THE 3D SOLID PROBLEM

All we can draw are planes. We cannot render the volume inside a solid.

In the drawing above, there is a solid and a void within the cube. The dark green solid part is only communicated via the application of tones to all sides. We imagine the solid. But we cannot draw the solidness.

This realization came as a shock, at least to me anyway. When you are drawing, transparently, all sides of an object, you can draw the flat or curved planes which enclose the object. Yet when you want to put a tone into a three dimensional volume, it turns out you can’t. You can’t apply a three dimensional tone. When you try to do this, you immediately default to 2D.

If you don’t believe me, then draw a three dimensional transparent cube on a piece of paper. Imagine that this is a solid cube. Now, try to apply a tone to the inside volume. Your tone application collapses to 2D.

“Put this tone on that plane.” We immediately know what we are being asked to do. That makes sense. A plane is two dimensional, and it makes sense for us to apply a tone on a plane. It makes sense for us to show reflectance or light variation on this two dimensional solid. None of us have any trouble doing this.

But how do you apply a tone to the volume of a three dimensional solid? Seems like we should be able to. Yet, first of all, it is difficult to say. “Please apply a tone into this volume?” We really don’t know what that statement means. Or if we say “Please apply a tone…what, thru this volume?” That does not make any sense either. And that’s because we can’t. And as we have seen, if we can’t do it visually, then our language lags far, far behind.

The only way to apply tones to the interior of a three dimensional solid is to divide it into planes, like this drawing above. When we do this, now the application of tones makes sense. We are now conveying the solid three dimensionality. Yet we had to default to two dimensional planes. And the fidelity of the solid is compromised because we had to cut it into slices.

Which at least suggests to us that we then cannot draw space. We can draw the planes that define and enclose the space. But we cannot draw the space. To which you might say, well, gee, of course you cannot draw space, because it is transparent. What’s to draw?

Yet if we think purely of what is inside a volume and don’t make the distinction as to whether it is open or solid, it seems to me that we run up against a rather severe limitation regarding what we think we are doing. If we can’t transparently depict the inside of a 3D solid, then can we really depict the inside of a volume? Are we even making the three dimensional drawings that we think we are making?

I guess in one way, this insight is an indictment against transparent drawing. Possibly the reason why we have avoided drawing transparently is this inability to draw solids.

Then again, in architectural or product design, all we are doing is manipulating planes. When ever do we employ a solid in our design solutions? Early computer GUI mice employed a solid; the small solid rubber ball inside the device is what made it work. Or a masonry fireplace is sort of a solid, although for it to work, it requires penetrations.

So we’ll just keep on drawing transparent planes. And if the arrangement of some of these planes form a solid on our drawing, we’ll keep our new insight at the back of our minds.