Course detail

Constructive Geometry

FSI-1KD-AAcad. 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 Monge projections and 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

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Pavel Štarha, Ph.D.

Department

Institute of Mathematics (ÚM)

Offered to foreign students

Of all faculties

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.

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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Borecká, K. a kol. Konstruktivní geometrie (2. vydání), Akademické nakladatelství CERM, Brno, 2006. ISBN 80-214-3229-2
Martišek, D. Počítačová geometrie a grafika, Brno: VUTIUM, 2000. ISBN 80-214-1632-7
Medek, V., Zámožík, J. Konštruktívna geometria pre technikov, Bratislava: Alfa, 1978.
Paré, E. G. Descriptive geometry. 9th ed. Upper Saddle River, NJ, 1997. ISBN 00-239-1341-X.
Slaby, S. M. Fundamentals of three-dimensional descriptive geometry. 2d ed. New York: Wiley, c1976. ISBN 04-717-9621-2.
Urban, A. Deskriptivní geometrie, díl 1. - 2., 1978.

Recommended reading

Borecká, K. a kol. Konstruktivní geometrie (2. vydání), Akademické nakladatelství CERM, Brno, 2006. ISBN 80-214-3229-2
Gorjanc, S. Plane Geometry. http://www.grad.hr/geomteh3d/radne_eng.html [online]. [cit. 2016-09-12].
Seichter, L. Konstruktivní geometrie

Classification of course in study plans

  • Programme B-STI-A Bachelor's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Pavel Štarha, Ph.D.

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 hod., compulsory

Teacher / Lecturer

doc. Ing. Pavel Štarha, Ph.D.

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.