Spline
A function made up of polynomials that each have a specific interval.
In other words a "piecewise polynomial function".
Very useful when we want a smooth curve that passes through certain points, such as for matching data, making smooth computer animations, etc.
Example: Make a smooth curve that touches (0,5), (2,2.5), (4,2), (6,3.5)
There are many ways this can be done, but here is one solution:
• Between 0 and 2: 0.05x3 − 1.45x + 5
• Between 2 and 4: 0.3x2 − 2.05x + 5.4
• Between 4 and 6: −0.05x3 + 0.9x2 − 4.45x + 8.6
Which makes the curve shown here (dotted lines are what each polynomial looks like beyond its interval)
Splines are not limited to two dimensions.
In other words a "piecewise polynomial function".
Very useful when we want a smooth curve that passes through certain points, such as for matching data, making smooth computer animations, etc.
Example: Make a smooth curve that touches (0,5), (2,2.5), (4,2), (6,3.5)
There are many ways this can be done, but here is one solution:
• Between 0 and 2: 0.05x3 − 1.45x + 5
• Between 2 and 4: 0.3x2 − 2.05x + 5.4
• Between 4 and 6: −0.05x3 + 0.9x2 − 4.45x + 8.6
Which makes the curve shown here (dotted lines are what each polynomial looks like beyond its interval)
Splines are not limited to two dimensions.