Is a Point Inside a Tilted Cube?

[DHack]

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.

 

[arildno]

I assume your cube is of fixed dimensions, but free to rotate/tilt about any of its initial edges/corners?

 

[DHack]

I assume your cube is of fixed dimensions, but free to rotate/tilt about any of its initial edges/corners?

Yep.

 

[mikeph]

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.

 

[CellCoree]

I would approach this problem by first defining the parameters and variables involved. The given information states that there is a cube that can be tilted in any direction, and the objective is to determine if a point is inside this cube.

To begin, I would define the dimensions of the cube and the coordinates of the point in question. Then, I would consider the possible orientations of the cube and how they could affect the position of the point in relation to the cube. This would involve using mathematical equations and geometric principles to determine the position of the point in relation to the cube in different orientations.

Next, I would consider the boundaries of the cube and how they could be affected by the tilting. This would involve analyzing the edges and vertices of the cube and how they could shift in different orientations.

Using this information, I would then develop a method or algorithm to determine if the point is inside the cube for any given orientation. This could involve creating a 3D model of the cube and the point, and using computer simulations or mathematical calculations to determine their relative positions.

In conclusion, determining if a point is inside a tilted cube requires a thorough understanding of the dimensions, orientation, and boundaries of the cube, as well as the coordinates of the point. By carefully analyzing these factors and using mathematical and geometric principles, it is possible to develop a method for determining the position of the point in relation to the tilted cube.