Surface line method

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Section cone-cylinder in three-panel projection : surface line method,
blue: cylinder (1st surface), green: cone (2nd surface), red: surface lines related to the construction of P and Q, purple: intersection curve
Construction of an ellipse as a plane section of a cone

The surface line method is a method of representing geometry to determine points of the intersection curve between a cylinder and a second surface (cylinder, cone, sphere, ...). The essential part is identical to the auxiliary level method . While the auxiliary levels can be freely selected with the auxiliary level method, the surface line method assumes an evenly distributed number of surface lines of the cylinder. For each surface line, an auxiliary plane is determined which contains the surface line and cuts simple curves (straight lines, circles) from the second surface. If the surface lines are cleverly chosen (see example), an auxiliary plane contains two surface lines at the same time, so that several points of the intersection curve can be constructed in plan and elevation using one auxiliary plane. If the surface lines are selected as in the example, then the surface lines 4 and 8 have the same floor plans as the surface lines 2 and 10 already drawn. For the intersection of the auxiliary plane through the surface lines 4 and 8, only the other intersection circle with the cone in base and Outlines can be drawn in order to determine further intersection points.

The surface line method can also be used if

  1. the second surface is a perpendicular circular cylinder . The circles of intersection then all have the same radius.
  2. the second face is a sphere . The sections of the sphere with a horizontal auxiliary plane are circles and also appear as circles in the plan.
  3. the second face is a torus with a horizontal guide circle. The sections of the torus with a horizontal auxiliary plane are circles and also appear as circles in the plan.
  4. the second face is an inclined plane . In this case , the intersection curve is an ellipse , the semi-axes of which, however, can easily be determined by drawing.
  5. the first surface is an inclined plane . Horizontal straight lines can be used as a substitute for the surface lines. The intersection curve is a conic section .
In the second picture the intersection curve is an ellipse. In this case, the main axes of the ellipses to be drawn can also be easily constructed in plan and elevation and the ellipses can then be approximated using the apex curvature circle method.
If the plane is steeper or even perpendicular, a parabola or hyperbola can be created as a sectional figure.

literature

  • Ulrich Kurz, Herbert Wittel: Böttcher / Forberg technical drawing. Springer-Vieweg, Wiesbaden 2014, ISBN 978-3-8348-1806-5 , p. 94.