THE RULES AND CONDITIONS OF PERSPECTIVE

15 January, 2009

The conditions of linear perspective are somewhat rigid. In the first place, we are supposed to look at objects with one eye only; that is, the visual rays are drawn from a single point, and not from two. Of this we shall speak later on. Then again, the eye must be placed in a certain position, as at E in the picture below, at a given height from the ground, S·E, and at a given distance from the picture, as SE. In the next place, the picture or picture plane itself must be vertical and perpendicular to the ground or horizontal plane, which plane is supposed to be as level as a billiard-table, and to extend from the base line, ef, of the picture to the horizon, that is, to infinity, for it does not partake of the rotundity of the earth.

 

 

 

 

Rule 1: All straight lines remain straight in their perspective appearance.

Rule 2: Vertical lines remain vertical in perspective.

Rule 3: Horizontals parallel to the base of the picture are also parallel to that base in the picture.

Rule 4: All lines situated in a plane that is parallel to the picture plane diminish in proportion as they become more distant, but do not undergo any perspective deformation. This is called the front view.

Rule 5: All horizontal lines which are at right angles to the picture plane are drawn to the point of sight.

Rule 6: All horizontals which are at 45° to the picture plane are drawn to the point of distance.

Rule 7: All horizontals forming any other angles but the above are drawn to some other points on the horizontal line.

Rule 8: Lines which incline upwards have their vanishing points above the horizon, and those which incline downwards, below it. In both cases they are on the vertical which passes through the vanishing point of their ground-plan or horizontal projections.

Rule 9: The farther a point is removed from the picture plane the nearer does it appear to approach the horizon, so long as it is viewed from the same position.

Rule 10: Horizontals in the same plane which are drawn to the same point on the horizon are perceptively parallel to each other.

 

The List Of Rules Stated Below Have Been Explained More Elaborately For Reference:

 

Rule 1:

 

All straight lines remain straight in their perspective appearance.

 

Rule 2:

 

Vertical lines remain vertical in perspective, and are divided in the same proportion as AB, the original line, and a·b·, the perspective line, and if the one is divided at O the other is divided at O in the same way.

 

 

It is not an uncommon error to suppose that the vertical lines of a high building should converge towards the top; so they would if we stood at the foot of that building and looked up, for then we should alter the conditions of our perspective, and our point of sight, instead of being on the horizon, would be up in the sky. But if we stood sufficiently far away, so as to bring the whole of the building within our angle of vision, and the point of sight down to the horizon, then these same lines would appear perfectly parallel, and the different stories in their true proportion.

 

Rule 3:

 

Horizontals parallel to the base of the picture are also parallel to that base in the picture. Thus a·b· in the figure below is parallel to AB, and to GL, the base of the picture. Indeed, the same argument may be used with regard to horizontal lines as with verticals. If we look at a straight wall in front of us, its top and its rows of bricks, &c., are parallel and horizontal; but if we look along it sideways, then we alter the conditions, and the parallel lines converge to whichever point we direct the eye.

 

 

This rule is important, as we shall see when we come to the consideration of the perspective vanishing scale. Its use may be illustrated by this sketch, where the houses, walls, &c., are parallel to the base of the picture. When that is the case, then objects exactly facing us, such as windows, doors, rows of boards, or of bricks or palings, &c., are drawn with their horizontal lines parallel to the base; hence it is called parallel perspective.

 

Rule 4:

 

All lines situated in a plane that is parallel to the picture plane diminish in proportion as they become more distant, but do not undergo any perspective deformation; and remain in the same relation and proportion each to each as the original lines. This is called the front view.

 

 

Rule 5:
All horizontals which are at right angles to the picture plane are drawn to the point of sight. Thus the lines AB and CD in the figure below are horizontal or parallel to the ground plane, and are also at right angles to the picture plane K. It will be seen that the perspective lines B, D, must, according to the laws of projection, be drawn to the point of sight.

 

 

 

This is the most important rule in perspective. An arrangement such as there indicated is the best means of illustrating this rule. But instead of tracing the outline of the square or cube on the glass, as there shown, I have a hole drilled through at the point S, which I select for the point of sight, and through which I pass two loose strings A and B, fixing their ends at S.

 

As SD represents the distance the spectator is from the glass or picture, I make string SA equal in length to SD. Now if the pupil takes this string in one hand and holds it at right angles to the glass, that is, exactly in front of S, and then places one eye at the end A (of course with the string extended), he will be at the proper distance from the picture. Let him then take the other string, SB, in the other hand, and apply it to point b´ where the square touches the glass, and he will find that it exactly tallies with the side b´f  of the square a·b´fe. If he applies the same string to a·, the other corner of the square, his string will exactly tally or cover the side a·e, and he will thus have ocular demonstration of this important rule.

 

Rule 6:

 

All horizontals which are at 45°, or half a right angle to the picture plane, are drawn to the point of distance. We have already seen that the diagonal of the perspective square, if produced to meet the horizon on the picture, will mark on that horizon the distance that the spectator is from the point of sight. This point of distance becomes then the measuring point for all horizontals at right angles to the picture plane.

 

Rule 7:

 

All horizontals forming any other angles but the above are drawn to some other points on the horizontal line. If the angle is greater than half a right angle, as EBG, the point is within the point of distance, as at V´. If it is less, as ABV´´, then it is beyond the point of distance, and consequently farther from the point of sight.

 

 

 

 

In the above figure, the dotted line BD, drawn to the point of distance D, is at an angle of 45° to the base AG. It will be seen that the line BV´ is at a greater angle to the base than BD; it is therefore drawn to a point V´, within the point of distance and nearer to the point of sight S. On the other hand, the line BV´´ is at a more acute angle, and is therefore drawn to a point some way beyond the other distance point.

 

NOTE: When this vanishing point is a long way outside the picture, the architects make use of a centrolineal, and the painters fix a long string at the required point, and get their perspective lines by that means, which is very inconvenient.

 

Rule 8:

 

Lines which incline upwards have their vanishing points above the horizontal line, and those which incline downwards, below it. In both cases they are on the vertical which passes through the vanishing point (S) of their horizontal projections.

 

 

 

This rule is useful in drawing steps or roads going uphill and downhill.

 

 

 

Rule 9:

 

The farther a point is removed from the picture plane the nearer does its perspective appearance approach the horizontal line so long as it is viewed from the same position. On the contrary, if the spectator retreats from the picture plane K (which we suppose to be transparent), the point remaining at the same place, the perspective appearance of this point will approach the ground-line in proportion to the distance of the spectator.

 

 

 

 

 

 

 

The spectator at two different distances from the picture.

 

Rule 10:

 

Horizontals in the same plane which are drawn to the same point on the horizon are parallel to each other.

 

 

 

 

This is a very important rule, for all our perspective drawing depends upon it. When we say that parallels are drawn to the same point on the horizon it does not imply that they meet at that point, which would be a contradiction; perspective parallels never reach that point, although they appear to do so. The above figure will explain this.


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