Academic staff:

- Maja Andrić Ph.D., Full Professor - Head of Department
- Neda Lovričević Ph.D., Associate Professor
- Nikolina Ratković Rubić, Assistant
- Dominka Tadić, Assistant

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 Π
_{1}, Π_{2}, Π_{3} - 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.