关于地面法向量的问题 about tloam HOT 5 CLOSED

@Gatsby23 Because we don't know the distribution of set points in advance, we need to calculate three principal axes. Geometrically, we find a normal vector that is as perpendicular to all the points in the set as possible. It is equivalent to zero inner product. A more detailed derivation is as follows:

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Thank you for your nice replay, thank you very much!

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Thanks for your work and answer! @zpw6106
I am confused about the three normal vector. Shouldn't they be in the same direction?

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@gackes They are different directions and the final normal vector is the weighted vector sum of the three principal axis vectors.

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In my mind , I think that x + by + cz + d = 0 and ax + y + cz +d =0 are consistent. So the results should be same. Why we can work out different results? Is there any different mathematical meaning about the there directions except for the normal vector of plane? @zpw6106

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