# Horizontal and Slope Lines

Téma:
Geometrie

## The Slope and Contour curve

The contour lines (or curves) of a surface are the sections of this surface by the horizontal planes (i.e. perpendicular to the vertical direction). The contour lines﻿ of a plane are called horizontal (principal) lines. Contours are one of several common methods used to denote elevation or altitude and depth on maps. Contour lines﻿ of topographic surface are closed curves surrounding summits or immits. Contour lines﻿ at surface of equal slope (plane, cone,...) are equidistant. The slope lines ( = lines of the steepest descent) cut at right angles the contour lines; and this property applies also to the top view projection.

## Horizontal and slope lines in a plane

Plane is given by points GHI on the cube. Horizontal projection plane is blue face of a cube, frontal projection plane is red face. The base (ground) line x12 is intersection line of projection planes, i.e.. Trace lines of the planes n, p are lines where the plane meets the planes of projections, i.e. and .
• Horizontal line h of a plane is parallel to the blue face.
• The line of steepest descent s (=slope line) is perpendicular to the horizontal line h. This line determines the slope angle of the plane. The right angle between lines s and h has true size in top view, i.e. - tool .

## Geotest 4136

In given point A of plane α construct the first steepest line s (i.e. both projections s1, s2). A horizontal line h and frontal line f of the plane are given. (GeoTest)
Solution: First slope line s is perpendicular to horizontal line h in top view. Choose arbitrary point and determine auxiliary first slope line as passing through a point H. First slope line is perpendicular to horizontal line in top view. Lines of steepest descent are mutually parallel, . Step 2: Arbitrary , top view of auxiliary first slope as Steps 3, 4: Front view of intersection points H, F . Step 5: Front view of auxiliary slope line as = H2F2. Step 6: Slope line s is parallel with auxiliary slope line as in both views .

## Geotest 4120

Construct a line of the steepest descent (both projections s1, s2) in the point A of given plane α orthogonal to the vertical plane of projection. The trace n of the plane α is given (GeoTest).