Using the parametric form of lines
While the line equation given in the previous section is something most people are familiar with from high school mathematics, it’s not particularly useful in graphics when you want to manipulate objects or work out intersections, animations, and collisions. Therefore, we tend to use the parametric form. The parametric form of an equation, rather than using x and y to calculate positions, uses time, represented by t. This might sound confusing at first but bear with me while I explain.
Consider Figure 10.3 (a). Notice how a line segment can be represented by two points and a vector going between them:
Figure 10.3: A line segment with a vector between the start and end points
The calculation for v is as follows:
v = b – a
We can also express it like so:
b = a + v
This tells us that if we start at point a and travel along the whole length of v, we will end up at b. Where would you be if you only...
