# Sveučilište u Splitu - Fakultet građevinarstva, arhitekture i geodezijeUniversity of Split - Faculty of Civil Engineering, Architecture and Geodesy

## Department of Geometry

 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.