Using the Rules of Perspective

Suppose we want to draw a cube with a design on it, and we want the front and back face of the box to be directly facing the viewer, so that it will be parallel to the picture plane.

  1. Start by drawing the front. Since we want it to be parallel to the picture plane, use Rule 5:
    A shape that lies entirely in a plane parallel to the picture plane has a perspective image that is an undistorted miniature of the original.
    Since we're aiming for a cube, the front face in real-life should be a square, and so the front face in perspective must be a square as well.

  2. The edges going from the front to the back will all be parallel to each other, so by rule 4, they will share a vanishing point.

    In fact, since the front is parallel to the picture plane, these new edges will be orthogonal to the picture plane, and hence this vanishing point will be the primary vanishing point.

    I can choose to put this vanishing point anywhere I want to, but I should be aware that when I choose it I am choosing the point opposite which the viewers should ideally be placing their eyes.
  3. The back face must again be a square, since the back is also parallel to the picture plane. My choices of where to put the back face are limited by the orthogonal lines we just drew.

    Within the confines of those lines, however, I can put the back face however far back I want to. Again, I just need to be aware that when I choose where the back goes, I am choosing the viewing distance -- the ideal distance back from the primary vanishing point that the viewers should be placing their eyes.

    I have a choice -- I can either choose where to put the back, and let that define the viewing distance, or I can choose the viewing distance, and let that define where the back goes.

    In your homework, you will be doing the latter, so here, I will illustrate the former.

    Here, I choose where to put the backNext, I find out what viewing distance that choice determined.

  4. Now I have finished drawing my cube, and I'm ready to decorate it. I draw a design on the front face; I'd like to draw the same design on the other two visible faces.

  5. Notice that this design is created by drawing 2 sets of 3 parallel lines; each set is parallel to one of the diagonals of the face.

    The corners are located on the lines that bisect the face horizontally and vertically. Also notice that the center of the design is located at the center of the face -- where the two diagonals and these two bisecting lines all intersect.

  6. These diagonals and bisectors will help us to repeat the design on the top and side. To draw them in, we'll need the primary vanishing point again.

  7. I need to know where on the bisecting lines to put the corners. In the original, the 4 corners are each 1/6 of the length of the side in from the edge. We will be learning shortly how to subdivide a rectangle into any number of rectangles we want to; for now, I'll just put two of the corners on each face in for us. (I could put all four in, but the subdividing method is much more time-consuming than using vanishing points to draw lines, so if you were doing the whole thing - including finding these corners - it would be more practical to just put in 2.)

  8. On the top, lines from these corners are parallel (in real life) to the diagonals, and so (in the image) will share the same vanishing points as the diagonals. We know that the diagonals' vanishing points are on the horizon line.

    Similarly, on the side, lines from the corners will share the same vanishing point as the diagonal, and that vanishing point will be on the vertical line through the primary vanishing point.

    So our first task is to find the vanishing point for one of the diagonals of the top face and the vanishing point for one of the diagonals on the side face. Then we can figure out where the first set of 3 parallel lines on each side should be.
  9. Now we know where the other two corners on each side are: where the blue lines intersect the red lines that bisect each side (not the diagonals).

    Here, I've added the other two sides to each square And now, I've erased all the extraneous lines.

    And now, I just color it in!

    Next - Subdividing and Duplicating rectangles

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