Ah bounce yuh wall

A decorative wall painting in a mechanic shop, Trinidad, West Indies

This creative wall painting says it all about speed, perspective and shadow. The typography, "We Install All Parts" is due to the driver picking up a skid and careening through the blue brick wall. Not only does the artist show his skill for the visual three-dimension look, but he also gives the shadow underneath the car a dimension to ponder as he struggles with where it should fall. Painters such as Leonardo da Vinci would be pleased that the lessons in the study of shadow and perspective were overlooked, thus entering a new field of observation called; What the hell is it?.
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PERSPECTIVE by Leonardo da Vinci

1. The vertical plane is a perpendicular line, imagined as in front of the central point where the apex of the pyramids converge. And this plane bears the same relation to this point as a plane of glass would, through which you might see the various objects and draw them on it. The different converging pyramids produced by the objects, will show, on the plane, the various sizes and remoteness of the objects causing them.

2. All those horizontal planes of which the extremes are met by perpendicular lines forming right angles, if they are of equal width the more they rise to the level of eye the less this is seen, and the more the eye is above them the more will their real width be seen.

3. The farther a spherical body is from the eye the more you will see of it. A simple and natural method; showing how objects appear to the eye without any other medium.

4. The object that is nearest to the eye always seems larger than another of the same size at greater distance.

5. How every large mass sends forth its images, which may diminish through infinity. The images of any large mass being infinitely divisible may be infinitely diminished.

6. Objects of equal size, situated in various places, will be seen by different pyramids which will each be smaller in proportion as the object is farther off.

7. Perspective, in dealing with distances, makes use of two opposite pyramids, one of which has its apex in the eye and the base as distant as the horizon. The other has the base towards the eye and the apex on the horizon. Now, the first includes the [visible] universe, embracing all the mass of the objects that lie in front of the eye; as it might be a vast landscape seen through a very small opening; for the more remote the objects are from the eye, the greater number can be seen through the opening, and thus the pyramid is constructed with the base on the horizon and the apex in the eye, as has been said. The second pyramid is extended to a spot which is smaller in proportion as it is farther from the eye; and this second perspective [pyramid] results from the first.

8. Simple perspective is that which is constructed by art on a vertical plane which is equally distant from the eye in every part. Complex perspective is that which is constructed on a ground-plan in which none of the parts are equally distant from the eye.

10. No surface can be seen exactly as it is, if the eye that sees it is not equally remote from all its edges. When an object opposite the eye is brought too close to it, its edges must become too confused to be distinguished; as it happens with objects close to a light, which cast a large and indistinct shadow, so is it with an eye which estimates objects opposite to it.

11. In all cases of linear perspective, the eye acts in the same way as the light. And the reason is that the eye has one leading line (of vision) which dilates with distance and embraces with true discernment large objects at a distance as well as small ones that are close. But since the eye sends out a multitude of lines which surround this chief central one and since these which are farthest from the centre in this cone of lines are less able to discern with accuracy, it follows that an object brought close to the eye is not at a due distance, but is too near for the central line to be able to discern the outlines of the object. So the edges fall within the lines of weaker discerning power, and these are to the function of the eye like dogs in the chase which can put up the game but cannot take it. Thus these cannot take in the objects, but induce the central line of sight to turn upon them, when they have put them up. Hence the objects which are seen with these lines of sight have confused outlines. The relative size of objects with regard to their distance from the eye.

12. Small objects close at hand and large ones at a distance, being seen within equal angles, will appear of the same size. There is no object so large but that at a great distance from the
eye it does not appear smaller than a smaller object near.

13. Among objects of equal size that which is most remote from the eye will look the smallest.

14. Why an object is less distinct when brought near to the eye, and why with spectacles, or without the naked eye sees badly either close or far off [as the case may be].

15. Among objects of equal size, that which is most remote from the eye will look the smallest.

16. No second object can be so much lower than the first as that the eye will not see it higher than the first, if the eye is above the second.

17. And this second object will never be so much higher than the first as that the eye, being below them, will not see the second as lower than the first.

18. If the eye sees a second square through the centre of a smaller one, that is nearer, the second, larger square will appear to be surrounded by the smaller one.

19. Objects that are farther off can never be so large but that those in front, though smaller, will conceal or surround them.

20. This proposition can be proved by experiment. For if you look through a small hole there is nothing so large that it cannot be seen through it and the object so seen appears surrounded and enclosed by the outline of the sides of the hole. And if you stop it up, this small stopping will conceal the view of the largest object.

21. Linear Perspective deals with the action of the lines of sight, in proving by measurement how much smaller is a second object than the first, and how much the third is smaller than the second; and so on by degrees to the end of things visible. I find by experience that if a second object is as far beyond the first as the first is from the eye, although they are of the same size, the second will seem half the size of the first and if the third object is of the same size as the 2nd, and the 3rd is as far beyond the second as the 2nd from the first, it will appear of half the size of the second; and so on by degrees, at equal distances, the next farthest will be half the size of the former object. So long as the space does not exceed the length of 20 braccia. But, beyond 20 braccia figures of equal size will lose 2/4 and at 40 braccia they will lose 9/10, and 19/20 at 60 braccia, and so on diminishing by degrees. This is if the picture plane is distant from you twice your own height. If it is only as far off as your own height, there will be a great difference between the first braccia and the second.

22. A second object as far distant from the first as the first is from the eye will appear half the size of the first, though they be of the same size really.

