Course detail

Constructive Geometry

FSI-1KDAcad. 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

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Pavel Štarha, Ph.D.

Department

Institute of Mathematics (ÚM)

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.

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 (CS)
Martišek, D. Počítačová geometrie a grafika, Brno: VUTIUM, 2000. ISBN 80-214-1632-7 (CS)
Paré, E. G. Descriptive geometry. 9th ed. Upper Saddle River, NJ, 1997. ISBN 00-239-1341-X. (EN)
Slaby, S. M. Fundamentals of three-dimensional descriptive geometry. 2d ed. New York: Wiley, c1976. ISBN 04-717-9621-2. (EN)
Urban, A. Deskriptivní geometrie, díl 1. - 2., 1978. (CS)

Recommended reading

Gorjanc, S. Plane Geometry. http://www.grad.hr/geomteh3d/radne_eng.html [online]. [cit. 2016-09-12]. (EN)

Classification of course in study plans

  • Programme B-ENE-P Bachelor's 1 year of study, winter semester, compulsory
  • Programme B-PRP-P Bachelor's 1 year of study, winter semester, compulsory

  • Programme B-ZSI-P Bachelor's

    specialization STI , 1 year of study, winter semester, compulsory

  • Programme B-STR-P Bachelor's

    specialization AIŘ , 1 year of study, winter semester, compulsory
    specialization KSB , 1 year of study, winter semester, compulsory
    specialization SSZ , 1 year of study, winter semester, compulsory
    specialization STG , 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. Cross sections, focal properties of conic sections, construction of conic sections, conjugate diameters of conic section.
2. Methods for mapping three-dimensional objects onto the plane - central and parallel projections. Introduction into the Monge's method of projection (the two picture protocol) - the orthogonal projection onto two orthogonal planes.
3. Monge's method: points and lines that belong to a plane, principal lines, horizontal and frontal lines.
4. Monge's method: rotation of a plane, circle in a plane. 3rd projection plane (profile projection plane).
5. Axonometric – basis
6. Axonometric – completion
7. Elementary surfaces and solids, cross sections
8. Solids and cross sections of the solids
9. Curves: Basics of projective geometry (points at infinity, axioms, incidence, projective axiom, geometric model of projective plane) kinematic geometry in the plane (trochoids). Rectification of the arc.
10. Helix: helical movement, points and tangent lines in Monge's method and axonometry.
11. Helical surfaces: helical movement of the curve, ruled (opened, closed, orthogonal, oblique) and cyclical surfaces.
12. Surfaces of revolution: derivation of parametric equations in projective space, surfaces of revolution construction, cross sections of the surfaces.
13. Developable surfaces: cylinder and right circular cone with cross-section curve.

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Pavel Štarha, Ph.D.

Syllabus

1.- 2. Rhinoceros 3D – Line, Plane, Circle, Polygon in 3D. A line perpendicular, conic sections, focal properties of conic sections
3.- 4. Monge's method
5.- 6. Axonometry
7.- 8. Elementary surfaces and solids, cross sections
9.- 10. Kinematic geometry in the plane, helix
11.- 12. Helical surfaces, Surfaces of revolution

Presence in the seminar is obligatory.