Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
CE325: 3D Computer Graphics
2. Coordinate Systems
Adrian F. Clark
alien@essex.ac.uk
VASE Laboratory, School of Computer Science and Electronic Engineering
University of Essex
2011–12
/home/alien/environment/tex/ces-
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
Outline
1
Coordinate systems
2
Defining the camera
3
Pre-defined objects
4
Camera motion
5
Interaction
/home/alien/environment/tex/ces-
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
The viewport
The rectangular window in which OpenGL draws is known
as the viewport. When OpenGL creates a window, the
viewport is set to fill it.
The bottom left corner of the viewport is given in window
coordinates, along with the viewport’s width and height.
glViewport (x, y, width, height)
This allows you to create several displays in the same
window.
If the camera’s aspect ratio does not match the viewport,
the displayed image will appear distorted. This is why the
viewport is normally set in the reshape callback, which
we shall discuss when we look at transformations.
/home/alien/environment/tex/ces-
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
World coordinates and handedness
In 3D, coordinate systems may be either left- or
right-handed
Maths and most computer graphics use right-handed
coordinates: if x runs along the screen and y up is, then z
is out of the screen
It is important that you do not confuse the coordinate
systems of the viewport (pixels in the window) with /home/alien/environment/tex/cesthe
x, y , z of the world
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
Setting the camera
The easiest way to set the position and orientation of the
OpenGL camera is via gluLookAt:
gluLookAt (camx, camy, camz, px, py, pz,
upx, upy, upz);
This sets the camera to be at position (camx, camy,
camz), looking at (px, py, pz) and with the up direction
being given by (upx, upy, upz)
If gluLookAt isn’t called, the camera is positioned at the
origin, looks down the negative z-axis, and has its up
direction parallel to the y -axis — equivalent to
gluLookAt (0.0, 0.0, 0.0, // camera position
0.0, 0.0, -1.0, // where we’re looking
0.0 1.0 0.0)
// up direction
/home/alien/environment/tex/ces-
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
Pre-defined objects
[see opengl-04.c]
Rectangles are so common that there is a dedicated
primitive for drawing them
void glRectf (GLfloat x1, GLfloat y1,
GLfloat x2, GLfloat y2)
which draws a rectangle in the plane z = 0 with sides
parallel to the x and y axes.
To draw a wireframe or solid cube, you can use
void glutWireCube (GLdouble size)
void glutSolidCube (GLdouble size)
to produce a cube of size size centred at the origin
/home/alien/environment/tex/ces-
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
To draw a wireframe or solid sphere, you can use
void glutWireSphere (GLdouble radius,
GLint slices, GLint stacks)
void glutSolidSphere (GLdouble radius,
GLint slices, GLint stacks)
to produce a sphere centred at the origin.
There are also GLUT primitives for drawing the cone, torus,
tetrahedron, octahedron, dedecahedron, and icosahedron.
One of the classic computer graphic objects is Newell’s
teapot, and GLUT provides an easy way to draw it:
void glutWireTeapot (GLdouble scale)
void glutSolidTeapot (GLdouble scale)
to produce a teapot scaled by scale centred at the origin.
/home/alien/environment/tex/ces-
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
Looking around an object
[see opengl-05.c]
We can use gluLookAt to move the viewpoint around an
object
There’s a little geometry in this:
x
= r cos θ
z = r sin θ
As θ changes from frame to frame, our viewpoint of the
object changes too
The code to manipulate θ lies in the idle callback
/home/alien/environment/tex/ces-
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
Double-buffering
The program also introduces the idea of double-buffered: it
draws into an off-screen frame buffer and then swaps the
off-screen one for the on-screen one as the screen
refreshes
This involves setting the display mode using
glutInitDisplayMode and invoking
glutPostRedisplay whenever the buffer-swapping is to
occur
Why do we need double-buffering? If we don’t, updates will
be jerky and the model will appear to flash or flicker
/home/alien/environment/tex/ces-
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
Keyboard interaction
[see opengl-06.c]
We have already used the keyboard callback to handle
keypresses for interaction. In fact, OpenGL calls this
routine only for keystrokes that have ASCII
representations.
Other keystrokes such as the arrow keys found on most
keyboards (which typically generate sequences of ASCII
codes) result in the invocation of the special character
callback.
/home/alien/environment/tex/ces-
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
Mouse interaction
Most programs will actually involve interaction with the
mouse rather than the keyboard. This is achieved by the
mouse callbacks, registered with:
glutMouseFunc for mouse clicks
glutMotionFunc for mouse movements with a button
pressed
glutPassiveFunc for mouse movements with a button
not pressed
OpenGL also provides functions for defining menus, both
attached and pop-up; but this is not the appropriate place
to go into details of their use.
/home/alien/environment/tex/ces-
Coordinate systems
Defining the camera
Pre-defined objects
Camera motion
Interaction
Where do we go from here?
We’ve got about as far as we can without knowing some
geometry
For example, we cannot explore the shading of 3D objects
without knowing how to work out normal vectors
So the next thing we’ll do is go over some trigonometry,
then we’ll move on to think about vectors, and then
transformations
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