Course detail
Constructive Geometry
FAST-BAA013Acad. year: 2020/2021
Perspective collineation and affinity,circle in affinity. Coted projection, Monge`s projection, topographic surfaces, theoretical solution of the roofs, orthogonal axonometry and linear perspective.
Language of instruction
Czech
Number of ECTS credits
5
Mode of study
Not applicable.
Guarantor
Department
Institute of Mathematics and Descriptive Geometry (MAT)
Offered to foreign students
Of all faculties
Learning outcomes of the course unit
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 construct a helix using specified elements, an orthogonal closed rule right helicoidal surface. They construct a hyperbolic paraboloid, circle and parabolic conoid using specified elements.
Prerequisites
Basics of plane and 3D geometry a stereometrie as taught at secondary schools.
Co-requisites
Not applicable.
Planned learning activities and teaching methods
Not applicable.
Assesment methods and criteria linked to learning outcomes
Not applicable.
Course curriculum
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.
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.
Work placements
Not applicable.
Aims
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 education, way of implementation and compensation for absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
Not applicable.
Recommended reading
Not applicable.
Classification of course in study plans
- Programme BPC-SI Bachelor's
specialization VS , 1 year of study, summer semester, compulsory
- Programme BPC-MI Bachelor's 1 year of study, summer semester, compulsory
- Programme BPA-SI Bachelor's 1 year of study, summer semester, compulsory
- Programme BPC-EVB Bachelor's 1 year of study, summer semester, compulsory
- Programme BKC-SI Bachelor's 1 year of study, summer semester, compulsory
Type of course unit
Lecture
26 hod., optionally
Teacher / Lecturer
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
26 hod., compulsory
Teacher / Lecturer
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.