Course detail
Constructive Geometry
FSI-1KD Acad. year: 2021/2022 Winter semester
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.
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
Czech
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.
The study programmes with the given course
Programme B-ENE-P: Energy, Bachelor's
branch ---: no specialisation, 5 credits, compulsory
Programme B-PRP-P: Professional Pilot, Bachelor's
branch ---: no specialisation, 5 credits, compulsory
Programme B-PDS-P: Industrial Design, Bachelor's
branch ---: no specialisation, 5 credits, compulsory
Programme B-ZSI-P: Fundamentals of Mechanical Engineering, Bachelor's
branch STI: Fundamentals of Mechanical Engineering, 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.