I need help with interpolation methods

Hi
Interpolation is predicting data within the domain (data space). Extrapolation is predicting a point outside the domain.

Let us say a vector with two points pt1 (10,10) and pt2(20,20) p1 has temperature value 30 and pt2 has temperature value 40. So here the distance (use Pythagoras theorem to find distance) between the points also 10 units, the different between the points also 10 units. So if temperature at point 10,10 is 30 then at point 13,13 supposed to be 33. So now how you calculate this.

the point 13 has 3 unit distance from 10,10 and 7 unit distance from 20,20. The value supposed be more similar to the nearest point i.e 10,10 which value 30. So we weight the distance with a inverse relationship

tempValue1= value1* percentage of 7 unit distance i.e 30*(7/10)= 21. Note I am using the cross multiplication of the distance

tempValue2= value2* percentage of 3 unit distance i.e 40*(3/10)= 12

predicted value= tempvalue1+tempvalue2= 21+12= 33

This is a simple form of vector interpolation. Now you may search google for advanced algorithms.

good luck

Hope Interpolation Methods[^] will give you an idea.