How can i get nodes in space?

I have two points in space (x,y,z) and i need to make a nodes between them but in orthogonal mode (i mean the angle between any two nodes will be 0, 90 ,270 ,180) and i need to know that nodes and I,J,K for it.

Sample point 1 (5360, 8850, 23962) & point 2 (9630, 4010, 11216).

[John D'Errico]

Ok. Those are two points in space. We got that. But what is orthogonal mode?

What "nodes" do you want to see?

[Mahmoud Sami]

That is the start and the end nodes the in between nodes can be generated random V=[5360 8850 23962;10000*rand(n-3,3); 9630 4010 11216];

Answer 1

[Walter Roberson]

Only points on the line connecting those two points can satisfy the condition. As soon as you add an point that is off of the connecting line, the angle between the new point and the endpoints will not be a multiple of 90 degrees.

   A----1---------2--B--------------3
        4

The angles A-1, A-2, A-3, B-1, B-2, B-3 are all multiples of 90 degrees (being 0 or 180 degrees), but as soon as you add point 4, then even though point 4 is 90 degrees to point 1, it cannot be a multiple of 90 degrees to point A or B.

I am going to guess that your coordinates are intended to be integers.

So, what you do is find point2 - point1 = [9630, 4010, 11216] - [5360, 8850, 23962] = [4270, -4840, -12746] . Now find the gcd() of all of those values: gcd(gcd(4270,-4840),-12746) = 2. Then (point2-point1)/the_gcd = [2135, -2420, -6373]. This is your fundamental vector.

The points that are 0 or 180 degrees from each other and point1 and point2 are then point1 + k*[2135, -2420, -6373] for each integer k.

How far can we go? Well, ceil(point1./t) = [3 -3 -3] so you can go as small as k = -3 while still staying with positive coordinates.

[Mahmoud Sami]

Sorry Sir but i can't understand the answer can explain the question more than this? I try to make shortest path between that two nodes so the start and the end is the most important. The question is how to make grid in orthogonal mode between two nodes. The reason for that is the connection between nodes needed to be 0 or 90 degree.

[Walter Roberson]

For shortest path, you need to know whether it is permitted to move diagonally or only up/down/left/right/forward/behind (6 directions) You also need to know about the obstacles.

In the absence of obstacles, the shortest path is not unique. You can use any combination of movements that results in an appropriate net change between coordinates. For example you could move directly parallel to the x axis until you matched x, then along the y axes until you matched y, then along the z axis until you matched z.

[Mahmoud Sami]

That is shortest path for pipes so it can move anywhere up/down/left/right/forward/behind (6 directions) with condition that the degree 0 or 90 between any two points that's affect the cost. The obstacles will be a blocks in space.

[Walter Roberson]

Is it correct that you want to minimize the number of turns?

[Mahmoud Sami]

Yes, the turn in my problem cost more (The 1 kg for elbow cost nearly double 1 kg of pipe)