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2023-01-19T23:03:54Z

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==Interpolation==
Interpolation is a type of estimation, a function that allow to estimate the value (x, y) between two known data points (x1, y1 ; x2, y2).

A common interpolation method used on ECU is the linear interpolation. The interpolation is more precise on high resolutions maps (multiples points)
===Linear interpolation===
[[File:Linear-inter.png|218x218px]]

The formula :

<math> y = y_1 + \left( x-x_1 \right) \frac{y_2-y_1}{x_2-x_1}</math>

where:
*x1, y1 are the first known coordinates
*x2, y2 are the second known coordinates
*x is the point with want at which we do the interpolation
*y is the interpolated value
====Using linear interpolation on 3D maps:====
#Interpolate the row above and below
#Interpolate the two interpolated values together

Here is a example, consider the following map:
{| class="wikitable"
! colspan="3" |Example map (load, engine speed)
|-
|'''Load /RPM'''
|'''100'''
|'''150'''
|-
|'''1000'''
|10
|20
|-
|'''2000'''
|20
|40
|}
To get the value at load : '''125''' and engine speed : '''1500''', we will need to do a linear interpolation since it is not in the map.

The table would look like this after step 1:
{| class="wikitable"
! colspan="4" |Example map (load, engine speed)
|-
|'''Load /RPM'''
|'''100'''
|'''125'''
|'''150'''
|-
|'''1000'''
|10
|15
|20
|-
|'''2000'''
|20
|30
|40
|}
Now we interpolate 15 and 30 together to get the value at 1500 rpm (step 2):
{| class="wikitable"
! colspan="4" |Example map (load, engine speed)
|-
|'''Load /RPM'''
|'''100'''
|'''125'''
|'''150'''
|-
|'''1000'''
|10
|15
|20
|-
|'''1500'''
|
|22.5
|
|-
|'''2000'''
|20
|30
|40
|}
At load : '''125''' and engine speed at '''1500''', we get the value '''22.5''' with linear interpolation

== Extrapolation ==
ECU does not work with extrapolation. Extrapolation is a an estimation of values that are outside the scope of a map data. There are multiple proposed methods for extrapolation : linear, polynomial, conic, etc.

Extrapolation is not reliable and need to be used with care (if used).

Interpolation, extrapolation - Revision history

Arte: Initial page