FAST-GA06Acad. year: 2017/2018
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.
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.
Basic knowledge of planar and 3D geometry as taught at secondary schools.
Recommended optional programme components
Recommended or required reading
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
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.
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.