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Course info
KMA / GPM
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Course description
Department/Unit / Abbreviation
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KMA
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GPM
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Geometric and Computational Modelling
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
6
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Seminar
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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1 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
Yes
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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KMA/AGE, KMA/AGM, KMA/NMO
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The course provides an overview of the geometrical methods used in modern graphics, CAx and GIS systems. Furthermore, the practical experience of using geometric modelers and mathematical software is developed.
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Requirements on student
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Credit: more than 50% of possible points for the following activities:
- Preparation and presentation of a paper on the basis of literature
- Successful completion of prescribed practical exercises undertaken in the team.
The written part od examination consists from more simpler questions and examples of the basic curriculum of the course. Authorized the use of literature. The time limit for working is 90 minutes. The oral part of examination deals with the general context and theme students work. Points connected to credit are involved in axam evaluation.
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Content
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1. Lecture: Applications of geometric modeling. Analytic geometry - Projective extension of homogeneous coordinates. Matrix form for transformation and projection.
Exercise: Repeat analytical and differential geometry.
2. Lecture: Differential geometry - Equations of curves, tangent, parameterization, first and second curvature. Frenet formula. Ferguson cubic.
Practice: Entering projects. Properties of Ferguson cubic.
3. Lecture: Spline function. Cubic spline curve. Splines of higher degrees. Spline under tension, nonlinear spline.
Exercise: Introduction to the use geometric features of mathematical software.
4. Lecture: Bézier curve - Bernstein polynomials, de Casteljau algorithm, a description of spline curves.
Exercise: Spline curve.
5. Lecture: B-spline bases, de Boor algorithm, features of B-spline curves. Rational Bezier curves and NURBS (non-uniform rational B-spline). $\beta$ - spline.
Exercise: Bezier curves, B-spline.
6. Lecture: Differential geometry - curvature on surfaces.
Exercise: Introduction to work with the geometric modeler.
7. Lecture: the tensor product surfaces - spline surfaces and Bézier surfaces.
Exercise: NURBS modeling, consultation exercises.
8. Lecture: Coons interpolation - bilinear, bicubic and Ferguson patch, patching.
Exercise: Coons patches.
9. Lecture: the tensor product surfaces - B-spline and NURBS surfaces.
Exercise: Bezier surfaces and NURBS surfaces
10. Lecture: barycentric coordinates, interpolation on a triangle. Subdivision techniques.
Exercise: barycentric calculus, subdivision techniques.
11. Lecture: The geometric model in CAD - edge, surface and volume model. Decomposition, CSG and B-representation. Topological characteristics of solids. Euler characteristics.
Exercise: Presentation of student projects.
12. Lecture: Parameterization of the model - parameterization methods, graph algorithms, test for good parameterization, methods of artificial intelligence.
Exercise: Presentation of student projects.
13. Lecture: Overview of CA systems, methods of geometric modeling. Basic trends in geometric modeling.
Exercise: Presentation of student projects.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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65
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Presentation preparation (report in a foreign language) (10-15)
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20
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Team project (50/number of students)
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30
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Preparation for an examination (30-60)
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45
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Total
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160
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
orientovat se v základních pojmech analytické geometrie v rovině a v prostoru, výhodou je také zvládnutí základních vlastností křivek a ploch metodami diferenciální geometrie |
orientovat se v základních pojmech lineární algebry |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
používat metody diferenciálního počtu |
pracovat s maticemi a vektory |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
rozumět teoretickým základům reprezentace křivek a ploch v moderních CAx, GIS a dalších graficky orientovaných systémech |
definovat interpolační spline křivku a umět ji použít |
definovat Bézierovy, B-spline a NURBS křivky a plochy a umět je použít |
definovat Coonsovy pláty a spline plochy a umět je použít |
Skills - skills resulting from the course: |
umět sestavit geometrický model pro složité jevy v souladu s moderními požadavky CAGD (Computer Aided Geometric Design) |
používat matematický software pro práci s objekty moderního geometrického modelování, pro tvorbu geometrických modelů a pro odvozování jejich důležitých vlastností |
připravit referát na odborné téma s problematikou geometrického modelování na základě odborné literatury |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Individual presentation at a seminar |
Skills - skills achieved by taking this course are verified by the following means: |
Seminar work |
Individual presentation at a seminar |
Competences - competence achieved by taking this course are verified by the following means: |
Seminar work |
Individual presentation at a seminar |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Lecture supplemented with a discussion |
Interactive lecture |
Practicum |
Project-based instruction |
Task-based study method |
Students' portfolio |
Skills - the following training methods are used to achieve the required skills: |
Practicum |
Task-based study method |
Students' portfolio |
Competences - the following training methods are used to achieve the required competences: |
Practicum |
Students' portfolio |
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