Course detail
Computer Geometry and Graphics
FSI-1PGAcad. year: 2011/2012
Computer geometry and Graphics introduces basic knowledge of projective geometry and computer graphics which is used in CAD systems and graphics modelers. The base of the subject is in connection of theoretical knowledge with the work in graphics modelers. Synthetic and analytic constritions of basic plane and spatial figures and methods of their mapping and software representation are the course substantiality.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
For students who did not attend the descriptive geometry on secondary school there is a possibility to attend the course Selected Chapters from Descriptive Geometry.
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
three seminar works per 10 points. Each work contains two parts: graph (max 5 points)
and Rhinoceros model (max 5 points). Course credit: minimal one point in each part of
each work and 15 total point.
Examination: written part consists of three drawing (20 + 10 points) and one calculation
(20 bodů). The last 20 points is possible to obtain in oral part of examination.
Grading scheme:
excellent (100 - 90 points),
very good(89 - 80 points),
good (79 - 70 points),
satisfactory (69 - 60 points),
sufficient(59 - 50 points),
failed (49 - 0 points).
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., Procházková, J,: Počítačová geometrie a grafika, sylaby přednášek
Velichová, D.: Konštrukčná geometria, STU, Bratislava 2003
Recommended reading
Urban, A.: Deskriptivní geometrie, díl 1. - 2., , 0
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Analytic representation of geometric mappings in projective plane (rotation, translation, axis and central symmetry, homothety), analytic representation of parallel and central projection.
3. Topological dimension, curve, surface. Focus and projective attributes of conics, the fundamentals of kinematic plane geometry (motion, fixed and moving centrode, circle arc rectification, rolling motion, cycloid and involute curve - synthetic and analytic construction, animation principle, software modeling)
4. Algorithm of curve construction, curve representation in graphic system, NURBS - the fundamentals of B-spline function theory, the attributes and calcul algorithms.
5. Elementary surfaces and solids (cone, cube, sphere, cylinder) - Monge's projection and axonometry
6. Slices of solids, the intersection of line and solid, intersection of solids (introduction) - Monge's projection and axonometry solutions
7. Intersection of solids (second part). Helix, Analytic representation of helix motion
8. Methods of surface generation in graphic system, developable surfaces (cylindric and conic surface, curve tangent surface, transition surfaces)
9. Undevelopable surfaces (conoid, cranc mechanism surface, oblique transition surface) - analytic representation, computer modeling
10. Rotation surfaces (torus, rotation quadric) - Monge's projection and axonometry, - analytic representation, computer modeling
11. Skrew surfaces and surfaces, cyclic and linear surfaces, - Monge's projection and axonometry, analytic representation, computer modeling
12. NURBS representation of planes and solids
13. Lighting of elementar solids - Monge's projection and axonometry, lighting models in computer graphics, Ray Tracing.
Computer-assisted exercise
Teacher / Lecturer
Syllabus
2. Image and color models. Solids in Rhinoceros (colour, solids operation, rendering)
3. Lines, elementary objects in raster images. Free-form modeling, surfaces, lighting, curves mapping
4. Curves and surfaces in computer graphics - NURBS. General surfaces - boundary curves, revolution surfaces, sweep and offset surfaces.
5. Textures. Precise-form modeling (coordinates, curve modeling)
6. Lighting, visibility. Precise-form modeling (machine components modeling)
7. 2D and 3D transforms, 3D -> 2D transforms
8. Animation. Kinematic geometry (cycloid curve, involute)
9. Linear perspective, two center projection, 3D images and films, virtual reality
10. Curves and surfaces, topological and Hausdorff's dimension, fractals and their modeling.
11. - 13. Seminar work