed:
texels are mapped onto triangles
specified by a modeler
We’re talking mapping individual texture pixels onto screen
high-resolution texture takes longer
Note: GPUs are optimized for all of this
(0, 0)
(1, 1)

32. Table & Camera Matrices
Table Data
Matrix Projections
Texturing
Table & Camera Matrices
3D Game World
Matrix Projections
Texturing
Game Matrices

33. Common question: how should we store this data?
For a cube
How many triangles
12 (2 per face)
How many vertices? 8
Common question: how should we store this data?

34. Making other shapes using Triangles
How many vertices, edges, & triangles to make a cube?
8 vertices?
18 edges
12 triangles
How about an x-wing fighter?
3099 vertices
9190 edges
6076 triangles

35. Make a data structure called triangle with 3D
One approach
Make a data structure called triangle with 3D
x, y, z
For each model, store a data structure of triangles
For cube, 12 triangles would fill data structure
How many vertices is that? 36
Not efficient

36. Graphics Data
While a scene is being rendered, where should the vertex data be stored?
storing it in system memory (RAM) requires slow copying to the video card
storing it directly in the graphics card is best
this is where vertex buffers come in

37. What is a Vertex Buffer? A memory store in the GPU for vertices
In Direct3D for example, one can use the VertexBuffer class
Can store all types of vertices (ex: transformed, with normal, etc …)
In OpenGL, we’ll use glVertext3D method
Note: other platforms also have vertex buffers

38. What is an Index Buffer?
Remember constructing 36 vertices to create a cube using triangles?
inefficient use of memory
a real cube only has 8 vertices (one for each cube corner)
In a large-scale application, redundant data is costly
Index buffers are a mechanism for sharing vertex data among primitives
a buffer that stores indices into vertex data
What does that mean?
an array (or vector, etc.) that describes shapes (e.g., triangles) using indices of constructed vertices in vertex buffer
groups of 3 indices describe one triangle

39. A Cube Index Buffer Solution
private short[] indices = {
0,1,2, // Front Face
1,3,2, // Front Face
4,5,6, // Back Face
6,5,7, // Back Face
0,5,4, // Top Face
0,2,5, // Top Face
1,6,7, // Bottom Face
1,7,3, // Bottom Face
0,6,1, // Left Face
4,6,0, // Left Face
2,3,7, // Right Face
5,2,7 // Right Face };

40. Advantages & Disadvantages of Index Buffers
What are the advantages?
more efficient memory management
What are the disadvantages?
vertices have to share color data
vertices have to share normal data
may result in lighting errors

41. What is a Depth Buffer?
A means for storing depth information for rendering
Used during rasterization to determine how pixels occlude (block) each other, algorithm:
convert each surface that’s drawn to a set of pixels
for each pixel, compute the distance from the view plane
before each pixel is drawn, compare it with the depth value already stored at that on-screen pixel
if the new pixel is closer (in front of) what’s in the depth buffer, the new pixel’s color & depth values replace those that are currently there
In Direct3D & OpenGL, can be simply turned-on:
depth buffer management is done for you
you may choose format:
z-buffers
w-buffers, a type of z-buffer that provides more precision
not as widely supported in hardware