Incision process

Representation of a house with a rectangular floor plan (below) and the elevation of a side wall (right) using the incision method

With the help of the incision process or rapid crack process , one can relatively easily and quickly produce clear images of spatial objects from two assigned cracks - floor plan and elevation - in descriptive geometry . The result is an axonometric picture. The advantage of the incision method compared to standard axonometry is that no coordinates of individual points have to be measured, multiplied by a factor and then entered into the axonometric image; rather, the picture is created by drawing two sets of parallels and the intersection of the straight lines assigned to them.

The incision process was introduced in 1937 by the Austrian mathematician Ludwig Eckhart under the name Schnellrissverfahren .

Description of the procedure

Principle of the incision process

Starting from two orthogonally assigned projections (cracks) of an object, proceed as follows:

1. You place the two cracks as you like (see below) in the drawing plane and
2. selects two different cutting directions and . ${\displaystyle {\vec {e}}_{1}}$ ${\displaystyle {\vec {e}}_{2}}$
3. Through the cracks of a point , a ray and are drawn in or in the direction. ${\displaystyle P',P''}$ ${\displaystyle P}$ ${\displaystyle {\vec {p}}_{1}}$ ${\displaystyle {\vec {p}}_{2}}$ ${\displaystyle {\vec {e}}_{1}}$ ${\displaystyle {\vec {e}}_{2}}$
4. The intersection of the two rays is the axonometric image of . ${\displaystyle {\vec {p}}_{1}\cap {\vec {p}}_{2}={\overline {P}}}$ ${\displaystyle P}$

Two of the three coordinate axes in the picture each point in one of the cutting directions and . The third axis (here:) results from cutting a point different from the origin on the axis to be constructed (see picture). ${\displaystyle {\vec {e}}_{1}}$ ${\displaystyle {\vec {e}}_{2}}$ ${\displaystyle {\overline {y}}}$

The justification of this method is based on the invariance of the partial ratio (on a straight line) with parallel projection .

The resulting image is generally an oblique parallel projection. In order to obtain an orthogonal projection, certain additional requirements must be met for the position of the cracks. See orthogonal axonometry .

Location of ground plan and elevation, cutting directions

favorable angles for the incision process

For a good visual effect, one should note the following angular ranges in the placement of ground plan and elevation: . ${\displaystyle 50^{\circ }<\alpha <90^{\circ };\ 5^{\circ }<\beta <\alpha ;\ \delta \approx \beta }$

literature

• Fucke, Kirch, Nickel: Descriptive Geometry. Fachbuch-Verlag, Leipzig 1998, ISBN 3-446-00778-4 .
• Cornelie Leopold: Geometric Basics of Architectural Representation. Verlag W. Kohlhammer, Stuttgart 2005, ISBN 3-17-018489-X .
• Wolf-Dieter Klix: Constructive Geometry. Fachbuch-Verlag, Leipzig, ISBN 3-446-21566-2 , p. 86 ( Google Books ).

Web links

• Descriptive geometry for architects (PDF; 1.5 MB). Script (Uni Darmstadt)

Individual evidence

1. ↑ K. Strubecker : Lectures of the Descriptive Geometry. Vandenhoeck & Ruprecht, Göttingen 1967, p. 121.