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zhoupengwei / tloam

T-LOAM: Truncated Least Squares Lidar-only Odometry and Mapping in Real-Time
GNU General Public License v3.0
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关于地面法向量的问题 #2

Closed Gatsby23 closed 3 years ago

Gatsby23 commented 3 years ago

image 关于这里地面法向量的计算，我没有太弄懂，为什么会计算三个主轴向量（代表的物理意义是什么？）后面的权重累和又代表什么？

zhoupengwei commented 3 years ago

@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: E43A58279BDBC452004BCE098AED59EF

Gatsby23 commented 3 years ago

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

gackes commented 2 years ago

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

zhoupengwei commented 2 years ago

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

gackes commented 2 years ago

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