Let’s assume we want to approximate a point cloud with a second degree polynomial : .

The point cloud is given by points with coordinates . The aim is to estimate , and where will fit the point cloud as mush as possible. We want to minimize for each point the difference between and , ie. we want to minimize . The matrix form of the system is given by:

Let’s define , and :

The system is now given by:

The optimal solution is given by:

Where is the pseudoinverse of given by .

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**Least square second degree polynomial approximation 0.67 KB**

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