Is a Point Inside a Tilted Cube?

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  • Thread starter Thread starter DHack
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Discussion Overview

The discussion revolves around determining whether a point is located inside a cube that can be tilted in any direction. The scope includes geometric reasoning and mathematical methods for assessing point inclusion within a three-dimensional shape under rotation.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant seeks guidance on how to determine if a point is inside a cube that can rotate freely.
  • Another participant clarifies the assumption that the cube has fixed dimensions but can tilt about its edges or corners.
  • A further participant questions the understanding of the problem, suggesting that if the cube has a known orientation, one could rotate the coordinate system to align with the cube's sides and then check the point's position relative to the transformed axes.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the method for determining point inclusion, and there are varying interpretations of the problem's parameters.

Contextual Notes

The discussion does not address specific mathematical steps or assumptions regarding the cube's orientation or the nature of the point being tested.

DHack
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I'm trying to figure out if a point is in a cube that could be tilted in any direction.
How would I do it? I can get anything you need for this problem.

Thanks in advance.
 
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I assume your cube is of fixed dimensions, but free to rotate/tilt about any of its initial edges/corners?
 
arildno said:
I assume your cube is of fixed dimensions, but free to rotate/tilt about any of its initial edges/corners?

Yep.
 
I don't fully understand the question.

Are you saying you have a cube with a known orientation (eg. you are given a unit vector normal to a surface, and the cube centre is fixed at (0, 0, 0)), and want to know if a general point (x, y, z) is in that cube?

Try to develop a method of rotating the coordinate system from the original one to one where the cube sides are perpendicular to the coordinate axes. Then all you need to do is transform your point to this system and ensure it is between each side along all three dimensions.
 

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