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Main menu for Browse IS/STAG
Course info
KMA / GM1
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Course description
Department/Unit / Abbreviation
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KMA
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GM1
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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 Modelling 1
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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,
5
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
2
[Hours/Week]
Tutorial
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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0 / -
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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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8 / -
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3 / -
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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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Winter semester
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Semester taught
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Winter 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 |
Yes
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Fundamental course |
Yes
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Fundamental theoretical course |
Yes
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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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KIV/GAM
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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 main aim of this course is to give students a thorough introduction to geometric methods used in modern computer graphics, CAx and GIS systems. Furthermore, the practical experience with using geometric and mathematical software is developed.
The course gives a short overview of fundamentals of (differential, algebraic, projective) geometry for geometric modelling, especially from the point of view of modelling with curves, surfaces and solids. Then it focuses on the basic theory of Bézier, B-spline and NURBS curves and surfaces, spline curves and surfaces (Coons patches), barycentric coordinates and triangular patches.
The course also aims at showing the students various possibilities of applications of geometric modelling e.g. in computer graphics or in engineering practise.
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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 of the examination consists from questions and examples from the basic curriculum of the course. The time limit for working is 90 minutes. The oral part of the examination deals with the general context.
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Content
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Spline function, cubic spline curve, splines of higher degrese, spline under tension, nonlinear spline. Bézier curve - Bernstein polynomials, de Casteljau algorithm. B-spline bases, de Boor algorithm, features of B-spline curves. Rational Bézier curves and NURBS (non-uniform rational B-spline) curves. Tensor product surfaces - spline surfaces, Bézier surfaces, B-spline and NURBS surfaces. Coons interpolation - bilinear, bicubic and Ferguson patch, patching. Barycentric coordinates, interpolation on a triangle. Applications of geometric modelling.
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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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52
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Team project (50/number of students)
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20
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Presentation preparation (report in a foreign language) (10-15)
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15
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Preparation for an examination (30-60)
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45
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Total
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132
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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 lineární algebry |
orientovat se v základních pojmech analytické geometrie v rovině a v prostoru, výhodou je také zvládnutí základních vlastností křivek a ploch metodami diferenciální geometrie |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
aplikovat metody diferenciálního počtu |
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 |
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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: |
Individual presentation at a seminar |
Seminar work |
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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 |
Competences - the following training methods are used to achieve the required competences: |
Task-based study method |
Students' portfolio |
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