Defining a point in space with two parameters.

[tar]

Wondering why, given an origin, one could not define another position based on two parameters, distance and direction.

 

Distance is understandable as a singular thing, in itself, with any particular unit or number or scale assignable to it.

 

If one was to dense pack spheres around an origin sphere there would be twelve directions possible, with each of these twelve an origin of its own, with twelve surrounding "directions". Given a particular task, a sphere size could conceptually dense pack all of space and any of the spheres could be located by counting out to a particular sphere in one of the twelve directions, calling that sphere your origin and counting the spheres in one of the twelve directions from there to your destination sphere.

 

Conventionally naming the twelve A, B, C, D, E, F, G, H, I, J, K, L, could you not find a point in space by saying F594 to name your new origin sphere and then H3?

 

Does seem clumbsy though, in that you could get to the same sphere by many different routes.

 

And I certainly do not have the plan nailed down in so far as figuring out, how many new origin spheres one would have to use to describe the most difficult to "get to" spheres. Probably would wind up being a 6 parameter space. Sort of redundant if one can get to the same spot with three.

 

BUT...if we could come up with a convention that could describe direction, with one number/symbol combination, then any point could be found by naming the direction, and then the distance.

[John Cuthber]

Most things would not be on a line from the origin through a particular sphere's centre.

So you need to account for something whose direction is "halfway between a and b" and "halfway between a and c".

So, you are back to 3 parameters.

You can't specify three dimensions with 2 numbers.

Also, "Given a particular task, a sphere size could conceptually dense pack all of space"

spheres don't pack densely- there are gaps.

[tar]

John Cuthber,

 

Well there are "gaps" between points on a line as well. We seem to overcome that with decimals.

 

Choice of units or sphere size could get you at least to within an atom's reach of a point. Which would be useful in most situations.

 

I did not nail down the concept yet, and am a bit slowed down by having to come up with a way to define an infinite amount of directions with one parameter, but it does not seem "impossible" to me.

 

In playing with ping pong balls in a dense pack pattern, the collection seems to show aspects of space, nicely, in whole number increments, and reveal relationships that are not so whole number understandable as when space is defined in cartesian coordinates, with various whole number ray lengths from the origin defined by the combination of three decimals.

 

Would be my goal to simply define the direction, once. And then simply define the distance once.

 

Regards, TAR2

[EdEarl]

Three dimensions can be divided into cubes, and each cube can be divided into smaller equally sized cubes, for example 1000 by dividing each dimension into ten equal segments.

 

If you use 12 dodecahedra (instead of spheres) it may be possible to divide a dodecahedron into an equal number of smaller dodecahedra (need a mathematician). If you can, the number may not be divisible by 10, which means using another base, rather than base 10, to represent coordinates.

 

Your system is difficult to imagine; thus, it will not be popular. If another number base is required, it will be further complicated. It is an interesting puzzle.

Edited May 31, 2013 by EdEarl

[Iggy]

Wondering why, given an origin, one could not define another position based on two parameters, distance and direction.

 

Distance is understandable as a singular thing, in itself, with any particular unit or number or scale assignable to it.

 

If one was to dense pack spheres around an origin sphere there would be twelve directions possible, with each of these twelve an origin of its own, with twelve surrounding "directions". Given a particular task, a sphere size could conceptually dense pack all of space and any of the spheres could be located by counting out to a particular sphere in one of the twelve directions, calling that sphere your origin and counting the spheres in one of the twelve directions from there to your destination sphere.

 

Conventionally naming the twelve A, B, C, D, E, F, G, H, I, J, K, L, could you not find a point in space by saying F594 to name your new origin sphere and then H3?

 

Does seem clumbsy though, in that you could get to the same sphere by many different routes.

 

And I certainly do not have the plan nailed down in so far as figuring out, how many new origin spheres one would have to use to describe the most difficult to "get to" spheres. Probably would wind up being a 6 parameter space. Sort of redundant if one can get to the same spot with three.

