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SECRETS OF COMPUTER
GAMES, GRAPHICS AND ANIMATIONS How is it possible to create animations for computer games and
graphics? For realistic motion of objects about a computer screen we need to know the physics related to describing and predicting the motion of objects. A full description of the realistic motion of any object in two-dimensions is given by the three vectors: position vector (displacement), velocity and acceleration. Displacement
vector Velocity vector
Acceleration Vector
The motion of object of an object of mass m is governed by the net force acting on that object as described by Newton’s Second Law Hence, if
you know the net force acting on the object, you can predict the
acceleration, velocity and displacement at all times. We can perform these
calculations assuming the acceleration a is
constant during a small time interval. We start with initial values for the
velocity and displacement and then calculate the velocity and position of the
object at each successive time interval Thus, if we know the position of a collection of objects as a function of time, it is a simple matter to write the code to make an animation of the motion. Consider the movement of five balls confined to a two-dimensional box. When a ball strikes a wall of the box, the ball is reflected. We want to construct a realistic model to animate the motion of all the balls. The Origin is the point (0, 0). The initial position of the five balls and their initial X and Y velocity components are shown in the figure below:
Predict
Observe Explain (POE) #1 The force acting on each ball is zero except when a ball collides with a wall of the box. Predict the motion of each ball and state the physical principles that you needed to make your predictions. Observe the animated gif.. Compare predictions with the observations and account for any discrepancies.
Predict
Observe Explain (POE) #2 A gravitational force acts on each ball. Predict the motion of each ball and state the physical principles that you needed to make your predictions. Observe the animated gif. Compare predictions with the observations and account for any discrepancies. Comment on the path of each ball, and their velocities and accelerations.
Predict
Observe Explain (POE) #3 Assume each ball carries the same positive electric charge and the box is placed inside a uniform electric field that is in the +X direction. Predict the motion of each ball and state the physical principles that you needed to make your predictions. Observe the animated gif.. Compare predictions with the observations and account for any discrepancies. Comment on the path of each ball, and their velocities and accelerations.
MATLAB
Download and run the script cg001.m. Carefully inspect the script to see how the motion of five balls confined to a two-dimensional box can be realistic modelled. In Matlab,
a [2D] vector can be represented as a complex number. The real part gives the
x-component of the vector and the imaginary part the y-component. For
example, the displacement as a complex number can be expressed as If you have any comments, corrections, suggestions or additions please email Ian Cooper matlabvisualphysics@gmail.com
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