Motion characteristics consist of two dynamic properties(action and path). The “action” of an object refering to its movement pattern of some type (i.e. circular, linear), and change in position “path” (i.e., the route an object took).
The overriding goal of exploring the correlations of math and animation, will be that of identifying structures (mathematical patterns and entities) that support mimicing movement patterns,and quantity of change of objects in space.
In the math domain, vectors and scalars are two of the fundamental units that represent motion. That is, a scalar that
represents a magnitude (a numerical value, quantity) and a vector that represents magnitude with a direction or amount
of displacement. An example of the difference between scalar and vector would be; 3 miles, representing the magnitude of distance;a scalar, versus 3 miles north, that represents both magnitude and direction (path).
As a scalar "3 miles" tell us quantity, but an unknown direction. Other examples of scalars are time (2pm), speed (30mph), density (15 grams), all magnitudes (size and quantity). Examples of vectors are 30 degrees north, a hundred feet up, rotate 90 degrees clockwise, giving both magnitude and direction. Run the video for additional understanding.
Vectors manifest in a variety of way and applications (i.e. engineering, physics), and applications that help us model real life functions. Since vectors describe space and differentiation (change)they are fundamental to exploring math and animation correlations. So I begin our investigation here, by learning the basic vector mathmatical operations and identifying how they are relevant from the standpoint of motion/animation.
