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.
Supervisor
Department
Learning outcomes of the course unit
Prerequisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
Czech
Aims
Specification of controlled education, way of implementation and compensation for absences
The study programmes with the given course
Programme B-ENE-P: Energy, Bachelor's
branch ---: no specialisation, 5 credits, compulsory
Programme B-PRP-P: Professional Pilot, Bachelor's
branch ---: no specialisation, 5 credits, compulsory
Programme B-STR-P: Engineering, Bachelor's
branch AIŘ: Applied Computer Science and Control, 5 credits, compulsory
Programme C-AKR-P: , Lifelong learning
branch CZS: , 5 credits, elective
Programme B-STR-P: Engineering, Bachelor's
branch KSB: Quality, Reliability and Safety, 5 credits, compulsory
Programme B-STR-P: Engineering, Bachelor's
branch SSZ: Machine and Equipment Construction, 5 credits, compulsory
Programme B-STR-P: Engineering, Bachelor's
branch STG: Manufacturing Technology, 5 credits, compulsory
Programme B-ZSI-P: Fundamentals of Mechanical Engineering, Bachelor's
branch STI: Fundamentals of Mechanical Engineering, 5 credits, compulsory
Type of course unit
Lecture
26 hours, optionally
Syllabus
1. Conic sections, focal properties of conic sections, pointwise construction of a conic, osculating circles, construction of a tangent from a given point, diameters and center of a conic, conjugate diameters
2. Analytic geometry in the plane and in space (problems involving lines and planes, classification of conic sections)
3. Kinematics, cyclic curves
4. Central and parallel projection and their properties (point, line, plane, parallel lines, perpendicular lines), collineations between planes, central collineation, axial affinity, ideal points (projective axiom, homogeneous coordinates of proper and ideal points), derivation of parametric equations of kinematic curves in the projective plane
5. Basics of axonometry, orthographic 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. analytical geometry
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.