Constructive Geometry (FSI-1KD)

Academic year 2025/2026
Supervisor: doc. Ing. Pavel Štarha, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
 
Learning outcomes and competences:
 
Prerequisites:
 
Course contents:

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.
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:
 
Controlled participation in lessons:
 
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Lecture

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

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.
Literature - fundamental:
1. Borecká, K. a kol. Konstruktivní geometrie (2. vydání), Akademické nakladatelství CERM, Brno, 2006. ISBN 80-214-3229-2
2. Martišek, D. Počítačová geometrie a grafika, Brno: VUTIUM, 2000. ISBN 80-214-1632-7
4. Paré, E. G. Descriptive geometry. 9th ed. Upper Saddle River, NJ, 1997. ISBN 00-239-1341-X.
5. Slaby, S. M. Fundamentals of three-dimensional descriptive geometry. 2d ed. New York: Wiley, c1976. ISBN 04-717-9621-2.
6. Urban, A. Deskriptivní geometrie, díl 1. - 2., 1978.
Literature - recommended:
2. Gorjanc, S. Plane Geometry. http://www.grad.hr/geomteh3d/radne_eng.html [online]. [cit. 2016-09-12].
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-ENE-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory 1 1 W
B-PRP-P full-time study --- no specialisation -- Cr,Ex 5 Compulsory 1 1 W
B-ZSI-P full-time study STI Fundamentals of Mechanical Engineering -- Cr,Ex 5 Compulsory 1 1 W
B-STR-P full-time study AIŘ Applied Computer Science and Control -- Cr,Ex 5 Compulsory 1 1 W
B-STR-P full-time study KSB Quality, Reliability and Safety -- Cr,Ex 5 Compulsory 1 1 W
B-STR-P full-time study SSZ Machine and Equipment Construction -- Cr,Ex 5 Compulsory 1 1 W
B-STR-P full-time study STG Manufacturing Technology -- Cr,Ex 5 Compulsory 1 1 W