Mathematics of animation curves
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1. Mathematics of linear interpolation
- So, we've seen two ways to calculate in-betweens: linear interpolation and Bézier curves. Now let's get into the math behind them. We're gonna build on some of what we learned in the environment modeling lesson, so if you need to review, click on this link. Let's start with the simpler version, linear interpolation. Let's focus on this segment. We know the value of y at frame 4 is 750 and the value at frame 8 is 190, but what's the value of y at frame 5, 6, or 7? The picture tells us that y can be represented as a linear function of x, where x is the frame number. Linear functions can be written in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Now we don't know the slope and intercept directly, but we do have two points on the line, which is enough information to calculate them. Now, once we have m and b, we can figure out y for any frame. Try out this next exercise to test your understanding of linear interpolation using the slope-intercept form.