Course Details

Constructive Geometry

Academic Year 2022/23

BAA013 course is part of 5 study plans

BPC-SI Summer Semester 1st year

BPC-MI Summer Semester 1st year

BPC-EVB Summer Semester 1st year

BPA-SI Summer Semester 1st year

BKC-SI Summer Semester 1st year

Perspective collineation and affinity,circle in affinity. Coted projection, Monge`s projection, topographic surfaces, theoretical solution of the roofs, orthogonal axonometry and linear perspective.

Course Guarantor

Mgr. Hana Halfarová, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Objective

Students should be able to construct conics using their focus properties, understand the principles of perspective colineation and affinity using such properties in solving problems, understand and get the basics of projection: Monge`s projection, orthogonal axonometry, and linear perspective. They should develop 3D visualization and be able to solve simple 3D problems, display simple geometric bodies and surfaces in each type of projection, their section with a plane and intercestions with a straight line. In a linear perspective, they should be able to draw a building. They should learn the basics of the theoretical solution of roofs and topographic surfaces.

Knowledge

Students should be able to construct conics using their focus properties, perspective colineation and affinity. Understand and get the basics of projection: coted, Monge`s projection, orthogonal axonometry, and linear perspective. They should be able to solve simple 3D problems, display the basic geometric bodies and surfaces in each projection, their section. In a linear perspective, they should be able to draw a building. They should be theoretically able to solve the roof and solve the location of the construction object in the terrain, both in coted projection.

Syllabus

1. Introduction - principles of parallel and central projection. Perspective collineation and affinity-basic properties.
2. System of basic problems, examples. Monge`s projection.
3. Monge`s projection.
4. Monge`s projection. Coted projection.
5. Coted projection.
6. Orthogonal axonometry.
7. Orthogonal axonometry. Basic parts of central projection.
8. Linear perspective.
9. Linear perspective.
10. Linear perspective. Topographic surfaces.
11. Topographic surfaces.
12. Theoretical solution of the roofs.
13. Theoretical solution of the roofs.

Prerequisites

Basics of plane and 3D geometry a stereometrie as taught at secondary schools.

Corequisites

Not required.

Language of instruction

Czech, English

Credits

5 credits

Semester

summer

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

To offer to students of all faculties

Course on BUT site

https://www.vut.cz/en/students/courses/detail/254565

Lecture

13 weeks, 2 hours/week, elective

Syllabus

1. Introduction - principles of parallel and central projection. Perspective collineation and affinity-basic properties.
2. System of basic problems, examples. Monge`s projection.
3. Monge`s projection.
4. Monge`s projection. Coted projection.
5. Coted projection.
6. Orthogonal axonometry.
7. Orthogonal axonometry. Basic parts of central projection.
8. Linear perspective.
9. Linear perspective.
10. Linear perspective. Topographic surfaces.
11. Topographic surfaces.
12. Theoretical solution of the roofs.
13. Theoretical solution of the roofs.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

1. Focus properties of conic sections of an ellipse. Construction of an ellipse on the basis of affinity – Rytz´s and trammel construction.
2. Perspective collineation, perspective affinity. Curve affine to the circle.
3. Monge`s projection. Basic problems.
4. Monge`s projection.
5. Monge`s projection. Coted projection.
6. Test. Orthogonal axonometry.
7. Orthogonal axonometry.
8. Linear perspective.
9. Linear perspective.
10. Test. Linear perspective.
11. Topographic surfaces.
12. Topographic surfaces. Theoretical solution of the roofs.
13. Theoretical solution of the roofs. Credits.