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Feature
Vector math
A lesson in understanding vectors
Issue: 4.2 (November/December 2005)
Author: Thomas Reed
Article Description: No description available.
Article Length (in bytes): 6,296
Starting Page Number: 34
RBD Number: 4216
Resource File(s): None
Related Link(s): None
Known Limitations: None
Excerpt of article text...
Many software programs, especially graphics-intensive ones, make use of a mathematical concept called the "vector." People who are not math-oriented may find the vector intimidating. In truth, they are not particularly complex at all. It is the terminology, including concepts such as cross-products and normalized vectors, that is frightening. In this article, I hope to eliminate, or at least reduce, this fear of the vector.
For those who are not at all familiar with the vector, it is a mathematical idea that represents both a direction and a length, or magnitude. For example, a moving car's velocity has both a direction (e.g.,, north) and a magnitude (e.g.,60 mph). This velocity can easily be described using a vector. Conceptually, a vector can be imagined as an arrow with a length determined by its magnitude, as seen in Figure 1.
A vector is typically represented by computer programs using three quantities: the x, y, and z components of its magnitude, each of which is just a number (also known as a scalar). While this representation makes certain things, like finding the length of the vector, more complex, it simplifies other things. In particular, the vector can be thought of as three separate vectors, each pointing along an axis.
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