Prospect (visual perception)

The visual prospect

General concepts

The visual prospect or ocular is the whole of the transformations by which a portion of the three-dimensional space world (and Euclidean on the scale of the man) are perceived by two-dimensional surface and curve (thus not-Euclidean) of the eye, independently of the stereoscopic properties of the frontal binocular vision . From the mathematical point of view, it is a projection by which the metric dimension of the objects is converted into angular dimension. The projective Géométrie is the branch of mathematics which models the properties of this projection, independently of physiological reality the eye. The eye considered individually (monocular vision) functions like a stigmatic lens which makes correspond to each point space of the cone of vision a point on retinal surface. The same object appears in a different way to the eye according to 3 parameters:

its distance to the eye
its offsetting compared to the axis of the glance
its slope in the 3 directions

A segment placed in front of oneself all the more appears large that it is close, and that it is located in a plan perpendicular to the axis of the glance. It all the more appears curved that it is close, and that it is excentré compared to the axis of the glance.

The cognitive Processus by which the brain mentally rebuilds in space the shapes of the objects perceived on the surface of the retina takes part so narrowly in the visual experiment which it remains largely Préconscient. One perceives like parallels two rails of train, whereas a photograph of course is noted that their lines meet at the horizon, and that they are always curved out of bell (towards the interior).

Precise details (and reserves) on some subjacent concepts

Perception in prospect is one fundamental property of the Vision and a direct consequence of the anatomy of the eye. For this reason, it is not the same one for each animal specie. One very often finds in the literature the expressions field of vision and cone of vision ; the explanatory diagrams and the illustrations often present the prospect to it as a projection on a plane surface which corresponds to the orthogonal section of the cone of vision; finally the same illustrations and diagrams are limited to the representation of only one eye.

As semantics suggests it, one speaks about field of vision to describe at the same time the visible portion of space and the expression of the vision, which is a surface.
In any mathematical rigor, a cone is “a regulated surface defined by a line (d), called generator, passing by a point fixes S called top and a variable point following a closed plane curve (c), called direct curve”. To speak about “cone of vision”, it is a) to consider the vision as monocular (the top is the convergence point in the eye) and 2) to underlie that the opening of the field of vision is strictly lower than 180° in all the directions.
To speak about the eye in the singular, and to compare it with the single lens of a camera, suggests a strictly monocular vision once more.

However all the vertebrate ones have two eyes. In the mammals, the two fields of vision are recut, so that the binocular vision is, for the majority of them, more than the sum of two monocular visions.

The opening of the field of vision is very variable from one animal specie to another. Thus, certain mammals like the cat or the horse have a field of vision which very largely exceeds 180° for each eye, which excludes to project this field of vision on a plane surface. Even those which have the more common field of 170° for each eye reach, because of ocular lateralization, a field combined higher than 200°, which makes quite as impossible a plane projection. The monodirectionnelle frontal binocular vision is in fact characteristic of a minority the vertebrate ones, of which the man. For this last, that implies that there is not one, but two tops for the “cone of vision”, and also two about parallel axes of the glance… N the other hand, the total field of vision is for the man about 180° laterally and 125° vertically, which opportunely makes it possible to delimit “what is visible for him” with “what it has in front of him”. It is in this only condition that there can be a projection of visible space on the plane surface and finished of a visual ellipse - what one commonly hears in fact by “field of vision”.

This ellipse is sometimes simplified in the shape of circle (what corresponds to the orthogonal section of a circular cone, whereas the visual cone of the animals “is flattened”), while it is found approximated by a very oblong rectangle in the proportions known as panoramic of the cinema displays (see 16/9). Another difference between the eye and the lens of a camera is that field of vision is not homogeneous in term of performance (acuity, photosensitivity, polychromy) and of attention: the active examination is reserved in the center, and the performance decrease by stage towards the periphery of the glance. The interest of this enshrining of the cones of vision, it is that only the field of view attentive is relevant when one “observes” an image.

Laws of the prospect

Illustration 2 and 3 make it possible to be convinced of the following principles:

has constant slope, the apparent dimension of a segment is function opposite of its distance to the eye

Remotely constant, the apparent dimension of a segment decrease while the angle of inclination of the segment compared to the plan perpendicular to the glance

increases

Any segment of the space which does not pass by the center of the glance appears curved in prospect; the intensity of the curve grows with offsetting.

From these basic principles result from the more complex principles for the visible solids. For example:

Two parallel straight lines in real space appear in prospect as bell-shaped curves converging towards the same point (which can be inside as outside the visual ellipse).

a surface square perpendicular to the axis of the glance in the real-world appears in prospect as a quasi-trapezoid of which none the angles is right, and whose with dimensions ones are curved out of bell towards the outside of the glance

Plus one surface square is close (i.e invades the field of vision), plus its appearance is deformed in term of angles and curves. The more it moves away (i.e narrows), the more it takes the simple appearance of an Euclidean projection of a space on a plan

a cube of which none the faces is parallel with the axis of the glance present inevitably 3 faces, whose no angle is right, and whose 9 visible edges are curves which converge 3 by 3 towards 3 points.

Graphic imitation of the effects of the visual prospect

(see also perspective graphics)

The mathematical expression exact of these principles is obviously very complex. It is it more especially as one considers the properties of solids and not space point by point. Even concepts seemingly simple as the “distance from one object to the eye” or “solid angle” of a surface in space appear particularly difficult even inapplicable as soon as one tries to employ them with rigor. This explains that the majority of the charts which seek to give an account of the visual prospect of it are more or less realistic approximations (see Photoréalisme), even conventions which give up an aspect or another of reality.

In the imagery of synthesis, these difficulties do not exist because of the way of calculating point by point, itself made possible of the operational power of the modern computers. The prospect is simulated by the photo-realistic software of way at every moment, so that it seems “self-explanatory”. In fact, the prospect is the only component of the creative process of an image which is not built by the graphic designer, but posed by the software. By making it “turn” or while turning around him in real-time according to laws of transformation which escape to him, the graphic designer with the illusion to generate a three-dimensional solid, a “figure 3D” - whereas it has a two-dimensional screen in front of the eyes.

to see too

Optical
descriptive Geometry

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