 

BUT...if we could come up with a convention that could describe direction, with one number/symbol combination, then any point could be found by naming the direction, and then the distance.

 

I agree with the others

 

Three spatial dimensions have three degrees of freedom for spatial translation, so you can't do with less than three parameters.

 

Using orthogonal directions someone could say something like, "Walk 10 meters ahead, then 6 meters to your left, and the gold will be one meter above you".

 

Dodecagonal directions would also have three degrees of freedom, they'd just sound like... "Walk 9 meters in direction B, then 5 meters in direction E, and the gold will be 2 meters in direction H".

 

Essentially you'd be using 6 axes (12 directions) in three dimensional space when 3 axes (6 directions) would be the simplest way to get the job done.

Edited May 31, 2013 by Iggy

[tar]

Iggy,

 

Well, I agree with the others too. I have been working this problem for years and always have come to that same conclusion, that its redundant to use 6 axis to do the job that 3 will do...except I had a glimmer the other night, that escapes me now, and I am working at recapturing it. Hence the thread.

 

While I understand the three degrees of freedom, they have something to do with how we think and see things. Things infront and behind. Things up and down. And things left and right. Seems to me, that to understand Cartesian coordinates you need to be standing at the origin with y above you, negative y below you, negative x to your left, positive x to your right, z in front of you, and negative z behind.

 

Since you have to be standing, and have two hands and a face to concieve of this coordinate system, and we all have such equipment, it works fine, and is quite readily taught and has become the standard and is popular.

 

However its quite anthropomorphic. Not that that is bad, we have no other starting point to start from but our own here, but that in playing with the ping pong balls and the dodecahedra its occured to me, that space is more like the dodecahedra in structure than a cube...hence my quest.

 

There are more spheres floating and bouncing around the place at all grain sizes, than cubes. Perhaps there would be reason to grasp the concept of 6 axis.

 

Building out the dodecahedron intersecting planes become evident. Four hexagonal(or triangular) planes, and three square planes...its really quite intriging...and speaks of a "regular" and symetrical space made of angles and relationships, not humanly intuitive or readily concieved of in cartisian coordinates, but simple and real and satisfying, none-the-less.

 

If each of these 12 directions is a repeating pattern and we would know what the pattern looked like, if we were facing it, and we could decribe with a number every singular aspect or "direction" possible in that direction. Since we can pick H as the 1/12 of direction we are facing, then the puzzle would be down to describing the possible direction aspects within this view with a number or symbol system.

 

Then H 4958B.34A01(base12) would be a unique and singular direction, one parameter. And with a distance parameter, two parameters could describe any point in space, from your origin.

 

Regards, TAR2

Edited June 1, 2013 by tar

[John Cuthber]

John Cuthber,

 

Well there are "gaps" between points on a line as well. We seem to overcome that with decimals.

 

Choice of units or sphere size could get you at least to within an atom's reach of a point. Which would be useful in most situations.

 

Regards, TAR2

But that decimal implies a fraction. That fraction, in turn requires two parameters (some fraction of the way from point a to point b.).

So you need two parameters to specify direction and then you need a third to specify the distance.

I thought I had implied that in my earlier post when I mentioned half way between two things..

 

On the other hand, if you are prepared to put up with limited resolution, you can do the job with just one parameter.

Start with an origin and have a bunch of cubes spiralling out from it.

Count the cubes and you have specified the location to within the nearest cube.(you would need positive and negative numbers).

[michel123456]

Wondering why, given an origin, one could not define another position based on two parameters, distance and direction.

 

 

(...)

BUT...if we could come up with a convention that could describe direction, with one number/symbol combination, then any point could be found by naming the direction, and then the distance.

Yes that makes sense to me.

 

But that decimal implies a fraction. That fraction, in turn requires two parameters (some fraction of the way from point a to point b.).

So you need two parameters to specify direction and then you need a third to specify the distance.

I thought I had implied that in my earlier post when I mentioned half way between two things..

