Course objectives:
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The aim of this course is a basic introduction to the numerical methods and to the modern geometric modeling of free-form objects.
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Requirements on student
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1. Credit: one of this possibilities
- oral (aprox. 15 minutes) and written presentation
- practical work and succesfull solution (programm in Matlab, model in Rhino)
- succesfull test in last week of semestr
Exam:
Written (90 minutes) and oral form, usage of literatur and computer is allowed.
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Content
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1. Solving the equation f (x) = 0 - separation of roots, secant method and tangent method, iteration.
2. Solving systems of linear algebraic equations - finite methods, iteration.
3. Interpolation - Lagrange polynomial, spline functions.
4. Approximation - method of least squares.
5. Numerical integration and solving differential equations - initial task.
6. Difference method and finite elements.
7. Solving partial differential equations - method of networking (nets).
8. Ferguson cubic and spline curves.
9. Bezier curves and surfaces.
10. B-spline and NURBS curves and surfaces.
11. Coons patches.
12. Geometric model in CAD - edge, surface and volume model. Overview of CA in terms of methods of geometric modeling. Basic trends in geometric modeling.
13. 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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39
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Presentation preparation (report) (1-10)
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9
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Preparation for an examination (30-60)
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40
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Individual project (40)
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10
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Preparation for comprehensive test (10-40)
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10
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Total
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108
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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: |
Students should be familiar with a high school algebra, calculus and analytical geometry. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
Student is informed on the numerical methods in linear algebra and mathematical analyses. She/he has a overview of principles, which are used in CAD/CAM systems and has good orientation in modelling technics. She/he is able to use mathematic software (Matlab) for basic geometric modeling.
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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 |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Laboratory work |
Students' portfolio |
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