[ HELP ] Basic mathematics ##### Please help #####

[other-side-of-d-moon]

Hello there !

I need you help to get a algorithm or any tool to calculate the the light angles received at points a b c d, whenever i changed the lamp position.




Please note : distance of the blue lines ( from the main spot light to the points a b c d ) are variables not fixed, that is why i said the position of the lamp is not fixed.

regards

 

[hshah8970]

You should mark the angles on the diagram and then re-upload the picture.

 

[enjunear]

A few new questions. First, it appears that the lamp is at a fixed position in space and that you want to find the location directly below it, on the ground?

1) Are the observation points (a,b,c,d) movable?

From the drawing, each point appears to know it's separation from two other points.
2) Do points a-d know where they are, relative to some fixed coordinate system?
3) or do they just know relative distances between each other?

4) For the distance measured to the lamp, is that distance the line-of-sight distance from the observation points (a,b,c,d) on the ground directly up to the lamp? (i.e. do you know the lengths of the dashed green lines? or do you know the length of the blue lines?)

(FYI, this adds a level of complexity, because the previous thread solutions worked in a 2-D plane, but this is now likely to be a 3-D problem, which would mean at least 3 simultaneous linear equations to solve, which is a much, much more complex algorithm)

5) What scenario is this for? Do you have 4 linked robots that are running around, trying to find the location of the lamp and then get underneath it?

 

[other-side-of-d-moon]

A few new questions. First, it appears that the lamp is at a fixed position in space and that you want to find the location directly below it, on the ground?

1) Are the observation points (a,b,c,d) movable?

From the drawing, each point appears to know it's separation from two other points.
2) Do points a-d know where they are, relative to some fixed coordinate system?
3) or do they just know relative distances between each other?

4) For the distance measured to the lamp, is that distance the line-of-sight distance from the observation points (a,b,c,d) on the ground directly up to the lamp? (i.e. do you know the lengths of the dashed green lines? or do you know the length of the blue lines?)

(FYI, this adds a level of complexity, because the previous thread solutions worked in a 2-D plane, but this is now likely to be a 3-D problem, which would mean at least 3 simultaneous linear equations to solve, which is a much, much more complex algorithm)

5) What scenario is this for? Do you have 4 linked robots that are running around, trying to find the location of the lamp and then get underneath it?

thank you enjunear for your reply

answers of your questions

1- points are NOT movable
2- yes known where they are
3-yes its line of sight BUT i do NOT know the length of the blue and green lines.

if its complex is there any software can do that ??

regards

 

[enjunear]

thank you enjunear for your reply

answers of your questions

1- points are NOT movable
2- yes known where they are
3-yes its line of sight BUT i do NOT know the length of the blue and green lines.

if its complex is there any software can do that ??

regards

Ok, something is missing. Points a,b,c,d know where they are (know their x,y positions on the map).
But a,b,c,d don't know how far away the lamp is, relative to themselves?

Somehow you need to know how far the lamp is from each observation point in order to compute it's position on "the map". I thought in your original posts that point "a" knew how far away "F" was (which would be the length of the green lines in your above image)?

 

[etmabreu]

You just need two things:

- Pythagorean theorem
- Definition of sin, cos and tan.

That's it.

 

[other-side-of-d-moon]

Ok, something is missing. Points a,b,c,d know where they are (know their x,y positions on the map).
But a,b,c,d don't know how far away the lamp is, relative to themselves?

Somehow you need to know how far the lamp is from each observation point in order to compute it's position on "the map". I thought in your original posts that point "a" knew how far away "F" was (which would be the length of the green lines in your above image)?

The height of the lamp is fixed but the distance of the blue lines ( from the main spot light to the points a b c d ) are variables not fixed, that is why i said the position of the lamp is not fixed.

 

[enjunear]

The height of the lamp is fixed but the distance of the blue lines ( from the main spot light to the points a b c d ) are variables not fixed, that is why i said the position of the lamp is not fixed.

@etmabreu: The OP asked for assistance with the math to solve this problem in another thread. This is a continuation of the subject. background here: link

@other-side
Since you are now saying that you don't know the distance from the lamp to any of the observation points, it's impossible to solve, since you have no information relating the lamp location to any known, fixed points on your map.

If you flip the picture on it's side, you get this basic layout, showing known and unknown quantities.

Known: height of lamp
Unknown: distance from lamp to any observation point (a,b,c,d)
Unknown: distance from observation point to point directly below lamp

Since you only know one side of the triangle, you cannot solve for the other two. You need two pieces of information to calculate the rest (e.g. two side lengths, or one side length and one angle other than the given right angle).

Without some information about the lamp to observation points, the only thing you can do is identify the series of equations that relate all of the points to each other, but you will not be able to solve them (more unknown variables than equations = unsolvable set of simultaneous linear equations). Unless you can determine more known values, you cannot get there from here.