Course Details

# Basics of Descriptive Geometry

VAC001 course is part of 2 study plans

stud.semestr.null 1st year

BPC-VP Winter Semester 1st year

Euclidean constructions in plane, identical and similarity transforms in plane, construction of ellipse by focus properties, basics of solid geometry, basics of parallel and central projection, perspective affinity, perspective collineation, circle in affinity, coted projection, orthogonal axonometry.

Course Guarantor

Mgr. et Mgr. Jan Šafařík, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Objective

Students should be able to construct: Euclidean constructions in plane, identical and similarity transforms in plane, ellipse by focus properties, understand the principles of perspective affinity, perspective collineation, using such properties in solving problems, understand and get the basics of projection: coted projection, orthogonal axonometry. They should develop 3D visualization and be able to solve simple 3D problems, display simple geometric solids and surfaces in each type of projection.

Knowledge

The students should be able to construct ellipse by focus properties, the principles of perspective affinity, perspective collineation. They will get the basics of projection: coted projection, orthogonal axonometry, basic problems and be able to solve simple 3D problems, display simple geometric solids and surfaces in each type of projection.

Syllabus

1. Constructions of basic figures in plane (euclidean constructions in plane, identical and similarity transforms). Extended Euclidean space. Construction of ellipse by focus properties.

2. Central and parallel projection. Perspective affinity, perspective collineation, examples.

3. Circle in affinity. Basic of solid geometry. Simple solids (pyramid, prism, cone, cylinder,sphere). System of basic problems. Coted projection

4. Coted projection.

5. Coted projection. Projection of circle.

6. Coted projection. Constructional problems.

7. Coted projection. Projection of a solid.

8. Orthogonal axonometry. Basic problems.

9. Orthogonal axonometry. Position problems.

10. Seminar evaluation.

Prerequisites

Basic knowledge of planar and 3D geometry as taught at secondary schools and basic skills of work with a ruler and pair of compasses.

Language of instruction

Czech

Credits

2 credits

Semester

winter

Forms and criteria of assessment

course-unit credit

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/252920

Lecture

13 weeks, 2 hours/week, elective

Syllabus

1. Constructions of basic figures in plane (euclidean constructions in plane, identical and similarity transforms). Extended Euclidean space. Construction of ellipse by focus properties.

2. Central and parallel projection. Perspective affinity, perspective collineation, examples.

3. Circle in affinity. Basic of solid geometry. Simple solids (pyramid, prism, cone, cylinder,sphere). System of basic problems. Coted projection

4. Coted projection.

5. Coted projection. Projection of circle.

6. Coted projection. Constructional problems.

7. Coted projection. Projection of a solid.

8. Orthogonal axonometry. Basic problems.

9. Orthogonal axonometry. Position problems.

10. Seminar evaluation.