# Thread: the perfect cube and the sphere

1. ## the perfect cube and the sphere

If I drew a cube to fit outside a perfect sphere, assuming the perspective lines are correct, that cube will be perfect, no matter what angle?

2. Um... what?

3. U know how a cirlce fits inside a square, well if you draw a circle and treat it as a sphere. Then you draw a cube holding that circle, then that cube won't end up as a disorted brick, because the sphere has to fit inside the cube perfectly.

4. How would you draw cube "holding" a circle?

5. Well, the cube will still be "distorted" by perspective, but dimension wise all sides will be equal... if that's what you're asking.

6. That method is not reliable.

Notice the cuboids 1 and 2 are not “perfect” cubes, in 2pt perspective.
Points A and B should be in vertical alignment. Points A,B,C and D should share the same vertical alignment.

Under some conditions, in 3pt perspective, you can get fare approximations.

A sphere enclosed by a cube (a cube with edge lengths equaling the diameter of the sphere) looks like this, in 3pp:

Last edited by bill618; April 26th, 2013 at 09:22 AM.

7. Hm, this is pointless. Insphere of a cube has nothing to do with the incircle of the cube's projected contour. In fact, such incircle is not guaranteed to exists for an arbitrary cube projection as this projection is almost always an irregular convex polygon with more than four sides, typically a hexagon. Projection's incircle can be constructed for a subset of projections that form quadrilateral contours, although this incircle is never a projection of the cube's insphere, except for the singular case when the projection point is infinitely distant (making the projection parallel rather than perspective) and the projection plane itself is parallel to a side of the cube.
Last edited by LaCan; April 26th, 2013 at 09:45 AM.

8. Sure, it’s mathematically pointless. But if someone, unwittingly, draws a cube reffed around a circle in ‘mild’ 3pp, that happens to be rotated so as to produce the general silhouette of a regular hexagon (or one approaching an isometric cube projection), they might draw the false conclusion that drawing a cube around a circle (which is what I’m sure the OP meant—as a sphere always has a circle contour, unless rendered elliptical by perspective distortion) will always produce a (reasonably) accurate cube.

In other words, the discussion may not be pointless to the OP.

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