Course detail
Descriptive geometry
FAST-AA02Acad. year: 2014/2015
Orthogonal axonometry, skew axonometry, skew projection. Linear perspective, photogrammetry. Helix, developable helicoidal surface, right closed rule helicoidal surface. Surfaces of revolution . Warped surfaces. Lighting. Teoretical designs of roofs. Introduction to topopgraphic surfaces.
Language of instruction
Czech
Number of ECTS credits
4
Mode of study
Not applicable.
Guarantor
Department
Institute of Mathematics and Descriptive Geometry (MAT)
Learning outcomes of the course unit
Students should be able to construct conics using their focus properties, perspective colineation and affinity. Understand and get the basics of projection: coted, Monge`s projection, orthogonal axonometry, and linear perspective. They should be able to solve simple 3D problems, display the basic geometric bodies and surfaces in each projection, their section. In a linear perspective, students should be able to draw a building. They construct a helix using specified elements, an orthogonal closed rule right helicoidal surface. They construct a hyperbolic paraboloid, circle and parabolic conoid, arcs using specified elements.
Prerequisites
Construction of conics using their focal properties.Perspective collineation, perspectoive affinity, affine image of a circle. Monge projection.
Co-requisites
Not applicable.
Planned learning activities and teaching methods
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.
Information is conveyed in the form of lectures and practiced in seminars. Consultation periods are available to students. Assigned work is part of the study activities of the students.
Information is conveyed in the form of lectures and practiced in seminars. Consultation periods are available to students. Assigned work is part of the study activities of the students.
Assesment methods and criteria linked to learning outcomes
Full-time study programme: Students have to pass two credit tests, submit two drawings and other homework, 100% of attendance.
Followed by an exam with a pass rate of at least 50%.
Followed by an exam with a pass rate of at least 50%.
Course curriculum
1. Basics of lihting. Technical lighting.
2. Rotation symmetric surfaces, sections of rotation-symmetric surfaces.
3. Lighting of surfaces of revolution .
4. Axonometry – basics.
5. Orthogonal axonometry.
6. Skew axonometry, skew projection.
7. Linear perspective.
8. Linear perspective.
9. Basics of photogrammetry. Reconstruction from a vertical picture.
10. Warped quadrics. Hyperbolic paraboloid. One-sheet hyperboloid.
11. Higher order warped surfaces.Theoretical designe of roofs.
12. Helix, developable helicoidal surface, helicoidal conoid.
13. Topografic surfaces.
2. Rotation symmetric surfaces, sections of rotation-symmetric surfaces.
3. Lighting of surfaces of revolution .
4. Axonometry – basics.
5. Orthogonal axonometry.
6. Skew axonometry, skew projection.
7. Linear perspective.
8. Linear perspective.
9. Basics of photogrammetry. Reconstruction from a vertical picture.
10. Warped quadrics. Hyperbolic paraboloid. One-sheet hyperboloid.
11. Higher order warped surfaces.Theoretical designe of roofs.
12. Helix, developable helicoidal surface, helicoidal conoid.
13. Topografic surfaces.
Work placements
Not applicable.
Aims
After the course the students should understand and know how to use the basics of orthogonal axonometry, skew projection, and linear perspective.
Specification of controlled education, way of implementation and compensation for absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Recommended optional programme components
Student can register for the optional subject BA91 in this semester. The contents of the course is an introduction to the issues of the subject of descriptive geometry.
Prerequisites and corequisites
Not applicable.
