Department of Geometry


Academic staff:

 

Study Course Semester Hours ECTS
Undergraduate University Study of Civil Engineering Descriptive Geometry
Applied Geometry
I.
 

II.
30+30
30+30
5,0
5,0
Undergraduate University Study of Architecture and Urban Planning Principles of Projections I
Principles of Projections II 
I.
 

II.
30+30
30+30
5,0
5,0
Undergraduate University Study of Geodesy and Geoinformatics Computer Geometry   II. 30+30 5,0
Undergraduate Professional Study of Civil Engineering Descriptive Geometry   II. 30+30 5,0

 

 

Learning Outcomes:

Undergraduate university study of Civil Engineering
Descriptive Geometry 
- a student will be able to:
-    identify, classify and constructconics using perspective collineation and affinity;
-    solve 2D and 3D problems using Monge's projection;
-    construct 3D images of objects given by Monge's projection using axonometric projection;
-    construct intersections of surfaces and planes;
-    recognize, analyze and comment the intersection curve of a surface and a plane;
-    distinguish various conics as intersection curves;
-    use and apply projection methods to solve civil engineering problems.

Applied Geometry - a student will be able to:
-    analyze and construct intersections of two solids (coni, cylindersand spheres);
-    solve 2D and 3D problems using the orthogonal projection;
-    analyze topographic maps and by orthogonal projection draw cuts and fills along a level or grade road and dam;
-    draw profiles of roads and calculate fill volumes;
-    solve roof structures (simple roofs and roofs with external/internal barriers) of the building using the roof planes method;
-    solve 2D and 3D problems using central projection (perspective);
-    recognize the laws of projections and apply them accordingly to solve different constructive problems.

 

Undergraduate University Study of Architecture and Urban Planning

Principles of Projections I 
- a student will be able to:

  • Define, classify and construct second-order curves (conics) using mapping
  • Parallel projection of 3D spatial elements onto a 2D medium according to applicable principles
  • Visualise, in a 3D space, the objects rendered by parallel projections onto a 2D medium, regardless of the tools used
  • Using Monge’s method of projections, construct 0D, 1D, 2D and 3D objects in general and special positions with regard to projection planes Π1, Π2, Π3
  • Using axonometric methods, construct a 3D image of an object assigned using Monge’s pairs of projections
  • Predict and construct planar sections of second-order surfaces using parallel projection methods
  • Apply the definitions and classification of conics to the defining and constructing of planar sections of assigned surfaces and develop the mantle from a surface, with a section curve, regardless of the visualisation tools used
  • Use and apply the principles of different projection methods in the technical sciences, create drawings and solve construction assignments using dynamic geometry software


Principles of Projections II - a student will be able to:

  • Using the plane method (orthogonal and general parallel projection), construct an intersection curve for two second-order surfaces
  • Construct an intersection curve for two surfaces of revolution, for construction purposes
  • Using orthogonal projection, construct the own and cast shadows of various objects and shadows cast into hollow objects
  • Apply the contour-based method to (access) road design
  • Apply central projection and the corresponding principles to the construction of 0D, 1D, 2D and 3D objects in general and special positions relative to the plane of projection
  • Using central projection, construct solids with bases in the general and horizontal plane
  • Apply several methods to the construction of natural perspective renderings of objects specified using Monge’s projection
  • Construct the own and cast shadows of various objects in perspective
  • Identify the principles of various methods of projection and apply them to construction assignments, regardless of the visualisation tools used
  • Create drawings and solve construction assignments using dynamic geometry software

 

Undergraduate University Study of Geodesy and Geoinformatics
Computer Geometry
- a student will be able to:
-    identify, classify and construct conics using perspective collineation and affinity;
-    solve 2D and 3D problems using Monge's projection;
-    solve 2D and 3D problems using the orthogonal projection;
-    recognize, analyze and comment the intersection curve of a surface and a plane;
-    distinguish various conics as intersection curves;
-    analyze topographic maps and by orthogonal projection draw cuts and fills along a level or grade road;
-    recognize the laws of projections and apply them accordingly to solve problems in geodesy;
-    draw and solve constructive tasks using computer programs of dynamic geometry.

 

Undergraduate professional study of Civil Engineering
Descriptive Geometry
- a student will be able to:
-    solve 2D and 3D problems using Monge's projection;
-    construct 3D images of objects given by Monge's projection using axonometric projection;
-    solve roof structures (simple roofs and roofs with external/internal barriers) of the building using the roof planes method; 
-    describe the orthogonal projection and solve 2D problems;
-    analyze topographic maps and by orthogonal projection draw cuts and fills along a level or grade road;
-    recognize the laws of projections and apply them accordingly to solve civil engineering problems;
-    draw and solve constructive tasks using computer programs of dynamic geometry.