MATLAB: Find the set of 3d data parrallel to the current 3d data

Let's say: I have two set of 3d points as illustration (also see attached file: 1.txt , &, 2.txt)

How can I find the set of new 3D data belong to “green line”? The new 3D points is parallel with data 1,& far away distance “d=10m”, & in other side of red line(data 2). I hope the result will be a set of 3D point (kx3 matrix).

Result shown as below illustration:

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Choose some points (P1,P2,P3) from your data

- vector of the first line (blue)

- some temporary vector between P2 and P3 points

- normal vector of a plane (cross product of

and

vectors)

- perpedendicular to line2(red) vector

- point in plane and at the distance 10 from line2(red)

Using the same vector as for line1 and line2 draw line3(green) and point P4

Related Solutions

MATLAB: Find the distance from a point to a plane (known two vectors)

No, we do not know that 2 vectors can create a plane. If these two vectors are used to define the normal vector of the plane, you need an additional point, which is element of the plane. If v1 is the normal and v2 is a point of the plane (or the other way around), the plane is well defined also. But "v1" and "v2" sounds more like two directional vectors, such that the normal is:

v1x2 = cross(v1, v2);
N    = v1x2 / norm(v1x2)

However, please clarify this at first. If you have the plane defined by a point P and a normal vector N, the distance of the point Q is very easy to obtain:

% Vector from P to Q:
PQ = Q - P;
% Dot product between line from Q to P1 and normal of the plane:
Dist = dot(PQ, N);

This can be found directly using the Hesse normal form. The same formula allows to determine the distance between two skew lines in 3D: The 2 lines are defined by two points P1 and P2 on them and the directional vectors N1 and N2. Then create a plane E through e.g. P1 and the normal cross(N1, N2) / norm(cross(N1, N2)). Now the distance between the two lines is the distance between P2 and E.

MATLAB: Distance from point to plane (plane was created from 3d point data)

You need to understand what the equation of a plane tells you.

A plane is defined by a point on the plane (P0), and the normal vector to the plane(N). Thus any point on the plane X satisfies the constraint

dot(X-P0,N) = 0

If the normal vector has unit length, so it is normalized to have norm(N)==1, then the solution to your problem is trivial.

The distance to the plane is then simple. It is just:

dot(X-P0,N)

If a point lies on the plane, then the distance to the plane is 0. And that is embodied in the equation of a plane that I gave above!

Finally, you might recognize that the above dot product is simply computed using the function dot, but even more simply written as a matrix multiply, if you have more than one point for which you need to compute this distance.

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Related Solutions

MATLAB: Find the distance from a point to a plane (known two vectors)

MATLAB: Distance from point to plane (plane was created from 3d point data)

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