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

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. PaedDr. Dalibor Martišek, Ph.D.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

Students will obtain the wide overview about the computer graphics and also about the parts of geometry which support the technical display systems (solids projection, curves and surfaces of technical practice, lighting). The student will be able to work in graphic studio and use the fundamental functions of the software with new theoretical knowledge. This approach learn him how to work with other graphic systems in short time.

Prerequisites

Knowledge of mathematics in secondary school level, especially geometry and descriptive geometry (two-plane (Monge's) projection, axonometry).
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

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.

Assesment methods and criteria linked to learning outcomes

Course/unit credit is conditional on the following: Active attendance at seminars and
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

Not applicable.

Work placements

Not applicable.

Aims

The gist of the subject is to introduce students basic knowledge of projective geometry and computer graphics which is used in CAD systems and graphics modelers. Students will learn the classic geometry and computer graphics as well. The base of the subject is in connection of theoretical knowledge with the work in graphics modelers. Students will work with graphics software Rhinoceros.

Specification of controlled education, way of implementation and compensation for absences

If a student does not satisfy the given conditions, the teacher can set an alternative condition. The seminars are compulsory, lectures are optionally but very recommend.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Martišek, D.: Počítačová geometrie a grafika, VUTIUM, Brno 2000
Martišek, D., Procházková, J,: Počítačová geometrie a grafika, sylaby přednášek
Velichová, D.: Konštrukčná geometria, STU, Bratislava 2003

Recommended reading

Paré, Loving, Hill Descriptive Geometry New York 1972
Urban, A.: Deskriptivní geometrie, díl 1. - 2., , 0

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B-MTI , 1 year of study, winter semester, compulsory
    branch B-PDS , 1 year of study, winter semester, compulsory

  • Programme B2341-3 Bachelor's

    branch B-S1R , 1 year of study, winter semester, compulsory
    branch B-STI , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

RNDr. Květoslava Borecká
doc. Ing. Pavel Štarha, Ph.D.
RNDr. Milana Faltusová
doc. PaedDr. Dalibor Martišek, Ph.D.

Syllabus

1. Image, raster and vector data, colour models. Projective space, the basic of the projection, central collineation and affinity, conic sections, circle in axis affinity and central collineation, two-plane (Monge) projection - elementary constructions.
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

26 hod., compulsory

Teacher / Lecturer

RNDr. Květoslava Borecká
doc. PaedDr. Dalibor Martišek, Ph.D.
doc. Ing. Pavel Štarha, Ph.D.
Mgr. Jana Hoderová, Ph.D.
RNDr. Milana Faltusová

Syllabus

1. Introduction to the computer graphics - raster and vector image. Image processing, CAD data visualization. Rhinoceros - introduction, view setting, elementary examples and commands.
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