Foreshortened Cylinder
horizon lime horizon lime
So it is important to realize that vertical vanishing lines and the horizon line (eye level) serve the same purpose and are similar in concept. Both "contain" the vanishing points for parallel sets of lines which lie on parallel planes. The horizon line serves all sets of lines on horizontal planes while a vertical vanishing line serves all sets of lines on parallel vertical planes. Both are found in the same manner; in fact the drawings above and below are identical except for being turned 90 degrees from each other.
The diagrams at the bottom of this page and on the previous page also show that the vanishing point for parallel lines on inclined planes (e.g., the edges of the book pages or the sides of the box top) is always directly above or below the vanishing point those lines would have if they were pivoted to a horizontal position.
Uphill And Downhill (Inclined Planes) [79]
The building lines, the windows, the brick coursing, and the steps, are all horizontal, therefore they converge to a vanishing point on the horizon line (eye level).
The sidewalk, street, curb, baby carriage, auto, and line of intersection between sidewalk and houses, are all inclined upwards, therefore they converge to a point directly above the first.
Now note the ice cream vendor's wagon and the pushcart. The wagon is on the level part of the street, so its lines naturally converge to vanishing points on the horizon line. The lines of the pushcart on the inclined plane, on the other hand, converge to points along the vanishing line of the inclined plane. But since both vehicles are turned at the exact same angle from the sidewalk, their vanishing points (left and right) lie on the same vertical vanishing lines, directly above and below one another.
51 pe view Here again (foreground) lines that are horizontal converge toward a horizon line vanishing point (near center), and those that are inclined (downwards) converge to a point directly below.
Now, when the road turns to the right, what happens to the horizontal lines of the houses? Their vanishing point remains on the horizon line but simply shifts accordingly to the right.
And if the road also goes downhill its vanishing point is directly below this new horizon point. (Note that both downhill vanishing points are on the same horizontal vanishing line because the angle of incline is the same.)
TO REPEAT: THE VANISHING POINT FOR PARALLEL LINES ON AN INCLINED PLANE IS ALWAYS DIRECTLY ABOVE OR BELOW THE VANISHING POINT THOSE LINES WOULD HAVE IF THEY WERE PIVOTED TO A HORIZONTAL POSITION. (See p. 77.)
horizon lime iü
Chapter 13: CIRCLES, CYLINDERS AND CONES
Circles And Ellipses: Circles, Except When They Are Parallel To
Observer's Face, Will Foreshorten And Appear As Ellipses pivot line
Si oe view
This silver dollar appears as a perfect circle only when seen "front face." When pivoted around a diameter line, it changes from a round to a "skinny" ellipse, till finally it appears as a thin line.
Stood upright and pivoted around a vertical line, this circle appears much the same as above,
Upright circles parallel to one another and at right angles to observer (i.e., to picture plane) will appear as increasingly rounder ellipses the further they are from center line of observer's vision. (Above.)
Horizontal circles stacked one above the other and at right angles to observer (picture plane) will appear as increasingly rounder ellipses the further they are from observer's eye level-horizon line. (Right.)
ellipses — despite the fact that in rigorous mechanical perspective circles at far left and right would come out as distorted ellipses.
Horizontal circles seen simultaneously, even the ones far to the left and right of center line of observer's vision, should all be drawn as true
[82] Drawing The Ellipse
The two-dimensional circles on the previous page could represent coins, phonograph records, pancakes, lenses, etc. (right). But circles are also key parts of three-dimensional objects such as cylinders and cones, and as such have wide application in representational drawing. Cylinders are the bases of an endless number of things such as cigarettes, oil tanks, threadspools, chimneys, etc. Cones are the bases of ice cream cones, hour glasses, martini glasses, funnels, etc. Therefore, the importance of learning to draw circles in perspective — i.e., ellipses—can hardly be overestimated.
What Is An Ellipse And How Can We Learn To Draw It?
An ellipse is an oval figure with two unequal axes (major and minor) which are always at right angles to one another. These axes connect, respectively, the figure's longest and shortest dimensions, and about each of them the curve of the ellipse is absolutely symmetrical. This means four identical quadrants, with each axis dividing the other exactly in half (x—x, y—y).
One should learn to draw an ellipse freehand with a loose, free-swinging stroke. Ellipses A and B are attempts at this. Anyone familiar with ellipses can visualize the major and minor axes and see that A is good while B lacks the necessary symmetry. (If we draw B's two axes, we can see the errors much more clearly. Notice how each quadrant differs.)
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You might find it helpful to sketch a rectangle around the tick marks. This creates four more guide lines within which the shapes can be judged and compared (above).
So a good way to begin learning to equal dimensions on either side of the center to locate extremities.
So a good way to begin learning to equal dimensions on either side of the center to locate extremities.
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