Academy of Technical and
Art Applied Studies Belgrade

Descriptive Geometry with Central Projection Course code: NACP | 6 ECTS credits

Basic information
Level of Studies: Undergraduate applied studies
Year of Study: 1
Semester: 1
Requirements:
Goal: The objective of this course is to enable students to master space, using the drawing in studying geometric shapes, to learn the precision of presentation and perception, as well as to create full spatial image about the shapes shown in the drawing through the appropriate geometrical analysis.
Outcome: Surveying in geodesy and the results of the measurements require understanding of space in all its segments while studying this coursethroughusage of different design methods in the educational process improves visual perception.
Contents of the course
Theoretical instruction:
  1. Introduction to descriptive geometry, center of projecting, projectionraysand projection plane. Orthogonal projection, coordinate trihedron, octants.
  2. Projection of a point, straight lineand line segment.
  3. Plane, special positions of a plane. Point and straight line in a plane.
  4. Oblique projection. Point, straight line, plane.Regular polyhedra - tetrahedron, hexahedron, octahedron, icosahedron.
  5. Transformation and rotation.
  6. Metric tasks - constructing spatial shapes in an arbitrary position.
  7. Collinear and affine relations. Plane intersections of solids.
  8. Sphere, point on a sphere, intersection of straight line the sphere, intersection of a sphere and plane.
  9. Conical intersections. Intersection of cone ellipses, parabola and hyperbole.
  10. Dimensional projection. Point, straight line and plane in dimensional projection.
  11. Solutions for a plateau and road. Design of cuttings and fills.
  12. Introduction to central projection – basic concepts. Projection of a point, vanishing point, intersection of a straight line throughpicture plane and the angle towardpicture plane.Intersections through the real projective plane. Mutual position of straight lines.
  13. Plane, trace and vanishing point detection. Point and straight line on a plane. Flat figures, division and transfer of a line segment in perspective. Scale vanishing point. Perspective of a square, hexagon, circle. Networks of straight figures. Solids in perspective – cube, prism, pyramid, cone ...
  14. Perspective of a structure – selection of the position of line of sight and picture plane. Perspective from an angle. Perspective cartographic projections. Classification of cartographic projections. Orthographic and stereographic projections.
Practical instruction (Problem solving sessions/Lab work/Practical training):
  1. Solving problems from the field discussedduring lectures, training.
Textbooks and References
Number of active classes (weekly)
Lectures: 3
Practical classes: 2
Other types of classes: 0
Grading (maximum number of points: 100)
Pre-exam obligations
Points
activities during lectures
0
activities on practial excersises
0
seminary work
0
colloquium
0
Final exam
Points
Written exam
0
Oral exam
0