How to create 2d plot of arbitrary, coplanar 3d curve

问题

I have a set of points which comprise a (in theory) co-planar curve. My problem is that the plane is arbitrary and can move between each time I collect the data (these points are being collected from a camera). I was wondering if you guys could help me figure out how to:

find the plane which is closest to the one which these points are co-planar on
project the points on this plane in such a way that gives me a 2-d curve

I believe that I know how to do point 2, it is really mainly point 1 that i'm struggling with, but I wouldn't mind help on the second point as well.

Thanks a ton!

回答1:

find 3 points A,B,C in your data

They must not be on single line and should be as far from each other as possible to improve accuracy.

construct U,V basis vectors

U = B-A
V = C-A

normalize

U /= |U|
V /= |U|

make U,V perpendicular

W = cross(U,V) // this will be near zero if A,B,C are on single line
U = cross(V,W)

convert your data to U,V plane

simply for any point P=(x,y,z) in your data compute:
```
x' = dot(U,P)
y' = dot(V,P)
```
in case you need also the reverse conversion:
```
P = x'*U + y'*V
```
In case you want/have an origin point A the conversions would be:
```
x' = dot(U,P-A)
y' = dot(V,P-A)
P = A + x'*U + y'*V
```
That will map A to (0,0) in your 2D coordinates.

In case you do not know your vector math look here:

Understanding 4x4 homogenous transform matrices

at the bottom you will find the equation for vector operations. Hope that helps ...

来源：https://stackoverflow.com/questions/44553886/how-to-create-2d-plot-of-arbitrary-coplanar-3d-curve

标签

math

plot

projection

curve