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Course detail
Constructive and Computer Geometry
Course unit code:  FSI1KG  

Academic year:  2016/2017  
Type of course unit:  compulsory  
Level of course unit:  Bachelor's (1st cycle)  
Year of study:  1  
Semester:  winter  
Number of ECTS credits:  5  



























Type of course unit:
Lecture:  26 hours, optionally 

Teacher / Lecturer:  Mgr. Jana Hoderová, Ph.D. 
Syllabus:  1. Extension of the Euclidean space. Mapping between two planes. Collineation and affinity. 2. Methods for mapping threedimensional 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. 
seminars:  14 hours, compulsory 
Teacher / Lecturer:  Mgr. Jana Hoderová, Ph.D. 
Syllabus:  1. Conics: definitions of ellipse, parabola, hyperbola. Points, tangents and points of tangency of the conics, hyperosculating circles. 2. Collineation and affinity. Conics: affine image of a circle. 3. Conics: construction of ellipse by trammel method, Rytz's axis construction of ellipse. Monge's method: points, lines, planes. 4. Monge's method: basic geometrical relationships  the relative positions of points, lines and planes, angles, distances. 5. Monge's method: circle that lies in the plane, basic solids. 6. Axonometry: points, lines, planes. Square and circle in projection planes. Circles and squares in the horizontal, frontal or profile planes. 7. Axonometry: basic geometrical relationships  the relative positions of points, lines and planes. Projection of basic solids. 8. Axonometry: Eckhard's method. Monge's method and axonometry: intersection of the stright line with a basic solid. 9. Written test. Monge's method and axonometry: intersections of the polyhedron or cone with a plane. 10. Kinematic geometry: points and tangents of cycloid, evolvent, epicycloid, etc. 11. Helix: points, tangent lines. Helix in Monge's method and in axonometry. 12. Surfaces of revolution: intersections of the quadric surfaces with a plane. Helical surfaces: ruled surfaces. 13: Helical surfaces: cyclical surfaces. Developable surfaces: cylinder and right circular cone with curve of cut. 
seminars in computer labs:  12 hours, compulsory 
Teacher / Lecturer:  Mgr. Jana Hoderová, Ph.D. 