Course detail

Basics of descriptive geometry

FAST-BA91Acad. year: 2009/2010

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, Monge`s projection, orthogonal axonometry..

Language of instruction

Czech

Mode of study

Not applicable.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

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: Monge`s, orthogonal axonometry, basic problems and be able to solve simple 3D problems, display simple geometric solids and surfaces in each type of projection.

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.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

Course curriculum

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. Tangent line to ellipse from a point and parallel to a given direction.
Central and parallel projection. Perspective affinity, perspective collineation, examples.
3. Circle in affinity,Rytz`s construction, trammel construction.
Basic of solid geometry. Simple solids (pyramid, prism, cone, cylinder,sphere). System of basic problems.
4. Monge`s projection. Projection of point, line, plane. Basic problems.
5. Monge`s projection. Basic problems. Projection of circle.
6. Monge`s projection. The third projection plane. Constructional problems.
7. Monge`s projection. Projection of a solid.
8. Orthogonal axonometry. Basic problems. Construction in coordinate planes.
9. Orthogonal axonometry. Position problems.
10. Orthogonal axonometry. Projection of solid.

Work placements

Not applicable.

Aims

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: Monge`s, 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.

Specification of controlled education, way of implementation and compensation for absences

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

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B-P-C-SI Bachelor's

    branch VS , 1 year of study, winter semester, recommended course

  • Programme B-P-C-ST Bachelor's

    branch VS , 1 year of study, winter semester, recommended course

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer