Course Details

Constructive Geometry

BAA013 course is part of 5 study plans

Bc. full-t. program BPC-EVB compulsory Summer Semester 1st year 5 credits

Bc. full-t. program BPC-SI > spVS compulsory Summer Semester 1st year 5 credits

Bc. full-t. program BPC-MI compulsory Summer Semester 1st year 5 credits

Bc. full-t. program BPA-SI compulsory Summer Semester 1st year 5 credits

Bc. combi. program BKC-SI compulsory Summer Semester 1st year 5 credits

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

Learning outcomes

Students should be able to construct conics using their focus properties, basics of stereometry, perspective colineation and affinity. Understand and get the basics of projection: Monge, coted, 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 able to construct basic constructions on topographic surfaces and basics of theoretical solution of the roofs.

Prerequisites

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

Corequisites

Not required.

Planned educational activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations - lectures, seminars.

Forms and criteria of assessment

Full-time study programme: Students have to pass two credit tests, submit two drawings and other homework.
Followed by an exam with a pass rate of at least 50%.
Combined study programme: Students will do 6 tests during the semester and send them to the lecturer. Their successful completion is a condition for getting the credit. An exam with a pass rate of at least 50% will follow.



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 theory of curves and surfaces, construct a helix using specified elements as well as an orthogonal closed rule right helicoidal surface. They should learn the basics of the theory of warped surfaces, construct a hyperbolic paraboloid, circle and parabolic conoid using specified elements.

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

2 hours/week, 13 weeks, elective

Syllabus of lectures

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.

Practice

2 hours/week, 13 weeks, compulsory

Syllabus of practice

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.