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Description
WARNING: PURELY SUBJECTIVE!!

So far, what this tutorial has taught was pretty much objective- that is, accurate and true, or at least close enough to it.

The main reason I included this page is because, while coming up with this didn't-really-work method, I stumbled across something really and honestly helpful- which will be explained two pages from now.

Actually, maybe the biggest reason this was included was, although it itself is of little value and does not work very often, it DID lead to what appears on page 2VP 10: Pyramids. So even if you experiment and it doesn't do what you wanted it to do, it may, through serendipity, suddenly reveal something else.

When drawing the cube, we dropped vertical lines down for the sides. But since the cube is clearly angled, wouldn’t they seem to start coming together?

Maybe- so, I came up with this. Again, this didn't work out very well. Here it is anyway...

After drawing in that first square, from then on all lines should be drawn faintly. You draw the cube as before, but do not darken any other lines.

Connect the corners of the bottom cube. You will have a sort of cross or “X” on it.

Extend the line from the 45 point going through the first square, until it hits one of the arms of the “X.” Draw in a line from the top corner above it (on the first square)- in this case, the left corner- down to where the 45 point line touches the “X.” It will come from the same place as the vertical line there, but is tilted in, and on that arm of the “X.”

Draw lines from the two vanishing points to the bottom of that tilted line. Those two new lines will cross over two other arms of the “X;” draw points on those two places, and from the corners above them draw lines to those two new points- those sides will also be tilted in.

Draw lines from the vanishing points to those new points- they will intersect on the fourth arm of the “X.” Draw in that side as with the others.

That’s it.

Now, this was meant to reflect exactly how tilted the cube is, but it usually doesn't. What it DOES do, however, is allow you to draw in one side angling in, and then properly draw in the other three, as if you were drawing a building seen from up high and at an angle. The main thing is that the bottom of those sides will “slide” along their arms of the “X.”

Of course, if you extended the “X” OUTSIDE of the bottom square, and ignored the 45 point, drawing a point on one of the arms of the “X” outside of the square- so your sides would tilt OUT, instead of in, well, you would have a sort of flat-topped pyramid. Expanding or reducing shapes is what came from this.

Description
WARNING: PURELY SUBJECTIVE!!

So far, what this tutorial has taught was pretty much objective- that is, accurate and true, or at least close enough to it.

The main reason I included this page is because, while coming up with this didn't-really-work method, I stumbled across something really and honestly helpful- which will be explained two pages from now.

Actually, maybe the biggest reason this was included was, although it itself is of little value and does not work very often, it DID lead to what appears on page 2VP 10: Pyramids. So even if you experiment and it doesn't do what you wanted it to do, it may, through serendipity, suddenly reveal something else.

When drawing the cube, we dropped vertical lines down for the sides. But since the cube is clearly angled, wouldn’t they seem to start coming together?

Maybe- so, I came up with this. Again, this didn't work out very well. Here it is anyway...

After drawing in that first square, from then on all lines should be drawn faintly. You draw the cube as before, but do not darken any other lines.

Connect the corners of the bottom cube. You will have a sort of cross or “X” on it.

Extend the line from the 45 point going through the first square, until it hits one of the arms of the “X.” Draw in a line from the top corner above it (on the first square)- in this case, the left corner- down to where the 45 point line touches the “X.” It will come from the same place as the vertical line there, but is tilted in, and on that arm of the “X.”

Draw lines from the two vanishing points to the bottom of that tilted line. Those two new lines will cross over two other arms of the “X;” draw points on those two places, and from the corners above them draw lines to those two new points- those sides will also be tilted in.

Draw lines from the vanishing points to those new points- they will intersect on the fourth arm of the “X.” Draw in that side as with the others.

That’s it.

Now, this was meant to reflect exactly how tilted the cube is, but it usually doesn't. What it DOES do, however, is allow you to draw in one side angling in, and then properly draw in the other three, as if you were drawing a building seen from up high and at an angle. The main thing is that the bottom of those sides will “slide” along their arms of the “X.”

Of course, if you extended the “X” OUTSIDE of the bottom square, and ignored the 45 point, drawing a point on one of the arms of the “X” outside of the square- so your sides would tilt OUT, instead of in, well, you would have a sort of flat-topped pyramid. Expanding or reducing shapes is what came from this.