Course detail
Constructive Geometry
FSI-1KD Acad. year: 2025/2026 Winter semester
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
Czech
Number of ECTS credits
5
Supervisor
Department
Entry knowledge
The students have to be familiar with the fundamentals of geometry and mathematics at the secondary school level.
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: F
50-59 points: E
60-69 points: D
70-79 points: C
80-89 points: B
90-100 points: A
Attendance at seminars is required. The way of compensation for an absence is fully at the discretion of the teacher.
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.
Students will acquire the basic knowledge of three-dimensional descriptive geometry necessary to solve real life situations in various areas of engineering.
The study programmes with the given course
Programme B-ENE-P: Energy, Bachelor's, compulsory
Programme B-PRP-P: Professional Pilot, Bachelor's, compulsory
Programme B-STR-P: Engineering, Bachelor's
specialization AIŘ: Applied Computer Science and Control, compulsory
Programme B-STR-P: Engineering, Bachelor's
specialization KSB: Quality, Reliability and Safety, compulsory
Programme B-STR-P: Engineering, Bachelor's
specialization SSZ: Machine and Equipment Construction, compulsory
Programme B-STR-P: Engineering, Bachelor's
specialization STG: Manufacturing Technology, compulsory
Programme B-ZSI-P: Fundamentals of Mechanical Engineering, Bachelor's
specialization STI: Fundamentals of Mechanical Engineering, compulsory
Type of course unit
Lecture
26 hours, optionally
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 conic
2. kinematics, cyclic curves
3. 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 plane
4. central, parallel projections and their properties (point, line, plane, parallel lines, perpendicular lines), collineation between planes, central collineation, axial affinity, basics of axonometry
5. orthogonal axonometry – bases of solids and height
6. orthogonal axonometry – solids and their sections
7. helix construction in axonometry
8. derivation of the helix parametric equation and its distribution
9. helical surfaces
10. Monge projection – the basics
11. Monge projection – solids and their sections
12. surfaces of revolution, derivation of parametric equations in projective space, construction of surfaces, cross-sections of rotation surfaces
13. parametric and general equations of quadrics
Computer-assisted exercise
26 hours, compulsory
Syllabus
1. Rhinoceros – conic sections
2. focal properties of conics, point construction of a conic, osculating circle, construction of tangent from a given point, diameters, and center of a conic
3. – 4. kinematics, cyclic curves
5. central, parallel projections and their properties (point, line, plane, parallel lines, perpendicular lines), collineation between planes, central collineation, axial affinity, basic axonometry
6. orthogonal axonometry – bases of solids and height
7. orthogonal axonometry – solids and their sections
8. helix construction in axonometry
9. derivation of the helix parametric equation and its distribution
10. helical surfaces
11. Monge projection – the basics
12. Monge projection – solids and their cross-sections
13. 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.