| Type: | Ph.D.-level, Open University
Language: English |
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Previous course: C0154
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No credit points with: C0154
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Prerequisite: 01123.
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Recommended semester: 4th -7th semester
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Scope and form: 2 lecture modules and 1 hour of problem solving per week.
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Examination: Project report (13-scale)
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Department: Department of Mathematics
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Aim: To familiarize the student with advanced geometric methods that are used in the study of abstract manifolds, geometric design or kinematics .
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Contents: The course 01454 used to be a course in Riemannian geometry. From now on the content will change from year to year. This year (2000) the course will be concerned with "Design of Shape and Motion". The issues covered are used in e.g. computer-games and graphics, and also in technical CAD-systems and robotics.
The content include: Bézier curves and surfaces, B-spline curves and surfaces, projective geometry, rational curves and surfaces. As an integrated part of the course the participants will implement the algorithms on the computer-system at DTU.
In the last part of the course the participants will work in groups on a
smaller project. Among possible subjects are
- Kinematic design, (computer-games and robotics).
- Design of developable surfaces.
- PH-curves (curves where the arc-length is a polynomial in the parameter).
- Numerical solution of the Serret-Frenet equations.
- Numerical solution of the geodesic equation.
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