Course detail

# Constructive Geometry

FSI-1KD-AAcad. year: 2020/2021

Principles and basic concepts of three-dimensional descriptive geometry. Perspective transformation. Orthographic projection. Curves and surfaces. Intersection of plane and surface. Piercing points. Torus, quadrics. Helix, helicoid. Ruled surfaces.

Descriptive geometry is supported by a computer.

Supervisor

Department

Learning outcomes of the course unit

Students will acquire the basic knowledge of three-dimensional descriptive geometry necessary to solve real life situations in various areas of engineering.

Prerequisites

The students have to be familiar with the fundamentals of geometry and mathematics at the secondary school level.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Borecká, K. a kol. Konstruktivní geometrie (2. vydání), Akademické nakladatelství CERM, Brno, 2006. ISBN 80-214-3229-2

Borecká, K. a kol. Konstruktivní geometrie (2. vydání), Akademické nakladatelství CERM, Brno, 2006. ISBN 80-214-3229-2

Gorjanc, S. Plane Geometry. http://www.grad.hr/geomteh3d/radne_eng.html [online]. [cit. 2016-09-12].

Martišek, D. Počítačová geometrie a grafika, Brno: VUTIUM, 2000. ISBN 80-214-1632-7

Seichter, L. Konstruktivní geometrie

Medek, V., Zámožík, J. Konštruktívna geometria pre technikov, Bratislava: Alfa, 1978.

Paré, E. G. Descriptive geometry. 9th ed. Upper Saddle River, NJ, 1997. ISBN 00-239-1341-X.

Slaby, S. M. Fundamentals of three-dimensional descriptive geometry. 2d ed. New York: Wiley, c1976. ISBN 04-717-9621-2.

Urban, A. Deskriptivní geometrie, díl 1. - 2., 1978.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

COURSE-UNIT CREDIT REQUIREMENTS: Draw up 2 semestral works (each at most 5 points), there is one written test (the condition is to obtain at least 5 points of maximum 10 points). The written test will be in the 9th week of the winter term approximately.

FORM OF EXAMINATIONS: The exam has an obligatory written and oral part. In a 90-minute written part, students have to solve 3 problems (at most 60 points). The student can obtain at most 20 points for oral part.

RULES FOR CLASSIFICATION:

1. Results from seminars (at most 20 points)

2. Results from the written examination (at most 60 points)

3. Results from the oral part (at most 20 points)

Final classification:

0-49 points: F

50-59 points: E

60-69 points: D

70-79 points: C

80-89 points: B

90-100 points: A

Language of instruction

English

Work placements

Not applicable.

Aims

The course aims to acquaint the students with the theoretical basics of descriptive geometry. It will provide them with a computer aided training in basic parts of geometry.

Specification of controlled education, way of implementation and compensation for absences

Attendance at seminars is required. The way of compensation for an absence is fully at the discretion of the teacher.

Classification of course in study plans

- Programme B-STI-A Bachelor's, 1. year of study, winter semester, 5 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Extension of the Euclidean space. Mapping between two planes. Collineation and affinity.

2. Methods for mapping three-dimensional objects onto the plane - central and parallel projections. Introduction into the Monge's method of projection (the two picture protocol) - the orthogonal projection onto two orthogonal planes.

3. Monge's method: points and lines that belong to a plane, principal lines, 1st and 2nd steepest lines.

4. Monge's method: rotation of a plane, circle that lies in a plane. 3rd projection plane (profile projection plane).

5. Rectangle and oblique parallel projection, Pohlke's theorem. Axonometry.

6. Axonometry: points, lines, planes, principal lines.

7. Axonometry: Eckhard's method. Elementary solids and surfaces.

8. Elementary surfaces and solids in Monge's method and axonometry. Intersection with stright line and with plane.

9. Curves: Bézier, Coons, Ferguson curves. Kinematic geometry in the plane. Rectification of the arc.

10. Helix: helical movement, points and tangent lines in Monge's method and axonometry.

11. Surfaces of revolution: quadrics and torus. Right circular conical surface and its planar sections. Hyperboloid as a ruled helical surface.

12. Helical surfaces: helical movement of the curve, ruled (opened, closed, orthogonal, oblique) and cyclical surfaces.

13. Developable surfaces: cylinder and right circular cone with curve of cut.

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

Syllabus

1 Conics.

2. Computer: Rhinoceros: Line, Ortholine,Circle, Ellipse etc.

3. Mongean system of descriptive geometry.

4. Computer: Rhinoceros: Polygon, Plane etc. Mapping between planes. Mapping between

a circle and a ellipse.

5. Mapping of circle.

6. Computer: Rhinoceros: Line, Plane, Circle, Polygon in 3D. A line perpendicular

to a plane surface, a plane surface perpendicular to a line, true length projection

of line AB, distance from a point to a line etc.

7. Basics of an axonometric projection.

8. Computer: Rhinoceros: Elementary solids and surfaces - Intersect, Subtract, Slice.

9. Slice and intersection of geometric solids and surfaces.

10. Computer: BORLAND DELPHI: Kinematic geometry,

Rhinoceros: Helix.

11. Torus, cylinder,cone etc. Helix, projection of helix, helicoids.

12. Computer: Rhinoceros: Helix, helicoid. Rotation surfaces.

13. Computer: Ruled surfaces. Deployable surfaces.

Presence in the seminar is obligatory.