Course detail
Constructive Geometry
FSI-1KDAcad. 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.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
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
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Martišek, D. Počítačová geometrie a grafika, Brno: VUTIUM, 2000. ISBN 80-214-1632-7 (CS)
Paré, E. G. Descriptive geometry. 9th ed. Upper Saddle River, NJ, 1997. ISBN 00-239-1341-X. (EN)
Slaby, S. M. Fundamentals of three-dimensional descriptive geometry. 2d ed. New York: Wiley, c1976. ISBN 04-717-9621-2. (EN)
Urban, A. Deskriptivní geometrie, díl 1. - 2., 1978. (CS)
Recommended reading
Elearning
Classification of course in study plans
- Programme B-ENE-P Bachelor's 1 year of study, winter semester, compulsory
- Programme B-STR-P Bachelor's
specialization STR , 1 year of study, winter semester, compulsory
- Programme B-ZSI-P Bachelor's
specialization STI , 1 year of study, winter semester, compulsory
- Programme B-PDS-P Bachelor's 1 year of study, winter semester, compulsory
- Programme B3S-P Bachelor's
branch B-PRP , 1 year of study, winter semester, compulsory
- Programme B-PRP-P Bachelor's 1 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus
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.
Elearning