3D VIEWING ILLUSTRATED

WHAT YOU SEE DEPENDS ON YOUR POSITION

• In the real world, what you see depends on where you stand, the direction you look, how you tilt your head, and so on.

3D VERSUS 2D

• In 3D, the y-axis typically points up instead of down. • Negative coordinates, which are rarely used in

2D, are quite common in 3D. • Because of this, the origin is at the center of

space as opposed to the top-left corner as in 2D

MAJOR DIFFERENCES BETWEEN 2D AND 3D

RIGHT HANDED COORDINATE SYSTEM

CAMERA POSITION

• Camera positioned at (5, 5, 5):• Looking at the southeast side

SOUTHWEST SIDE

• Move the camera to position (-5,5,5):• Looking at the southwest side

LOOKDIRECTION

• The lookdirection is a vector that tells the camera where to look.• For the camera below the lookdirection is (-1,-1,-

1):

MOVING THE CAMERA

• Moving the camera does not change the lookdirection:

THE LOOKDIRECTION IS BASED ON A LOOKAT POINT

• Changing the lookdirection:

LOOKAT AND LOKDIRECTION

• The easiest way to determine the lookdirection is specify a lookat point in the scene and subtract the camera position from it:

lookat – camera position• For the above camera position, if the lookat is

(0,0,0), then look direction is:• Lookdirection = (0,0,0) – (-5,5,5) = (5, -5, -5)

SOUTHWEST VIEW

• Given an orthographic camera and the above lookdirection we get the following scene:

THE UP DIRECTION

• The lookdirection is not enough to get the correct view:

UP DIRECTION NOT CHANGED

UP DIRECTION WRONG

CORRECT

CORRECT

TRANSFORM UP DIRECTION

UP DIRECTION ANALOGY

if you're designing a flight simulator, up is the direction perpendicular to the plane's wings, from the plane toward the sky when the plane is on the ground.

DEFAULT CAMERA POSITION

ROTATING THE CAMERA

• We will call rotation around the look vector (or z axis) Roll. • Rotation around the up vector (or y axis) is called

Yaw. • Rotation around the Right vector (x axis) is called

Pitch. • Below is a picture of an aircraft showing roll, pitch

and yaw in terms of the aircraft's local axis. Note: we can use a similar system for our object rotations

ROLL, PITCH AND YAW