Function Approximation

[ksoehn]

Hi,

 

I am attempting on developing a basic mapping program ( very basic) an I am wondering if there is a way to approximate the shape of a function based on a few data points (3-5). I know that the function will be parabolic in nature and am wondering which numerical method or series I should begin looking at to guess at which point the maximum will be at.

 

Background: I have 3-5 sensors (a set distance apart) that measure the time that an object is blocking the sensor. They return a value corresponding to the time that the sensor was blocked. For the sake of argument let’s say that the values I get are 2 seconds for sensor 1, 5 seconds for sensor 2 and 4 seconds for sensor 3 and the sensors are each 2 ft apart. ( I have attached a picture to help explain the situation that I am describing). Based on these values can I approximate the shape of the parabola and guess where the maximum value will exist?

 

I can vaguely remember some concepts from Calculus and numerical methods in University and it would be great if someone could help give me a starting point or recommend a method of approximation ( or if I should repost this in another section of the site)

 

Thank you in advance for any help that you can provide.

-Ksoehn

 

sensor explanation.pdf

[mathematic]

You could use a least square approach to get the best fitting parabola.