Circle of vision

Elements of a central projection

Central projection of a row of houses with visual circle (red, inside) and distance circle (green, outside)

Central projection of the row of houses with visual circle (distance increased by 50%)

The viewing circle is in the descriptive geometry of the circle of intersection of the view cone (see Fig. U.) With the image plane . The visual circle describes the area of an image that is perceived by an observer without being distorted.

description

When looking at a three-dimensional scene or an image, the human eye perceives those things clearly and undistorted when a fixed point is fixed, which are in a cone (the cone of vision ) whose half- opening angle is approximately . If you look at an image in central projection , for example a photograph , you get the best image effect, that is, the image replaces the 3D scene when the viewer ${\ displaystyle 30 ^ {\ circ}}$

looking at the picture with one eye
this eye is in the eye point (the projection center ) and
the eye fixes the main point (the plumb point from the eye point on the image board ).

During this visual process, everything that lies within the visual circle is perceived clearly and without distortion . The circle of vision is the intersection of the cone of vision with the image table (see picture). The center of the visual circle is the main point and its radius is

{\ displaystyle r_ {s} = \ tan 30 ^ {\ circ} \ cdot d \ approx 0.58 \ cdot d}

.

Practical meaning

It is unlikely that when viewing an image, the eye will be positioned exactly in the eye point of the central projection. This means that the observer can usually perceive parts of the scene that are outside the visual circle and therefore appear distorted (see example row of houses). To avoid this, you can either omit (hide) all objects or parts of the object that are outside the visual circle, or change the eye point and the main point so that the entire scene is within the visual cone and thus the image is within the secular circle. In the example of the row of houses, with a fixed image table and fixed main point, the eye point was changed by increasing the distance.

In practice , however, the image will not be cropped by a circle, but by a square with vertical and horizontal sides and an H as the center. This means that a pyramid of vision (instead of a cone of vision ) is used to limit the object.

Relationship to the distance circle

The distance circle is related to the visual circle . The distance circle of a central projection is the circle with the center in the main point (like the visual circle), which has the distance as radius (see picture, green circle). The distance circle thus provides direct information about the numerical value of the distance. The distance circle can be imagined as the intersection of a cone with half the opening angle with the illustration. ${\ displaystyle d}$ ${\ displaystyle 45 ^ {\ circ}}$

literature

Rudolf Fucke, Konrad Kirch, Heinz Nickel: Descriptive Geometry. Fachbuch-Verlag, Leipzig 1998, ISBN 3-446-00778-4 .
Ulrich Graf, Martin Barner: Descriptive Geometry. Quelle & Meyer, Heidelberg 1961, ISBN 3-494-00488-9 , pp. 293, 266.
C. Leopold: Geometric Basics of Architectural Representation. Verlag W. Kohlhammer, Stuttgart 2005, ISBN 3-17-018489-X , p. 233.

Web links

Diagram design (PDF; 15.7 MB) Institute for Representation and Design at the University of Stuttgart