230-0441/03 – Descriptive Geometry (DG)

• to train development of space abilities • to handle by different types of projection methods, to understand to their principles, to be familiar with their properties, advantages and disadvantages • to acquaint with geometric characteristics of curves and surfaces that are used in technical practice of a given specialization

Descriptive geometry is a practical discipline which tries to improve development of space and creative abalities and logical thinking. First it shows commonly used types of projection methods. At the socond part the geometric characteristics of relevant curves and surfaces folows.

Kreyszig, E.: Differential geometry. New York: Dover Publications, 1991. ISBN 0-486-66721-9. Kobayashi, S.: Transformation groups in differential geometry. Berlin: Springer, 1972. Classics in mathematics. ISBN 3-540-05848-6. Umehara, M. and Yamada, K.: Differential geometry of curves and surfaces. Kaiteiban. Translate Rossman, W.. Singapore: World Scientific, 2017. ISBN 978-981-4740-23-4. Falconer, K. J. Fractal geometry: mathematical foundations and applications. 3rd ed. Chichester: Wiley, 2014. ISBN 978-1-119-94239-9.

Conditions for passing the course Conditions for awarding credit: - participation in the exercises, 20% of absences can be excused, - submission of the programs assigned by the exercise leader in the prescribed format, - passing the written tests, each test can be corrected once. For meeting the conditions, the student will receive 5 points. For the tests, the student can receive 0 - 15 points. (A student who receives credit will be graded 5 - 20 points). Requirements for the exam: A condition for participating in the exam is a registered credit from the relevant subject. The written part of the exam will be evaluated 0 - 60 points, its successful completion will be considered a gain of 25 points. The oral part of the exam will be evaluated 0 - 20 points, its successful completion will be considered a gain of 5 points. After adding up the points obtained for the credit, written and oral parts of the exam, the student will be evaluated as excellent, very good, good and failed, according to the table of the VŠB - TUO study and examination regulations. To register for the exam according to the table, the student must successfully complete both parts of the combined exam and achieve the required number of points. Point evaluation: Points obtained Grade 86 - 100 excellent 66 - 85 very good 51 - 65 good 0 - 50 failed Question set 1. Projection - basic concepts. 2. Collineation between two planes - basic properties. 3. Central collineation in a plane - basic properties, vanishing point, vanishing line. 4. Axial affinity in a plane - basic properties. 5. Dimensioned projection - principle, representation of a point, line, plane. 6. Line - stop, graduation, interval, deviation from the projection line. 7. Main and gradient lines of the plane, gradient scale. 8. Basic tasks of position in dimensioned projection. 9. Actual size of a line segment in dimensioned projection. 10. Perpendicular to a plane in dimensioned projection. 11. Plane perpendicular to a line in dimensioned projection. 12. Rotation of a plane around a trace into the projection line in dimensioned projection. 13. Projection of a circle in dimensioned projection. 14. Rectangular axonometry - principle, ax. triangle, axis cross, units on axes. 15. Rectangular axonometry - representation of a point, line, plane. 16. Rectangular axonometry - basic tasks of position. 17. Rectangular axonometry - representation of a circle in coordinate planes. 18. Ellipse - definition, focal properties. 19. Hyperbola - definition, focal properties. 20. Parabola - definition, focal properties. 21. Construction of conic sections from given elements. 22. Affine image of a circle. 23. Associated diameters of an ellipse, Rytz construction. 24. Strip construction of an ellipse. 25. Section of a prism by a plane. 26. Section of a pyramid by a plane. 27. Section of a cylinder by a plane. 28. Tangent plane of a cylinder and a cone. Tangent plane of a sphere. 29. Intersections of a line with a prism and a cylinder. 30. Intersections of a line with a pyramid and a cone. 31. Topographic surfaces - representation, tangent plane, slope. 32. Constant slope curve on a topographic surface. 33. Profile of a topographic surface, its use. 34. Section of a topographic surface by a plane. 35. Intersections of a straight line with a topographic surface. 36. Longitudinal profile of a curve. 37. Intersections of a curve with a topographic surface, leveling surface of a curve. 38. Constant slope surface by a given curve. 39. Connection of an object with the terrain. 40. Protective pillar. 41. Block diagram.