Course detail

Computer Geometry and Graphics

FSI-1PG-KAcad. year: 2016/2017

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

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

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 + 20 points) and one calculation
(20 bodů). The last 10 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

Borecká, K. a kol.: Konstruktivní geometrie, CERM, s.r..o. Brno, 2002
Martišek, D.: Počítačová geometrie a grafika, VUTIUM, Brno 2000
Medek, V. - Zámožík, J.: Konštruktívna geometria pre technikov,
Paré, Loving, Hill Descriptive Geometry New York 1972
Steve M. Slaby Fundamentals of Three-Dimensional Descriptive Geometry New York 1976

Recommended reading

Borecká, K. a kol.: Konstruktivní geometrie, , 0
Seichter, L.:: Konstruktivní geometrie, , 0
Urban, A.:: Deskriptivní geometrie, díl 1. - 2., , 0

Classification of course in study plans

  • Programme B3S-K Bachelor's

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

Type of course unit

 

Guided consultation

17 hod., optionally

Teacher / Lecturer

RNDr. Milana Faltusová

Syllabus

1. Euclidean space, topologic dimension, curve, surface, solid. Projective space, dividing ratio and cross ratio, projection

2. Basic mappings in plane and space, their analytic representation (rotation, translation, axis and central symmetry, homothety), analytic representation of parallel and central projection).

3. Analytic curves, Point function, tangent and normal of curve, curvature. Analytic surfaces, isolines, tangent plane, normal, normal and Gaussian curvature (basic information)

4. Focus and projective attributes of conics, circle - ellipse affinity, Triangle, stripe and Rytz construction. Curve representation in CAD systems, affine point combination, control points. Beziere curves, B-spline curves and surfaces, NURBS curves.

5. 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)

6. Elementary surfaces and solids (prism, pyramid, cylinder, cone, sphere) two-plane (Monge) Monge projection (MP) and orthogonal axonometry (OA), NURBS surfaces, NURBS representation of elementary curves and surfaces.

7. Slices of solids, the intersection of line and solid, intersection of solids - Monge's projection and axonometry solutions

8. Helix, analytic representation, MP and OA projection.

9. Methods of surface generation in graphic system, Basic generating principles. Developable surfaces (cylindric and conic surface, curve tangent surface, transition surfaces). 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, cyclic and linear surfaces, - Monge's projection and axonometry, analytic representation, computer modeling

12. Hausdorff dimension, fractal. Self-similarity and self-afinity, random walk method, midpoint method, L-systems

13. Lighting of elementar solids, lighting models in computer graphics, Ray Tracing, Ray Casting