trepunktsinterpolasjon

Trepunktsinterpolasjon, also known as three-point interpolation, is a method used to estimate an unknown value between two known data points, assuming a linear relationship between them. Given three points (x0, y0), (x1, y1), and (x2, y2), where x1 is between x0 and x2, and we want to find the value y at a specific x that lies between x0 and x1, trepunktsinterpolasjon uses the two points (x0, y0) and (x1, y1) to define a line.

The underlying principle is that if we assume a straight line connects (x0, y0) and (x1, y1), then the slope of the line segment between these two points can be calculated. This slope is then used to predict the corresponding y-value for the desired x-value. The formula for this can be derived from the equation of a line. If the desired x-value is x, the interpolated y-value, denoted as y, can be found using the formula: y = y0 + (x - x0) * (y1 - y0) / (x1 - x0).

This method is a simple form of interpolation and is particularly useful when the underlying data is expected to change linearly over the interval of interest. It is computationally inexpensive and easy to implement, making it suitable for basic estimation tasks. However, its accuracy is limited, especially if the true relationship between the data points is non-linear. For more complex curves or higher accuracy requirements, more sophisticated interpolation techniques like polynomial interpolation or splines are typically employed.