 

On the other hand, if you are prepared to put up with limited resolution, you can do the job with just one parameter.

Start with an origin and have a bunch of cubes spiralling out from it.

Count the cubes and you have specified the location to within the nearest cube.(you would need positive and negative numbers).

(emphasis mine)

Yes, that would be like assigning a number to each point of space. There are an infinity of points of space and there is an infinity of numbers, so that could be done, unless one of those infinities is bigger than the other one.

 

Now that I am thinking a little more about it, it is like replacing a point of coordinates 1,2,3 with the number 123. Or am I wrong somewhere?

[robinpike]

On the other hand, if you are prepared to put up with limited resolution, you can do the job with just one parameter.

Start with an origin and have a bunch of cubes spiralling out from it.

Count the cubes and you have specified the location to within the nearest cube.(you would need positive and negative numbers).

 

That co-ordinate method is interesting because it shows that a single number co-ordinate system can be used to define any position in 3 dimensional space.

 

Note that any co-ordinate system, whether it is our normal 3 dimensional grid / 3 number system, to any other system that is thought of, has assumed parameters beyond the number of co-ordinates that it uses.

 

For example, in the standard three co-ordinate system, the other parameters are the directions of the 3 straight routes through the cubes in relation to some fixed point and the size of the cubes.

 

Similarly, in the one co-ordinate system, it is the direction of the spiral route through the cubes in relation to some fixed point and the size of the cubes.

[Iggy]

While I understand the three degrees of freedom, they have something to do with how we think and see things. Things infront and behind. Things up and down. And things left and right. Seems to me, that to understand Cartesian coordinates you need to be standing at the origin with y above you, negative y below you, negative x to your left, positive x to your right, z in front of you, and negative z behind.

 

Since you have to be standing, and have two hands and a face to concieve of this coordinate system, and we all have such equipment, it works fine, and is quite readily taught and has become the standard and is popular.

 

However its quite anthropomorphic.

 

Having "two hands and a face" and "being able to stand" have nothing to do with the number of axes of a cartesian coordinate system. Cartesian coordinates are not an anthropomorphism.

 

The decision to label spatial coordinates with 3 axes comes from the fact that there are 3 spatial dimensions. It has to do with the number of dimensions, not popularity, and not human anatomy.

 

 

Not that that is bad, we have no other starting point to start from but our own here, but that in playing with the ping pong balls and the dodecahedra its occured to me, that space is more like the dodecahedra in structure than a cube...hence my quest.

 

There are more spheres floating and bouncing around the place at all grain sizes, than cubes. Perhaps there would be reason to grasp the concept of 6 axis.

 

An arrangement of spheres does not make a geometry, or a coordinate system. It's called a "lattice" -- what you have.

 

Spheres are common because they minimize surface area per volume. Like John said, they don't make the best space fillers. The density of your lattice is [math]\frac{\pi}{3 \sqrt{3}}[/math], so roughly 40% of space is unbound by your spheres.

 

 

Building out the dodecahedron intersecting planes become evident. Four hexagonal(or triangular) planes, and three square planes...its really quite intriging...and speaks of a "regular" and symetrical space made of angles and relationships, not humanly intuitive or readily concieved of in cartisian coordinates, but simple and real and satisfying, none-the-less.

 

I find the shapes apparent in lattices interesting too. This doesn't make them particularly good at the things coordinate systems are particularly good at.

 

 

If each of these 12 directions is a repeating pattern and we would know what the pattern looked like, if we were facing it, and we could decribe with a number every singular aspect or "direction" possible in that direction. Since we can pick H as the 1/12 of direction we are facing, then the puzzle would be down to describing the possible direction aspects within this view with a number or symbol system.

 

Then H 4958B.34A01(base12) would be a unique and singular direction, one parameter. And with a distance parameter, two parameters could describe any point in space, from your origin.

 

Regards, TAR2

 

We already have a coordinate system based on angles of direction and distance -- polar coordinates (or spherical coordinates in 3D).

