| Course title | Computer Geometry |
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| Course code | KMI/PGEO |
| Organizational form of instruction | Seminar |
| Level of course | Master |
| Year of study | 1 |
| Semester | Winter and summer |
| Number of ECTS credits | 5 |
| Language of instruction | Czech |
| Status of course | Compulsory-optional |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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The course is intended for students of Computer Science interested in areas where basic notions of geometry are used (e.g. computer graphics, data analysis, geographical information systems). 1. Review of vector spaces: Vector spaces and subspaces, linear independence, bases and coordinates. Linear mappings and their matrices. 2. Review of affine spaces: Affine spaces and subspaces. Affine combinations, affine hulls. Coordinates in affine spaces: Affine bases and coordinates, independence of points, point bases and barycentric coordinates, transformation matrices. Affine mappings and their matrices. Equations of affine subspaces. 3. Mutual position of affine subspaces. 4. Orientation: Orientation of vector and affine spaces and subspaces. Orientation of sets, introducin orientation by vectors. Oriented affine mappings. 5. Convexity: Convex combinations, convex hulls, convex sets. Polytomes and half-spaces. 6. Euclidean spaces: Vector spaces with scalar product and their properties. Euclidean spaces and subspaces, orthogonal and orthonormal affine bases and coordinates. Deviation and distance of affine subspaces. Isometry and similarity. 7. Projective spaces: Projective spaces and subspaces, projective extension of affine spaces. Homogenous coordinates. Projective mappings and transformations and their matrices. Duality principle. 8. Introduction to differential geometry of curves: The notion of curve in Euclidean space, continuity, derivative. Length of a curve, parametrization by length. Tangent, normal, binormal. Frenet frame. Special curves used in computer graphics.
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| Learning activities and teaching methods |
| unspecified |
| Learning outcomes |
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Students become familiar with basic concepts of geometry used in Computer Science.
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| Prerequisites |
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unspecified
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| Assessment methods and criteria |
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unspecified
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| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Applied Computer Science - Specialization in Software Development (2024) | Category: Informatics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Computer Science - Specialization in Artificial Intelligence (2020) | Category: Informatics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Applied Computer Science - Specialization in Computer Systems and Technologies (2024) | Category: Informatics courses | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Computer Science - Specialization in General Computer Science (2020) | Category: Informatics courses | 1 | Recommended year of study:1, Recommended semester: Summer |