Course detail

# Descriptive geometry

Focal properties of conics. Perspective affinity, affine image of a circle, perspective colineation, colinear image of a circle. Coted projection. Projecting on two perpendicular planes. Basics of orthogonal axonometry, central projection. Linear perspective (perspective of an object using relative and free methods). Basics of photogrammetry. Vertical picture. Stereography projection.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Students should be able to construct conics from the properties of their foci, perspective colineation, perspective affinity. Understand the basics of projections: Monge`s, orthogonal axonometry, central projection and perspective projection. Display the basic geometric bodies in each projection. Construct sections of bodies. Project a building using a perspective projection. Vertical picture, reconstruction of the elements of internal orientation.

Prerequisites

Basic knowledge of planar and 3D geometry as taught at secondary schools.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

Lectures
1. Extended Euclidean space. Perspective affinity, collineation.Curve affine to a circle.
2. Curve in collineation to a circle. Geodetic curve, developable surfaces. Coted projection.
3. Coted projection. Plane section af a ball.
4. Coted projection. Straight line and plane of a given slope. Special construction.
5. Monge`s projection.
6. Monge`s projection. Sphere. Orthogonal axonometry.
7. Orthogonal axonometry.
8. Central projection.
9. Linear perspective projection.
10. Linear perspective projection.
11. Reconstruction of the elements of internal orientation.
12. Stereography projection.
13. Stereography projection.

Aims

Know how to construct conics from the properties of their foci. Understand and apply the principles of perspective colineation and perspective affinity. Understand the basics of Monge`s projection and orthogonal axonometry, central projection and perspective projection. Display basic geometric bodies in each projection. Construct sections of bodies by a plane. Constructions in a plane in central projection and the projection of a simple body. Project a building using a perspective projection. Understand the geometric principles of photogrammetry. Vertical picture, reconstruction of the elements of internal orientation.

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.

Classification of course in study plans

• Programme B-K-C-GK Bachelor's

branch GI , 1. year of study, winter semester, 6 credits, compulsory

• Programme B-P-C-GK Bachelor's

branch GI , 1. year of study, winter semester, 6 credits, compulsory

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Exercise

26 hours, compulsory

Teacher / Lecturer

eLearning