 

If that is what you're going for then there is no need to break things down into 12 directions, nor imagine covering the space with spheres.

 

Look at the galactic coordinate system, for example.

Edited June 1, 2013 by Iggy

[tar]

So if we would have to be assuming some parameters to spiral out our point size, it would probably be best to assume something actual. That is, take something from nature and or ping pong balls as to how an entity actually fits into space. What are the parameters which which it HAS to operate.

 

The spiraling cubes leave me with the question of how to fill space in a regular pattern, that winds up covering up, down, left, right, foward and back.

 

There may be a clue in a dodechahedra in that one can form such, by cutting the corners off a cube to the midpoint of the edges of the cube. Leaving one with a 14 sided figure, 8 equal length triangles, and 6 diamonds or squares each of them with edges of the same lengths as the triangle's edges. Dense packing ping pong balls around a central ping pong ball, winds you up with the same shape, with the center of each of the surrounding ping pong balls, on each of the corner points of the dodecahedron. And you have described the six axes all regularly angled from the others, and have positioned the intersecting hexagonal and square planes required to "fill" space in all directions, in a regular, whole number (sphere diameter) manner.

 

Perhaps the spiraling out function would be something similar to a three dimensional fractal pattern. Or somehow Fibonocci would come into play, but I would rather find the answer in the way that things actually fit into space, than to assume a thing and impose it.

Sorry Iggy,

 

We cross posted.

 

I will submit that I am working with a lattice, and I will also submit to the success of the work others have done to form the coordinate systems that we use.

 

Though I will retain the right to call any explanation or description we come up with, human friendly, of human origin and utility and understandable in a human fashion. Besides you can't say that 3D is simply the way it is, when we simultaneously decided that it takes at least four to describe it.

 

The cartesian system is a lattice of sorts, with each one dimensional point on the corner of a unit cube, with each edge divisible and the diagonal between corners figurable with sines and cosines, tangents and the like. The sphere is assumed or emerges from the plan. Why not start with the matrix of spheres and let the triangles and cubes emerge from that?

 

Regards, TAR2

[Iggy]

Sorry Iggy,

 

We cross posted.

 

I will submit that I am working with a lattice, and I will also submit to the success of the work others have done to form the coordinate systems that we use.

 

Though I will retain the right to call any explanation or description we come up with, human friendly, of human origin and utility and understandable in a human fashion.

 

Fair enough

 

 

Besides you can't say that 3D is simply the way it is, when we simultaneously decided that it takes at least four to describe it.

 

You know I didn't say "3D is simply the way it is". I said that there are three *spatial* dimensions. I said "spatial dimensions" many times to avoid what you just tried.

 

I said that we use three axes to label three dimensional space because it has three dimensions, and not for the reason you gave about people having one face and two hands.

 

 

The cartesian system is a lattice of sorts, with each one dimensional point on the corner of a unit cube,

 

A point is zero-dimensional. A line is one.

 

 

with each edge divisible and the diagonal between corners figurable with sines and cosines, tangents and the like.

 

The Pythagorean theorem (a² + b² = c²) finds the length of any diagonals in Euclidean geometry. This comports with the metric of the cartesian coordinate system where the distance between two points (in two dimensions for simplicity) is:

 

[math]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/math]

 

This is the simplest formula (the formula for distance) that a coordinate system can have. The formula for translation, rotation, scaling, and things like that no less important.

 

Have you considered what these formula would be and how they would function in your system?

 

 

The sphere is assumed or emerges from the plan.

 

A sphere can be drawn on a plane. You would have to consider what formula draws a sphere in your system.

 

 

Why not start with the matrix of spheres and let the triangles and cubes emerge from that?

 

A matrix is different from a lattice.

 

Coordinates are represented with points. You can draw lines between coordinate points to make a square, but that is quite a bit different from having the coordinates themselves be spheres. I honestly don't know what purpose you are trying to serve with that.