Basic literature
BULANTOVÁ,J.,HON,P.,PRUDILOVÁ,K.,PUCHÝŘOVÁ,J.,ROUŠAR,J.,ROUŠAROVÁ,V.,SLABĚŇÁKOVÁ,J.,ŠAFAŘÍK,J.: Deskriptivní geometrie, multimediální CD. FAST VUT v Brně, 2004. (CS)
Piska, R., Medek, V.: Deskriptivní geometrie I.. SNTL Praha, Alfa Bratislava, 1975. (CS)
Piska, R., Medek, V.: Deskriptivní geometrie II.. SNTL Praha, Alfa Bratislava, 1975. (CS)
Piska, R., Medek, V.: Deskriptivní geometrie I.. SNTL Praha, Alfa Bratislava, 1975. (CS)
Piska, R., Medek, V.: Deskriptivní geometrie II.. SNTL Praha, Alfa Bratislava, 1975. (CS)
Recommended reading
Holáň, S., Holáňová, L.: Cvičení z deskriptivní geometrie II., III.. VUT Brno, 1994. (CS)
Puchýřová, J., Bulantová, J., Prudilová,K., Zrůstová,L.: Úlohy o přímkových plochách (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Puchýřová, J., Bulantová, J., Prudilová,K., Zrůstová,L.: Úlohy v kosoúhlém promítání (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Šafařík, J.: Technické osvětlení (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Šafářová, H.: Teoretické řešení střech (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Vala, J.: Deskriptivní geometrie I., II.. VUT Brno, 1997. (CS)
Puchýřová, J., Bulantová, J., Prudilová,K., Zrůstová,L.: Úlohy o přímkových plochách (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Puchýřová, J., Bulantová, J., Prudilová,K., Zrůstová,L.: Úlohy v kosoúhlém promítání (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Šafařík, J.: Technické osvětlení (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Šafářová, H.: Teoretické řešení střech (ke stažení na webové stánce Ústavu matematiky FAST VUT v Brně). 2006. (CS)
Vala, J.: Deskriptivní geometrie I., II.. VUT Brno, 1997. (CS)
Classification of course in study plans
Type of course unit
Lecture
26 hod., optionally
Teacher / Lecturer
Syllabus
1. Basics of lihting. Technical lighting.
2. Rotation symmetric surfaces, sections of rotation-symmetric surfaces.
3. Lighting of surfaces of revolution .
4. Axonometry – basics.
5. Orthogonal axonometry.
6. Skew axonometry, skew projection.
7. Linear perspective.
8. Linear perspective.
9. Basics of photogrammetry. Reconstruction from a vertical picture.
10. Warped quadrics. Hyperbolic paraboloid. One-sheet hyperboloid.
11. Higher order warped surfaces.Theoretical designe of roofs.
12. Helix, developable helicoidal surface, helicoidal conoid.
13. Topografic surfaces.
2. Rotation symmetric surfaces, sections of rotation-symmetric surfaces.
3. Lighting of surfaces of revolution .
4. Axonometry – basics.
5. Orthogonal axonometry.
6. Skew axonometry, skew projection.
7. Linear perspective.
8. Linear perspective.
9. Basics of photogrammetry. Reconstruction from a vertical picture.
10. Warped quadrics. Hyperbolic paraboloid. One-sheet hyperboloid.
11. Higher order warped surfaces.Theoretical designe of roofs.
12. Helix, developable helicoidal surface, helicoidal conoid.
13. Topografic surfaces.
Exercise
26 hod., compulsory
Teacher / Lecturer
Syllabus
1. Revision – Monge projection.
2. Projections of a simple bodies and surfaces, their sections and intersections with a straight line. Technical lighting.
3. Tangent plane of a surface of revolution, section of a surface of revolution.
4. Lighting a surface of revolution.
5. Orthogonal axonometry. Metric problems in coordinate planes.
6. Orthogonal axonometry. Projections of simple bodies and surfaces, their sections and intersections with a straight line.
7. Projecting in skew projection. Projection of a circle in a coordinate plane. Displaying simple bodies. Cutting method.
8. Linear perspective. Intersection method. Constructing a free perspective.
9. Linear perspective. Method of rotated ground plan. Other methods of projecting a perspective.
10. Linear perspective. Vertical picture. Reconstructing an object from a perpendicular picture.
11. Warped hyperboloid, construction. Hyperbolic paraboloid. Hyperbolic paraboloid given by skew tetragon. Roofing by hyperbolic paraboloid.
12. Higher-order warped surfaces. Theoretic design of roofs.
13. Constructing a helix. Right helicoidal conoid. Credits.
2. Projections of a simple bodies and surfaces, their sections and intersections with a straight line. Technical lighting.
3. Tangent plane of a surface of revolution, section of a surface of revolution.
4. Lighting a surface of revolution.
5. Orthogonal axonometry. Metric problems in coordinate planes.
6. Orthogonal axonometry. Projections of simple bodies and surfaces, their sections and intersections with a straight line.
7. Projecting in skew projection. Projection of a circle in a coordinate plane. Displaying simple bodies. Cutting method.
8. Linear perspective. Intersection method. Constructing a free perspective.
9. Linear perspective. Method of rotated ground plan. Other methods of projecting a perspective.
10. Linear perspective. Vertical picture. Reconstructing an object from a perpendicular picture.
11. Warped hyperboloid, construction. Hyperbolic paraboloid. Hyperbolic paraboloid given by skew tetragon. Roofing by hyperbolic paraboloid.
12. Higher-order warped surfaces. Theoretic design of roofs.
13. Constructing a helix. Right helicoidal conoid. Credits.