| Code |
11509
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
|
| Workload |
OT(15H)
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| Scientific area |
Informatics
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|
Mode of delivery |
- Face-to-face and brainstorming.
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|
Work placements |
N/A.
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|
Learning outcomes |
- To introduce the postgraduates into the broad field of computer graphics.
- To educate the postgraduates with strong skills in scientific research methodologies.
- To educate the postgraduates for a research career or an academic career in geometric computing and computer graphics.
- Be able to deliver a time performance analysis of at least two convex hull algorithms.
- Be able to describe an efficient geometric search algorithm such as, for example, the 2-nearest points algorithm.
- Be able to explain the importance of function theory in representing geometric objects (i.e., curves, surfaces, and solids); in particular, students must be able to distinguish parametric from implicit formulations of geometry.
- Be able to identify at least a representation scheme for solids that is useful in the segmentation of human anatomical shapes in 3D medical imaging.
- Be able to develop a novel algorithm in geometric computing.
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Syllabus |
Convexity and convex hulls. Geometric search algorithms. Proximity algorithms and triangulation. Bézier curves and surfaces. B-spline curves and surfaces. NURBS. Implicit curves and surfaces. Polygonization and rendering of implicit surfaces. Solids and multi-dimensional geometric objects. Geometric application in engineering, animation, virtual reality, biology, biochemistry, and medicine.
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Main Bibliography |
- F. Preparata and M. Shamos, “Computational Geometry: An Introduction”, Springer-Verlag, 1985.
- G. Farin, “Curves and Surfaces for Computer-Aided Geometric Design”, Academic Press, 2002.
- A. Gomes, I. Voiculescu, J. Jorge, B. Wyvill, and C. Galbraith, “Implicit Curves and Surfaces: Mathematics, Data Structures, and Algorithms”, Springer-Verlag, 2009.
- M. Agoston, “Computer Graphics and Geometric Modeling”, Springer-Verlag, 2005.
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Language |
Portuguese. Tutorial support is available in English.
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