Computer Geometry and Graphics (FSI-1PG-A)

Academic year 2018/2019
Supervisor: doc. PaedDr. Dalibor Martišek, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: English
Aims of the course unit:
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.
Learning outcomes and competences:
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.
Course contents:
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.
Teaching methods and criteria:
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).
Controlled participation in lessons:
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.
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Lecture 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
    Computer-assisted exercise 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
Literature - fundamental:
1. Martišek, D., Procházková, J,: Počítačová geometrie a grafika, sylaby přednášek
2. Velichová, D.: Konštrukčná geometria, STU, Bratislava 2003
3. Borecká, K. a kol.: Konstruktivní geometrie, CERM, s.r..o. Brno, 2002
4. Martišek, D.: Počítačová geometrie a grafika, VUTIUM, Brno 2000
5. Medek, V. - Zámožík, J.: Konštruktívna geometria pre technikov,
Literature - recommended:
1. Urban, A.:: Deskriptivní geometrie, díl 1. - 2., , 0
2. Paré, Loving, Hill Descriptive Geometry New York 1972
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B3S-A full-time study B-STI Fundamentals of Mechanical Engineering -- Cr,Ex 5 Compulsory 1 1 W
B3S-P full-time study B-STI Fundamentals of Mechanical Engineering -- Cr,Ex 5 Compulsory-optional 1 1 W