• Semester 1, position 3

The objectives of this course are to acquire knowledge for comprehending, constructive processing and modeling of the objects of three-dimensional space. Practicing and mastering the basic operations and methods for efficient geometric analysis and synthesis of various abstract and concrete forms can be considered as the study program objective. Moreover, particularly important goal of this course is the theoretical preparation and development of creative skills for effective use of modern software packages for three-dimensional modeling and design.

Mastering the program, students obtain and improve ability to use geometric operations and methods for creative observation and modeling of three-dimensional space. In addition, the adoption of the scheduled curriculum, a student acquires the knowledge and skills for effective visual communication in engineering practice.

Theoretical course includes: 1) Learning the principles of the Constructive geometry and graphics (CGG), introducing the concepts of projection, orthogonal projections, coordinate systems and spatial coordinates, defining elements, relations, and CGG postulates; explanation of the basic CGG methods; 2) Application of the CGG methods; treatment of classical positional and metric problems; 3) The constructive geometrical analysis and treating of a plane in arbitrary position; the plane revolution, the oblique plane figures; 4) The constructive geometrical analysis and treating of an objects on an incline plane, the spatial positional and metric problems; 5) The polyhedron truncation (truncation of pyramids and prisms), learning the basic principles and constructive geometrical methods of developing surfaces (the net); building the concrete models of truncated prisms and pyramids;

Practical lectures are conducted through a cycle of exercise consisting of 6 auditory and 6 independent individual exercises. Auditory exercises students accomplish in college with the help of assistants, and independent practice through homework. The exercises are performed with the following contents: 1. The orthogonal projections delineation, training the use of spatial coordinates, three-dimensional coordinate system and the main issues and postulates of CGG; 2. Practising the basic methods of CGG (transformation and revolution) 3. Application of CGG methods (the measure of lengths, angles, area); practicing the classical positional and metric problems; 4. The constructive geometrical analysis and treating of a plane in arbitrary position, practicing the procedures of geometric plane revolution and modeling of geometrical figures on an oblique plane; 5. Spatial positional and metric problems; constructive analysis and synthesis of geometrical objects on an incline plane; 6. Truncation of pyramids and prisms; practicing the methods and procedures of surface developing (the net) and modeling of a truncated pyramids and prisms;

The course of Constructive geometry and graphics is mandatory for all students.

Handbook for practice: A constructive geometry in the graphics - PRACTICUM; authors: Dr. Branislav Popkonstantinović, Mr. Zoran ate, Mr. Rasa Andrejevic, Goran Šiniković; Faculty of Mechanical Engineering, Belgrade 2010. Note: The textbook and handbook are available in printed form.

Total assigned hours: 30

New material: 8
Elaboration and examples (recapitulation): 4

Auditory exercises: 6
Laboratory exercises: 0
Calculation tasks: 6
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 2
Test: 0
Final exam: 4

Activity during lectures: 0
Test/test: 40
Laboratory practice: 0
Calculation tasks: 30
Seminar paper: 0
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 30

Solomon Woolf: An Elementary Course In Descriptive Geometry, Merchant Books; 3rd edition, 2007; Практикум: Конструктивна геометрија и графика - практикум; аутори: Бранислав Попконстантиновић, Зорана Јели, Раша Андрејевић, Горан Шиниковић, Машински факултет у Београду, 2005.