Course Details

Descriptive geometry

Academic Year 2023/24

GA06 course is part of 1 study plan

​ B-P-C-GK / GI Winter Semester 1st year

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). Stereography projection.

Course Guarantor

Mgr. et Mgr. Jan Šafařík, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Objective

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. Stereography projection.

Knowledge

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. Stereography projection.

Syllabus

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. Linear perspective projection.

12. Stereography projection.

13. Stereography projection.

Prerequisites

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

Language of instruction

Czech

Credits

6 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

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/271676

Lecture

13 weeks, 3 hours/week, elective

Syllabus

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. Linear perspective projection.

12. Stereography projection.

13. Stereography projection.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

1. Focal properties of conics.

2. Perspective collineation, perspective affinity. Constructing an ellipse based on affinity.

3. Collinear image of a n-gonal and a circle.

4. Coted projection.

5. Coted projection. Aplications.

6. Monge´s projection.

7. Monge´s projection. Sphere. Test.

8. Orthogonal axonometry.

9. Central projection.

10. Linear perspective.

11. Test. Linear perspective.

12. Linear perspective. Vertical picture, reconstruction of the elements of internal orientation.

13. Stereography projection. Seminar evaluation.