 

Edited June 1, 2013 by Iggy

[tar]

Iggy,

 

Well I suppose I am after a way to define a direction (from an origin) in space with one parameter.

 

Points themselves take up no space at all. Being such, you can not fill space with points.

 

Perhaps the lattice built out from a central sphere is not bounding 40% of space, but any arrangement of points you design is bounding exactly none of space. At least a sphere is real, bounding a particular amount of space, and dense packed spheres fit space, and say something about it, in terms of what it is, and is not. At least to me.

 

As to what the math would be like in such a system, I have not come close to figuring out. I have enough trouble trying to figure out even the angles involved, between the intersecting planes. I do not know how to work with solid angles. Its perplexing enough for me that I can draw 90 degree angles on a ping pong ball making a three sided figure.

 

But, if you would want to set equally spaced rays out from the Cartesian Origin so to define equal and divisible amounts of direction, it is difficult. You know you must have one eighth of direction in each of the volumes bounded by the planes of the axes, but not easy to see how to divide that amount of direction up into equal parts. If you could divide a quadrant up into eight equal parts, all of the same shape, and then each of them into eight parts of equal parts and so on, each "volume" touching the origin, you could use a base eight number with an octal point, to give a number to a direction.

 

Seems like the area your rays would describe on the surface of a unit sphere centered on the origin would be the best way to determine if your rays were defining equal amounts of direction.

 

In anycase the math gets to complicated for me, to be taking all the squareroots and do all the sine cosine stuff. keeping the "square" space of xyz coordinates in mind. Its easier for me to just see how the ping pongs balls actually fit into space. Making me think, that when it comes to numbering direction, the six axes system might be more suited for the job, than the three axes one.

 

Regards, TAR2

[ogr8bearded1]

Instead of many balls surrounding your vessel, wouldn't it be better to imagine one sphere surrounding it? Such as imagine yourself at the centre of a clear globe with longitude and latitude lines drawn on it. Point the nose of the vessel in the direction you want to travel and the corresponding lat. and long. the nose points to are used to describe that direction. At the same time, so as not to get lost, you would still need to track your progress on a standard cube shaped 3D map with a set 0,0,0 co-ordinate.

[Iggy]

Iggy,

 

Well I suppose I am after a way to define a direction (from an origin) in space with one parameter.

 

Points themselves take up no space at all. Being such, you can not fill space with points.

 

I see no point in filling arbitrary spaces when creating a coordinate system (ie the thing that locates a point in space)

 

That would be something a coordinate system could do, but not a constraint of the coordinate system itself.

 

 

Angles "define a direction (from an origin)". Each additional dimension thus introduces a new angle needed to locate a point, as in "turn left 35 degrees and walk 4 meters" introduces an angle and a distance.

 

 

Perhaps the lattice built out from a central sphere is not bounding 40% of space

 

I apologize. I had that number wrong. Yours occupies 70%... [math]\frac{3}{3 \sqrt{2}}[/math]

 

 

but any arrangement of points you design is bounding exactly none of space.

 

Nor should 'the bounding of space' be any kind of constraint or necessary step in locating a point.

 

Filling a space with an arrangement of ordered spheres for the purpose of locating a point requires identifying the arbitrary direction at which you place and align the spheres. This amounts to more than two parameters, thus the title of the thread simply can't be correct, at least not in the sense that I'm looking at it.

 

 

As to what the math would be like in such a system, I have not come close to figuring out. I have enough trouble trying to figure out even the angles involved, between the intersecting planes. I do not know how to work with solid angles. Its perplexing enough for me that I can draw 90 degree angles on a ping pong ball making a three sided figure.

 

But, if you would want to set equally spaced rays out from the Cartesian Origin so to define equal and divisible amounts of direction, it is difficult. You know you must have one eighth of direction in each of the volumes bounded by the planes of the axes, but not easy to see how to divide that amount of direction up into equal parts. If you could divide a quadrant up into eight equal parts, all of the same shape, and then each of them into eight parts of equal parts and so on, each "volume" touching the origin, you could use a base eight number with an octal point, to give a number to a direction.

