Plane section of cone and cylinder in computer geometry

Abstract

In this paper a mathematical apparatus for determination of plane section of cone and cylinder was formed. By using the descriptive geometric approach the contour lines of these quadrics were determined. The fact that the tangent lines of a circle could be transformed to the tangent lines of an ellipse using affinity was employed. In that way surfaces are represented by contour lines (tangent lines of basic ellipse in oblique projection) and thus they have a realistic view. Intersecting plane α is a plane normal to a frontal plane. For determination of intersecting points of intersecting curve between the plane α and the quadrics, the lock of auxiliary planes, which contain the vertex of quadrics, was used. Each auxiliary plane from the observed lock intersect the surface in two lines which intersect the given plane α in two points. By using a sufficient number of auxiliary planes the intersecting curve as a set of pairs of points for all auxiliary planes is determined and the intersecting curve was drawn by lightening of these pairs of points on the graphical screen.

Keywords

• quadrics
• plane section
• computer geometry