The VRML coordinate system is a right-hand system with the x axis pointing to the right, the y axis pointing upward and the z axis pointing toward the user.
This paragraph introduces basic concepts and terminology for control and manipulation of objects in virtual realities (VR), as used in the Virtual Reality Markup Language (VRML). Readers familiar with VRML may want to skip this.
An arbitraty motion of a body in 3-dimensional space can be described by 6 parameters or degrees of freedom:
If no further constraints apply, these 6 parameters suffice to describe any 3-dimensional motion.
As a sidenote, in robotics it is customary to define as many degrees of
freedom as all the machine parts have, with the understanding that there
are constraints on elongation and pan-tilt range.
For example, a robot arm with three extensible telescope sections and three
rotatable joints can be described as having nine degrees of freedom
(3x elongation, 3x joint rotation, 3x joint angle), each of which has
specific physical limits.
This extended model is necessary to completely describe the state of the
robot.
However, the state of the tool at the end of the robot arm could still be
described by only 6 parameters.
The VRML coordinate system is a right-hand system with the x axis pointing to the right, the y axis pointing upward and the z axis pointing toward the user.
The rotations around the x, y and z axes are called pitch, yaw and roll, borrowing nautical terms that describe the motion of a ship on the sea: Pitch is the up- and downward motion of the ship's bow as it hits the waves, yaw is the actual deviation from the course, and roll is the particularly sickening rotation along the ship's longitudinal axis.
When talking about mouse movements, we will call the direction of the user's view the x axis and the left-to-right direction the y axis. Most mice nowadays come with an additional wheel control. The wheel is usually called the z axis, but for consistency we will call it x-rotation, the positive direction being away from the user.
In VR environments, not all degrees of freedom are used all the time. VRML defines three common modes of user interaction, using different subsets of parameters to control the situation:
Of those modes, walk and examine are closest to our real-world experience and
thus are the easiest and most intutitive to use.
In fly mode, the discrepancy between actual sense of gravity and virtual lack
of it makes finding one's way around very difficult, and requires training and
specialized control gear to be used effectively.
Imagine a VRML representation of a product in a virtual catalogue. How would you conveniently manipulate it with your mouse to view it from all sides?
You would need ways to control three degrees of freedom, i.e. x, y, and z-rotation. Three rotation axes *can* be mapped to a wheel mouse:
x mouse motion becomes z-rotation of the object, y motion becomes x-rotation,
and x-rotation (the wheel) becomes y-rotation (ouch! this is totally
counter-intutive).
Breathe deeply, fasten your seat belt, and watch out for RSI syndrome :(
A standard mouse is a 2D device: it can intuitively model translations along 2 axes. You might use the wheel as a third axis, but then how would you perform rotations ? Modifier keys, or dragging with buttons pressed ?
All these workarounds have severe disadvantages:
Thus, for anything more demanding than WWW gimmicks, the user needs a new way of interacting with the computer that is better suited to the task of navigating and controlling VR environments.
The spaceball connects to the computer via an RS-323 serial port (there are also gameport variants, and newer versions than the one discussed here additionally provide USB) and offers true 6 degrees of freedom, plus a number of user-assignable buttons.
The rubber ball can be pushed or pulled and rotated along all 3 axes. When released, an elastic bearing pulls it back to center position. When rotated or displaced from the center, it generates a continous stream of events.
It is designed as an addition to keyboard and mouse, not necessarily as a mouse replacement:
There is an important difference to keep in mind between the mouse and the spaceball: the former offers absolute positioning, whereas the latter works with relative positioning.
The mouse function φ maps motion of the device to motion of the mouse pointer: φmouse: smouse · c → spointer. The driver will apply a constant user-definable scaling factor.
The spaceball functions φ and ψ map displacement to linear motion and
torque to rotation. While the ball is off-center, the pointer (or rather the
controlled VR object) keeps moving:
φsball: (ssball)c1 → s'object (= vobject),
ψsball: (αsball)c2 → α'object (= ωobjekt),
where x' denotes the derivative in the time domain.
The driver will apply a user-definable acceleration exponent.
While the mouse has a linear relationship between input and effect, the spaceball integrates the input: linear and angular speed are the first derivatives of displacement and torque in the time domain.
This is the reason why a spaceball is difficult to use as a mouse replacement. Its behaviour is similar to the mouse surrogate "joysticks" found in some notebooks.