 

Seems like the area your rays would describe on the surface of a unit sphere centered on the origin would be the best way to determine if your rays were defining equal amounts of direction.

 

In anycase the math gets to complicated for me, to be taking all the squareroots and do all the sine cosine stuff. keeping the "square" space of xyz coordinates in mind. Its easier for me to just see how the ping pongs balls actually fit into space. Making me think, that when it comes to numbering direction, the six axes system might be more suited for the job, than the three axes one.

 

Regards, TAR2

 

There is a lot of literature on the arrangement you're considering. In geometry circles it's called "hexagonal close-packed". You could google that for some cool facts and descriptions. It is fun stuff.

 

Edited June 2, 2013 by Iggy

[tar]

Instead of many balls surrounding your vessel, wouldn't it be better to imagine one sphere surrounding it? Such as imagine yourself at the centre of a clear globe with longitude and latitude lines drawn on it. Point the nose of the vessel in the direction you want to travel and the corresponding lat. and long. the nose points to are used to describe that direction. At the same time, so as not to get lost, you would still need to track your progress on a standard cube shaped 3D map with a set 0,0,0 co-ordinate.

org8bearded1,

 

The latitude and longitude lines are a little contrived, in a sense. The latitude lines circles on the sphere, of different circumferences and the longitude lines circles that intersect, for no particular reason at only two points, a North and a South Pole. The two seem to be delinating two different things, not of the same size and characteristics. Somewhat like a failed attempt to put a 90degree grid on a sphere. At the North pole, one step can take you across longitude lines that would take you hundreds of thousands of steps to cross. On the other hand the sphere is rather friendly to angles described by the dense packing of spheres in the intersecting hexagonal pattern embedded in the dudecahedron. The 3d square coordinates are visible, but those pesky corners are cut off, making it easier to see how space fits around a point. In a cube setup, you go in 6 directions in whole numbers and have to go in the other direction in square roots and combinations of square roots and pi and such.

In the hexagonal, you can go whole number out, in 12 different directions. In all directions, so to speak. You still have to do math to go between the axes, but its the same math (though I don't know what that would be, yet). Its triangular 60degree math of some sort.

 

Regards, TAR2

 

Diagram titles include "cut the corners off a cube", "draw lines between opposing faces", "small marker balls", and "small marker balls, lettered".

 

The six purple axes define the twelve directions I am talking about. The 7 multicolored lines connect the center of the faces of the dudecahedron, tying the system to xyz coordinates.

 

The marker balls are located at the corners of the dudecahedron. Their relative positions are the exact position twelve larger balls would take, if fit around a central ball of the same size, in the four intersecting hexagonal plane pattern described. (drawing full size balls that did not obscure one another in a two dimensional rendering was beyond my "paint" skills.)

Edited June 3, 2013 by tar

[John Cuthber]

 

 

 

Now that I am thinking a little more about it, it is like replacing a point of coordinates 1,2,3 with the number 123. Or am I wrong somewhere?

As I said, it works as long as you are prepared to put up with poor resolution.

Your system can't cope with 1,2.5,3

 

Similarly, if you want to specify an arbitrary point in space with the system you have pictured above you need to be able to say

"2.7 units out from the origin along a line that's 73% of the way between the line OA and OB and 21% of the way between the lines OA and OC"

that's still 3 parameters: 2.7, 73 and 21.

There's really no way round needing all 3 if you want to have arbitrary precision

[tar]

There is a lot of literature on the arrangement you're considering. In geometry circles it's called "hexagonal close-packed". You could google that for some cool facts and descriptions. It is fun stuff.

 

 

 

Iggy,

 

Was fun for me to have descovered the figure and the dense pack arrangement on my own, a number of years ago, and then find it had a name and studied attributes. Nothing new, under the sun, but discovery is fun, anyway.

