Constructive Geometry (FSI-1KD-A)

The aim of the course is to deepen spatial imagination, to introduce students to the principles of representation and important properties of some curves and surfaces. The aim of the course is to introduce students to the basics of the international language of engineers, i.e. descriptive geometry, so that they can then creatively apply this knowledge in professional subjects and in the use of computer technology.

The constructive geometry course summarizes and clarifies basic geometric concepts, including basic geometric projections, and introduces students to some types of projections, their properties and applications. Emphasis is placed on Monge projections and orthogonal axonometry. The basics of plane kinematic geometry are also presented. A large part of the course is devoted to the representation of curves and surfaces of engineering practice and some necessary constructions such as plane sections and intersections.
The constructions are complemented by modeling in Rhinoceros software.

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 practical and theoretical part. In a 90-minute practical part, students have to solve 3 problems (at most 60 points). The student can obtain at most 20 points for theoretical part.

RULES FOR CLASSIFICATION:
1. Results from seminars (at most 20 points)
2. Results from the practical part (at most 60 points)
3. Results from the theoretical 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

1. Cross sections, focal properties of conic sections, construction of conic sections, conjugate diameters of conic section


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, horizontal and frontal lines.


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


5. Axonometric – basis


6. Axonometric – completion


7. Elementary surfaces and solids, cross sections


8. Solids and cross sections of the solids


9. Curves: Basics of projective geometry (points at infinity, axioms, incidence, projective axiom, geometric model of projective plane) kinematic geometry in the plane (trochoids). Rectification of the arc.


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


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


12. Surfaces of revolution: derivation of parametric equations in projective space, surfaces of revolution construction, cross sections of the surfaces


13. Developable surfaces: cylinder and right circular cone with cross-section curve

1.- 2. Rhinoceros 3D – Line, Plane, Circle, Polygon in 3D. A line perpendicular, conic sections, focal properties of conic sections
3.- 4. Monge's method
5.- 6. Axonometry
7.- 8. Elementary surfaces and solids, cross sections
9.- 10. Kinematic geometry in the plane, helix
11.- 12. Helical surfaces, Surfaces of revolution

Presence in the seminar is obligatory.