function that creates a cube from one point and size?

Question

2.00/5 (1 vote)

See more:

Hi everyone,
I'm ask here for this.

There is a C++ or OpenCV function that from a point and a size, it's able to determine the 8 vertices (x, y, z) of the cube created on that side?

Posted 8-Nov-13 4:46am

Domus1919

Add a Solution

Comments

Andreas Gieriet 8-Nov-13 10:57am

So you ask if there is a function or you need to write such a function?
Such a function need additional information unless you assume axis-aligned.
Is the point one of the vertices (whcih?) or the center of the cube?
What exactly is the problem?
Cheers
Andi

Domus1919 8-Nov-13 11:01am

The point it's a vertex, the size it's one side..it's possible determinate other 7 vertexes?

Andreas Gieriet 8-Nov-13 11:02am

Axis-aligned?
I must assume so.
Draw it on a sheet of paper: place the cube first so that the lower left vertex is on (0/0/0).
Then make one vertex each on the x-axis, y-axis, z-axis. Then make the remaining 5 vertices.
Finally add the point ot each vertex by adding the point coordinates to each vertex coordinate.
Cheers
Andi

Sergey Alexandrovich Kryukov 8-Nov-13 11:18am

I never heard from OP it's axis aligned. What a waste!
—SA

2 solutions

Add a Solution

Add your solution here

Treat my content as plain text, not as HTML

Preview 0

…

Existing Members

Sign in to your account

...or Join us

Download, Vote, Comment, Publish.

Your Email
Password
Forgot your password?

Your Email
This email is in use. Do you need your password?
Optional Password

I have read and agree to the Terms of Service and Privacy Policy
Please subscribe me to the CodeProject newsletters

When answering a question please:

Read the question carefully.
Understand that English isn't everyone's first language so be lenient of bad spelling and grammar.
If a question is poorly phrased then either ask for clarification, ignore it, or edit the question and fix the problem. Insults are not welcome.
Don't tell someone to read the manual. Chances are they have and don't get it. Provide an answer or move on to the next question.

Let's work to help developers, not make them feel stupid.

This content, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

Andreas Gieriet · Accepted Answer · 2013-11-08T05:11:00

Solution 1

If axis aligned, do the following:
1) place the vertex at the origin (0/0/0).
2) the base area is given by the four vertices where z is always 0: (0/0/0), (0/s/0), (s/0/0), (s/s/0)
3) likewise make all vertices in the z-plane (z = s): (0/0/s), (0/s/s), (s/0/s), (s/s/s)
4) move the cube to your point by adding that point to each vertex: (x/y/z) --> (x+a/y+b/z+c)
That's it.
Cheers
Andi

Posted 8-Nov-13 5:11am

Andreas Gieriet

Comments

Sergey Alexandrovich Kryukov 8-Nov-13 11:17am

This is not how a problem was formulated (I answered), but maybe this is what OP wanted... Re-posted... :-)
—SA

Domus1919 8-Nov-13 11:26am

Thanks to Andreas and Sergey. Ok. It's clear situation now.

Sergey Alexandrovich Kryukov · Accepted Answer · 2013-11-08T05:16:00

You don't need this function from some API. Why do you think that someone will develop function for all partial cases from elementary geometry. I would not make any sense.

I answered to the question on this topic here: C++ how make an Array of recursive Objects like 8-branches tree?[^].

No, this is not just one point and the size. Look thoroughly. Imagine you have a cube in your hand. Isn't it simple enough?

I tried to explain that defining the cube by defining 8 3D point of it was wrong. If your input is those 8 points, the resulting body may or may not be a cube, but if this is a cube, this data is redundant. The situation is even more complex. The 3D points are specified as 3 floating-point numbers, which are approximate. This way, there is no definitive yes-no answer to the question "are those 8 points a vertices of an exact cube". With what accuracy? You don't want to solve related problems, you need to avoid them. But, importantly, arbitrary 8 points mean 23 degrees of freedom. Apparently, this data is redundant to define a cube.

It is apparent that any solid body has exactly 6 degrees of freedom on 3D space. These 6 parameters would define the location of it without redundancy. Another degree of freedom is the size of the cube, as you don't consider it fixed. Take one point and fix it. It takes 3 degrees of freedom, say 3 Cartesian coordinates of it. Where is one of the neighboring vertices? Choose the size of the cube as the length of it rib. Then the second vertex will be anywhere on the sphere centered at the point of the first vertex. To fix the second vertex would take two more degrees of freedom, two angles in whatever system. When you fixed two vertices, you got a solid body freely rotating around the axis. Fix an angle on this axis. This is the 6th degree of freedom. And then, use elementary mathematics to calculate coordinates of 8 vertices, if you still need all of them. (Not sure why. It depends on your problem.) One delicate moment is this: you can consider the vertices/ribs/sides of a cube non-distinguishable. If you perform symmetric operation, say, rotate to 90° the way one face takes the place of another face, you got the same cube.

Anyway, you are the one who wants to do these calculations.

—SA