Frontal perspective

Frontal perspective (below) of a row of houses

In descriptive geometry, a frontal perspective is a special type of central projection (projection of an object with rays emanating from a point, the eye point, onto an image panel), in which essential parts of the object (e.g. a house front) are parallel to the image panel Lie level. Assuming three essential directions (length, width and height) of the object that are perpendicular to each other, only the straight lines perpendicular to the image table, the so-called contour lines , provide a vanishing point, and this is equal to the main point (see central projection ). That is why a frontal perspective is also called a perspective with a vanishing point . In the first example, the front of the house is even located directly in the panel and thus appears undistorted in the frontal perspective. If the front of the house were only parallel and not in the picture panel, then your picture in the frontal perspective would be a (scaled) picture similar to the original. The strength of a frontal perspective is the possibility of adding a spatial image to an existing elevation by choosing a suitable main point (vanishing point of all contour lines). This procedure is reminiscent of the preparation of a cavalier perspective (see axonometry ). A two vanishing point perspective makes a somewhat more harmonious impression (see central projection), as it does not emphasize one side of the object so much.

Frontal perspective of a house

Preparation of a frontal perspective

Frontal perspective of a house: specification and solution

The floor plan and elevation of a house , as well as the floor plan and elevation of the eye point O are given. The picture panel contains the front of the house (see specifications in the second picture, left). Since we want to integrate the elevation into the perspective image, we identify it as the main point . The horizon runs horizontally (parallel to the baseline of the house front = stand line) through the main point. The projections of all edges that run perpendicular to the house front have H as the vanishing point. Now only the length of the house (distance of the rear from the front) has to be constructed. For this we use one of the two distance points on the horizon. There are two horizontal straight lines which enclose an angle of with the image table . Their two vanishing points lie to the left and right of the main point at a distance d, the distance, and are therefore called distance points . We use the left distance point to project the length of the house from the base line onto the corresponding house edge on the side front. The triangle merges into the triangle (see picture) through the central projection . This completes the frontal perspective of the house. ${\ displaystyle \ pi}$ ${\ displaystyle O ''}$ ${\ displaystyle H}$ ${\ displaystyle h}$ ${\ displaystyle 45 ^ {\ circ}}$ ${\ displaystyle D}$ ${\ displaystyle A, B, C}$ ${\ displaystyle {\ overline {A}}, {\ overline {B}}, {\ overline {C}}}$

Note: The distance points are the measurement points of the contour lines (see reconstruction ).

Two more examples

Frontal perspective of a bridge, default
Frontal perspective of a bridge, solution

Frontal perspective of a bridge

Frontal perspective: grid for an interior

Frontal perspective of a room by Johann Erdmann Hummel , around 1820

Frontal perspective photography: Old Royal Naval College Chapel Interior, Greenwich, London, UK

In the example of the frontal projection of a bridge , circles must be projected. In the case of a central projection, a circle can merge into a circle or an ellipse or a hyperbola or a parabola or a segment. The hyperbola, parabola, and segment cases are special cases and generally rarely occur. But the case “image is an ellipse” also requires some effort, since a central projection is not a linear image, i. For example, the center of the circle does not merge into the center of the image ellipse. All the great efforts involved in depicting circles dissolve in a frontal perspective, in which circles appear only in the picture table or parallel to it (see bridge). Circles in the picture board are not distorted and circles parallel to the picture board are mapped into larger or smaller circles. Here, circle centers merge into circle centers and diameter into diameter. In the example of the bridge, too, the elevation is extended to a frontal projection. The distances between the railway sleepers are transferred with the distance point from the base line to the associated depth line. ${\ displaystyle D}$

The frontal perspective is also very well suited to depict interior spaces quickly and attractively. For this one selects the main point H, the base line s, a track of a side wall and an even subdivision of the base line and this vertical track. The purpose of the subdivision is to create a square grid for the floor and the side walls. First, you draw connections between the subdivision points on the base line / track and the main point. This results in the longitudinal straight lines of the grid on the floor and side walls. The longitudinal subdivision is obtained by projecting the subdivision of the base line from the distance point onto one or more longitudinal straight lines (depth lines) that have already been drawn. Which distance point (there are two: one to the left and one to the right of the main point at the distance of the distance) one chooses is in principle indifferent. You should choose the distance point that disturbs the image the least and provides the least “dragging cuts”. ${\ displaystyle D}$

literature

Fucke, Kirch, Nickel: Descriptive Geometry. Fachbuch-Verlag, Leipzig 1998, ISBN 3-446-00778-4 , pp. 232-236
Graf, Barner: Descriptive Geometry. Quelle & Meyer, Heidelberg 1961, ISBN 3-494-00488-9 , p. 266.

Web links

Descriptive geometry for architects (PDF; 1.5 MB). Script (Uni Darmstadt), pp. 96, 158, 197