Přístupnostní navigace
E-application
Search Search Close
Course detail
FSI-1KD-KAcad. year: 2025/2026
The constructive geometry course summarizes and clarifies basic geometric concepts, including basic geometric projections, and introduces students to some types of projections, their properties and applications. Emphasis is placed on orthogonal axonometry. The basics of plane kinematic geometry are also presented. A large part of the course is devoted to the representation of curves and surfaces of engineering practice and some necessary constructions such as plane sections and intersections.The constructions are complemented by modeling in Rhinoceros software.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
COURSE-UNIT CREDIT REQUIREMENTS: Draw up 2 semestral works (each at most 5 points), there is one written test (the condition is to obtain at least 5 points of maximum 10 points). The written test will be in the 9th week of the winter term approximately. At least 10 points is required. Active participation in the exercise is also required, which the teacher has the right to verify with the student's knowledge or his/her own notes on the topic being discussed.
FORM OF EXAMINATIONS: The exam has an practical and theoretical part. In a 90-minute practical part, students have to solve 3 problems (at most 80 points). The student can obtain at most 20 points for theoretical part.
RULES FOR CLASSIFICATION:1. Results from the practical part (at most 80 points)2. Results from the theoretical part (at most 20 points)
Final classification:0-49 points: F50-59 points: E60-69 points: D70-79 points: C80-89 points: B90-100 points: A
Aims
The aim of the course is to deepen spatial imagination, to introduce students to the principles of representation and important properties of some curves and surfaces. The aim of the course is to introduce students to the basics of the international language of engineers, i.e. descriptive geometry, so that they can then creatively apply this knowledge in professional subjects and in the use of computer technology.
Study aids
Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
specialization STG , 1 year of study, winter semester, compulsoryspecialization AIŘ , 1 year of study, winter semester, compulsoryspecialization SSZ , 1 year of study, winter semester, compulsory
Guided consultation in combined form of studies
Teacher / Lecturer
Syllabus
1. Conic sections, focal properties of conics, point construction of a conic, osculating circle, construction of a tangent from a given point, diameters and center of a conic2. kinematics, cyclic curves3. non-proper points (axioms, incidence, Euclid's postulate, projective axiom, geometric model of projective plane and projective space, homogeneous coordinates of proper and non-proper points, sum and difference), derivation of parametric equations of kinematic curves in the projective plane4. central, parallel projections and their properties (point, line, plane, parallel lines, perpendicular lines), collineation between planes, central collineation, axial affinity, basics of axonometry5. orthogonal axonometry - bases of solids and height6. orthogonal axonometry - solids and their sections7. helix construction in axonometry8. derivation of the helix parametric equation and its distribution9. helical surfaces10. Monge projection - the basics11. Monge projection - solids and their sections12. surfaces of revolution, derivation of parametric equations in projective space, construction of surfaces, cross-sections of rotation surfaces13. parametric and general equations of quadrics
Guided consultation
1. Rhinoceros - conic sections2. focal properties of conics, point construction of a conic, osculating circle, construction of tangent from a given point, diameters, and center of a conic3. - 4. kinematics, cyclic curves5. central, parallel projections and their properties (point, line, plane, parallel lines, perpendicular lines), collineation between planes, central collineation, axial affinity, basic axonometry6. orthogonal axonometry - bases of solids and height7. orthogonal axonometry - solids and their sections8. helix construction in axonometry9. derivation of the helix parametric equation and its distribution10. helical surfaces11. Monge projection - the basics12. Monge projection - solids and their cross-sections13. surfaces of revolution, derivation of parametric equations in projective space, construction of surfaces of revolution, cross-sections of surfaces
Attendance at the exercises is compulsory.