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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Bican L. (2004). Lineární algebra a geometrie. Praha, Academia.
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Budinský B. (1983). Analytická a diferenciální geometrie. Praha, SNTL.
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Horák P.; Janyška J. (2002). Analytická geometrie. Masarykova univerzita.
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Pressley A. (2001). Elementary Differential Geometry. Springer.
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Riddle D.R. (1998). Analytic Geometry. Brooks Cole.
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Žára J., Felkel P., Beneš B., Sochor J. (2005). Moderní počítačová grafika, 2. vydání. Computer Press.
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