Perspective Tutorial: 2VP 10

Shrinking or expanding a square, and a pyramid.

Two pages ago I showed how I would draw the sides of a cube (or any such block) going in, or even out, if I wanted a flat-topped pyramid.

It is the basic idea that the sides will slide along the arms of the cross or “X” that this page will show- this is a very handy thing to know.

And so, first, Fig. 27…

First, draw a square, following the rules explained earlier. This time, you do not need TP1 or TP2, so you needn’t bother with any of that. All you need is the square.

Now, to get a smaller one!

As before, connect the corners to get your “X.” On the arm of the “X” closest to you, draw a point, this will be point 1.

From both vanishing points, draw lines through point 1.

Those two lines, as before, will cross over two more arms of the “X.” Draw points on those arms- these will be points 2 and 3.

Draw two lines from the vanishing points through both points 2 and 3. On the fourth arm of the “X” two of those lines should neatly intersect. That will be point 4.

Darken the lines connecting all four points, and you have your smaller square! If the line from the 45 point goes through its corners- as shown- then you have it!

Now, the uses here are many! If you want to pile a smaller block on a bigger one, you have its base! That smaller block will be nice and centered on the bigger one- and if you move the sides outward, at the same angles, you can draw a Mayan Pyramid! This is why I included that subjective thing before- it led to this.

If you wanted to expand the square, you would simply extend the arms of the “X” outside of the square, and then follow the same procedure, with that first point outside of the square. This is also good if you want to draw an overhang or ledge from the block- unlike Fig. 13, this ledge would be quite accurate. You can do this for a square you are viewing from above (as here) or just flip the page upside down, and see it from below…


Fig. 28 shows how to draw a pyramid. First, draw a cube, but use faint lines. This time, draw an “X” on the top and bottom squares. Then, from the points on the sides and the front corner, draw lines going to the middle of the “X.”

If you want a solid pyramid, that’s it.

For a translucent one, merely draw one more line from the back corner to the middle of the “X.” Here I also connected the middle of both “Xs,” to show the center part of the pyramid.

If you drew the block longer or shorter, you’d have a squatter or taller pyramid.

And it’s all based on the two vanishing point method. Everything just sort of builds up from that basic concept, as multiplication is based on simple addition.

This is explained in greater detail here:

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