Finding Origin using 2 Points, Angle and Plane

Question

I'm having a problem of finding the origin $O(x,y,z)$ of 2 3D points $P_1 (1,2,2)$ and $P_2 (2,3,5)$, distance $OP_1 = OP_2$, angle = 60 degrees and Plane Equation: $$E: 1.15714286x + 1.8547619y-z-2.86101191=0.$$ I used the distance equation, plane equation, and cross vector of products but I found 2 origin $O_1$ and $O_2$. I don't know which one I should choose to correct my answer.

Are there any ways to identify it?

score 0 · Answer 1 · answered Jul 27 '20 at 16:22

0

The problem has indeed two solutions. You can't differentiate them if you don't provide an additional information. Orientation of the plane can be one.

answered Jul 27 '20 at 16:22

mathcounterexamples.net

70,018

If I have P3 (3,4,8.02946427) and P4 (4,5,11.04136903) and angel 60 degrees, P3 and P4 also land on the same plane E. I also found another 2 origins O3 O4 but it has relationship O1P1 = O1P2 = O2P1 = O2P2 = O3P3 = O3P4 = O4P3 = O4P4. Is there any way to calculate it? – Samann Long Jul 27 '20 at 16:27
No. Without an additional thing, you won't be able to distinguish between the two solutions. – mathcounterexamples.net Jul 27 '20 at 16:31
what kind of additional things that might be found a correct solution ? – Samann Long Jul 27 '20 at 17:07
Can you provide thé background if your question ? Math exercises? From a software probkem ? – mathcounterexamples.net Jul 27 '20 at 17:10
From a software problem, I want to Origin of Robot Arm moving from one position P1 to P2, and then P3 to P4. From P1, P2, I used IMUs to measure angel and that's why I get position Pi and Angles. But after I applied the above calculation, I got 2 origins and I can't specify where is the real position of Robot Arm ? – Samann Long Jul 27 '20 at 17:14
What is the plane representing in the problem ? Same question for the origin. – mathcounterexamples.net Jul 27 '20 at 18:20
It's the same plane equation – Samann Long Jul 28 '20 at 06:18
Yes, but what represents the plane and the origin vs. your robot? – mathcounterexamples.net Jul 28 '20 at 06:36
From Robot Arm moving up and down, we can get those 4 points when it moves stable. We use Least Square to create Plane Equation E for those 4 points. Because when we work with Robot Arm and any machine, they are having a lot of local coordinates that's why we need to create one plane for it. – Samann Long Jul 28 '20 at 06:58
Let us continue this discussion in chat. – mathcounterexamples.net Jul 28 '20 at 07:17

Finding Origin using 2 Points, Angle and Plane

1 Answers1