 

The sphere I am envisioning we can imagine ourselves within, is the central ping pong ball. Have not yet determined the nature of the longitudinal lines, but I am thinking it will not have any latitudinal lines, just longitudinal with 12 poles, perhaps. Or four equators on the hexagonal planes and three on the square planes?

 

Regards, TAR2

 

As I said, it works as long as you are prepared to put up with poor resolution.

Your system can't cope with 1,2.5,3

 

Similarly, if you want to specify an arbitrary point in space with the system you have pictured above you need to be able to say

"2.7 units out from the origin along a line that's 73% of the way between the line OA and OB and 21% of the way between the lines OA and OC"

that's still 3 parameters: 2.7, 73 and 21.

There's really no way round needing all 3 if you want to have arbitrary precision

John Cuthber,

 

I understand what you are saying, but is NNW any less or more one direction as NNNW?

 

Under the circumstances, a decimal or fractionin a distance is introducing the same kind of complexity. Bisecting an angle, so to speak.

 

The key here, or the question here, is can we come up with a way to divide direction in a natural and regular, and predictable and precise way. If so, it can be one parameter, infinitely divisible along the agreed upon plan.

 

Regards, TAR2

Edited June 3, 2013 by tar

[John Cuthber]

The problem is that NNW is a direction in a plane.

If you want to specify a direction in 3D then you need 2 angles- a latitude and a longitude.

To specify a point in 3D you also need a direction.

So, as I said (and countless others have said before me) you need 3 dimensions to specify a point in three dimensions.

 

This isn't a debating issue, it's a fact.

[tar]

John Cuthber,

 

Come to think of it, there is no particular reason to have 3 positive directions, and 3 negative ones, as desribed in Cartesian Coordinates. From an origin, any direction you go is still "away", and in this sense a positive accrual.<br /><br />To get to a point in Cartesian coordinates you have to make three trips in positive or negative directions each parallel to one of the axes.<br /><br />With a directional parameter, you just go a prescribed distance in the one positive direction mentioned.<br /><br />Go 3 in J.<br /><br />Regards, TAR2

Edited June 3, 2013 by tar

[John Cuthber]

True, for example polar coordinates are (by convention) always positive.

But there are still 3 of them.

You keep saying direction as if it's one parameter. It's two.

In 3d you still need 2 parameters to specify the direction.

Nothing you are going to say will alter this fact

[tar]

John Cuthber,

 

Conventionally speaking, I have no argument.

 

But even though the system is not well defined, nor agreed upon, just by looking at my diagram, you know what direction I mean by J, and no latitude or longitude, left or right, hieght or width, altitude, or declination was mentioned.

 

You can simply go in J.

 

Regards, TAR

Edited June 3, 2013 by tar

[John Cuthber]

Yes,

I know what direction "j" is.

but, as I have already said,

I can't specify a direction other than j without using one of the other named directions as a reference so I need 2 parameters.

Your system would work if everything were always exactly on one of your chosen lines, but in the real world only a small fraction (strictly, zero) of points will be on that line.

You need another parameter to account for them.

And you still will need three after you reply to this.

[Iggy]

With a directional parameter, you just go a prescribed distance in the one positive direction mentioned.<br /><br />Go 3 in J.<br /><br />Regards, TAR2

 

In cartesian coordinates, why not just go 3 in x?

[michel123456]

As I said, it works as long as you are prepared to put up with poor resolution.

Your system can't cope with 1,2.5,3

 

Similarly, if you want to specify an arbitrary point in space with the system you have pictured above you need to be able to say

"2.7 units out from the origin along a line that's 73% of the way between the line OA and OB and 21% of the way between the lines OA and OC"

that's still 3 parameters: 2.7, 73 and 21.

There's really no way round needing all 3 if you want to have arbitrary precision

I don't think so.

Give the resolution and construct the number, that's all.

If you need resolution 10 decimals, the number will be like 112233. With hundreds decimals the number becomes like 111222333. At the end it is only a transcription problem on how to write down a number of arbitrary fine resolution.

Edited June 3, 2013 by michel123456