23. If you place the vertical plane at one braccio from the eye, the first object, being at a distance of 4 braccia from your eye will diminish to 3/4 of its height at that plane; and if it is 8 braccia from the eye, to 7/8; and if it is 16 braccia off, it will diminish to 15/16 of its height and so on by degrees, as the space doubles the diminution will double.

24. Begin from the line _m f_ with the eye below; then go up and do the same with the line _n f_, then with the eye above and close to the 2 gauges on the ground look at _m n_; then as _c m_ is to _m n_ so will _n m_ be to _n s_. If _a n_ goes 3 times into _f b, m p_ will do the same into _p g_. Then go backwards so far as that _c d_ goes twice into _a n_ and _pg_ will be equal to _g h_. And _m p_ will go into _h p_ as often as_d c_ into _o p_.

Although the objects seen by the eye do, in fact, touch each other as they recede, I will nevertheless found my rule on spaces of 20 braccia each; as a musician does with notes, which, though they can be carried on one into the next, he divides into degrees from note to note calling them 1st, 2nd, 3rd, 4th, 5th; and has affixed a name to each degree in raising or lowering the voice. Let _f_ be the level and distance of the eye; and _a_ the vertical plane, as high as a man; let _e_ be a man, then I say that on the plane this will be the distance from the plane to the 2nd man.

The differences in the diminution of objects of equal size in consequence of their various remoteness from the eye will bear among themselves the same proportions as those of the spaces between the eye and the different objects.

25. Find out how much a man diminishes at a certain distance and what its length is; and then at twice that distance and at 3 times, and so make your general rule.

26. The eye cannot judge where an object high up ought to descend.

27. If two similar and equal objects are placed one beyond the other at a given distance the difference in their size will appear greater in proportion as they are nearer to the eye that sees them. And conversely there will seem to be less difference in their size in proportion as they are remote from the eve.

28. This is proved by the proportions of their distances among themselves; for, if the first of these two objects were as far from the eye, as the 2nd from the first this would be called the second proportion: since, if the first is at 1 braccia from the eye and the 2nd at two braccia, two being twice as much as one, the first object will look twice as large as the second. But if you place the first at a hundred braccia from you and the second at a hundred and one, you will find that the first is only so much larger than the second as 100 is less than 101; and the converse is equally true. And again, the same thing is proved by the 4th of this book which shows that among objects that are equal, there is the same proportion in the diminution of the size as in the increase in the distance from the eye of the spectator.

29. The practice of perspective may be divided into ... parts. The space for the number is left blank in the of which the first treats of objects seen by the eye at any distance; and it shows all these objects just as the eye sees them diminished, without obliging a man to stand in one place rather than another so long as the plane does not produce a second foreshortening.

30. But the second practice is a combination of perspective derived partly from art and partly from nature and the work done by its rules is in every portion of it, influenced by natural perspective and artificial perspective. By natural perspective I mean that the plane on which this perspective is represented is a flat surface, and this plane, although it is parallel both in length and height, is forced to diminish in its remoter parts more than in its nearer ones. And this is proved by the first of what has been said above, and its diminution is natural. But artificial perspective, that is that which is devised by art, does the contrary; for objects equal in size increase on the plane where it is foreshortened in proportion as the eye is more natural and nearer to the plane, and as the part of the plane on which it is figured is farther from the eye.

31. And let this plane be _d e_ on which are seen 3 equal circles which are beyond this plane _d e_, that is the circles _a b c_. Now you see that the eye _h_ sees on the vertical plane the sections of the images, largest of those that are farthest and smallest of the nearest.

32. Natural perspective acts in a contrary way; for, at greater distances the object seen appears smaller, and at a smaller distance the object appears larger. But this said invention requires the spectator to stand with his eye at a small hole and then, at that small hole, it will be very plain. But since many (men's) eyes endeavour at the same time to see one and the same picture produced by this artifice only one can see clearly the effect of this perspective and all the others will see confusion. It is well therefore to avoid such complex perspective and hold to simple perspective which does not regard planes as foreshortened, but as much as possible in their proper form. This simple perspective, in which the plane intersects the pyramids by which the images are conveyed to the eye at an equal distance from the eye is our constant experience, from the curved form of the pupil of the eye on which the pyramids are intersected at an equal distance from the visual virtue.

33. This diagram distinguishes natural from artificial perspective. But before proceeding any farther I will define what is natural and what is artificial perspective. Natural perspective says that the more remote of a series of objects of equal size will look the smaller, and conversely, the nearer will look the larger and the apparent size will diminish in proportion to the distance. But in artificial perspective when objects of unequal size are placed at various distances, the smallest is nearer to the eye than the largest and the greatest distance looks as though it were the least of all; and the cause of this is the plane on which the objects are represented; and which is at unequal distances from the eye throughout its length. And this diminution of the plane is natural, but the perspective shown upon it is artificial since it nowhere agrees with the true diminution of the said plane. Whence it follows, that when the eye is somewhat removed from the [station point of the] perspective that it has been gazing at, all the objects represented look monstrous, and this does not occur in natural perspective, which has been defined above. Let us say then, that the square _a b c d_ figured above is foreshortened being seen by the eye situated in the centre of the side which is in front. But a mixture of artificial and natural perspective will be seen in this tetragon called _el main_ that is to say _e f g h_ which must appear to the eye of the spectator to be equal to _a b c d_ so long as the eye remains in its first position between _c_ and _d_. And this will be seen to have a good effect, because the natural perspective of the plane will conceal the defects which would [otherwise] seem monstrous.