Interpolating

Yesterday's table has a catch: at 25.9 °C the pump runs at 10, at 26.0 °C suddenly at 20. It jumps at every step. For ventilation that is noisy, for a control loop restless. A line that interpolates between the table values is better.

Calculating between support points#

The table values are now support points: points the curve passes through. For a reading in between you need two things:

1. Which two neighbours? The integer part of the position.
2. How far between them? The remainder, a fraction from 0 to 1.

At 27 °C the position is (27 − 20) / 2 = 3.5. The neighbours are slot 3 (20) and slot 4 (30), the fraction is 0.5. The result lies in the middle: 25.

lerp with an index#

You have known lerp since day 61: lerp r? a b frac computes a + (b − a) · frac.

floor idx temp                # temp already holds the position
clamp idx idx 0 LAST
sub frac temp idx           # remainder between 0 and 1
get a db idx
add idx idx 1
get b db idx
lerp value a b frac

The index may be at most 6 here, because slot 7 has no right neighbour any more. If the reading lies above the last point, the fraction becomes larger than 1 – lerp limits it to 1 itself. Below the first point it becomes negative and lerp turns it into 0. So the edges of the curve are right on their own.

Curves#

With interpolation a few points are enough for a smooth curve:

Where the curve bends sharply, put the points closer together. Where it is almost straight, a few are enough.