Lines, Curves and Surfaces in 3D
Lines, Curves and Surfaces in 3D
Lines, Curves and Surfaces in 3D
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Least Squares Fit of a Plane (Cont.)<br />
Therefore, us<strong>in</strong>g the above fact <strong>in</strong> previous equations <strong>and</strong> solv<strong>in</strong>g for<br />
a, b <strong>and</strong> c gives:<br />
CM0268<br />
MATLAB<br />
DSP<br />
GRAPHICS<br />
562<br />
a =<br />
b =<br />
∑ ∑<br />
xi z i y<br />
2<br />
i − ∑ ∑<br />
y i z i xi y i<br />
∑ ∑ x<br />
2<br />
i y<br />
2<br />
i − ( ∑ , (4)<br />
x i y i )<br />
∑ ∑ 2<br />
yi z i x<br />
2<br />
i − ∑ ∑<br />
x i z i xi y i<br />
∑ ∑ x<br />
2<br />
i y<br />
2<br />
i − ( ∑ , (5)<br />
x i y i ) 2<br />
c = 0. (6)<br />
1<br />
All we now need to do is to translate back.<br />
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