A presentation method of students’ assignment in geometry-intersection of two surfaces of second order

Abstract

There are two courses concerning geometric topics in the freshman studies at the Faculty of Civil Engineering in Belgrade: Descriptive Geometry for civil engineers and Computational Geometry, for geodetic engineers. In the curriculum of Descriptive Geometry course students are elaborating the topic – intersections of two surfaces of second order (cone and cylinder, two cones, two cylinders, etc.) through tasks in oblique projection, drawing manually. In the other, Computational Geometry course, students are solving the same geometric tasks by applying Boolean operations on 3D solid models of geometric primitives in Auto CAD software. In this paper the combination of these two methods, i.e. drawing procedures will be presented. The main problem in students' understanding of geometric procedures concerns visualization of 3D objects from 2D images. The authors created unconventional presentation of their geometric assignment provided in AutoCAD software in which 2D drawings (orthographic and oblique projections) and 3D models are united as tools for mastering the topic - intersections of two surfaces of second order - cone and cylinder. The consecutive "steps" of the drawing procedure i.e. geometric solution are conducted by layer control, parallel in 2D and 3D Auto CAD's environment. The unusual task setting is in the oblique projection, in which given direction of projection ray is parallel to the axis of a cylinder. Several examples of intersection curve are presented in two variations of task settings. Elaboration of such geometric task intended to be a contribution to the collection of solved tasks available for students' use in the website of the Faculty of Civil Engineering in Belgrade.