Vol.3, No 2, 2005 pp. 195 - 207
UDC 514.752.2:681.3.06(045)=20

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PLANE SECTION OF CONE AND CYLINDER
IN COMPUTER GEOMETRY
Ratko Obradović, Zoran Milojević
University of Novi Sad, Faculty of Technical Sciences, 21121 Novi Sad,
Serbia and Montenegro

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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 ? is a plane normal to a frontal plane. For determination of intersecting points of intersecting curve between the plane ? 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 ? 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.
Key words: quadrics, plane section, computer geometry

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RAVAN PRESEK KONUSA I CILINDRA
U KOMPJUTERSKOJ GEOMETRIJI U ovom radu je formiran matematički aparat za određivanje ravnog preseka konusa i cilindra. Korišćenjem nacrtno geometrijskog pristupa određene su konturne izvodnice ovih kvadrika pri čemu je iskorišćena činjenica da se tangente kruga afino preslikavaju u tangente elipse. Na ovaj način površi su prikazane preko konturnih izvodnica (tangenti bazisne elipse u kosoj projekciji) čime su dobile realističan izgled. Ravan koja seče površ je zračna ravan ? koja je upravna na frontalnicu. Za određivanja tačaka presečne krive date ravni i kvadrike korišćen je pramen pomoćnih ravni koji sadrži vrh kvadrike. Svaka pomoćna ravan iz posmatranog pramena seše površ po dvema izvodnicama koje opet prodiru zadatu ravan ? u dve tačke. Postavljanjem dovoljnog broja pomoćnih ravni presečna kriva se dobija kao skup parova tačaka za sve pomoćne ravni, a sama kriva se crta osvetljavanjem ovog skupa tačaka na grafičkom ekranu.