| 01243 Differential Geometry and Design of Shape and Motion |
| Danish title: Differentialgeometri og design af form og bevægelse |
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Language: English ECTS-creditpoints: 10, External examination.
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Exam schedule:
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E4-A (dec 18 2001), F4-A (jun 04 2002) |
| Recommended semester: 4th -7th semester |
| Scope and form: Lectures, exercises, and computerlab sessions. |
| Evaluation: Oral presentation and approval of coursework
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| Examination: 13-scale |
| Previous course: 01123, 01454 |
| Prerequisites: 01012 / 01013 / 01014 and 01020 / 01021 or 01002 / 01003 or 01005 |
| Preferred prerequisites: Some programming experience |
| Aim: To introduce the students to the differential geometry of curves and surfaces, and to applications in the design of curves, surfaces, and motion. |
Contents: Bézier and B-spline curves and surfaces. Curves in the plane and in space, the Frenet apparatus. Surfaces in space, first and second fundamental form. Projective geometry, quaternions and rotations in space. In the last part of the course the participants will work in groups on a smaller project. Among possible subjects are
-Design of developable surfaces.
-Design of convex planar curves.
-Planar curves with constant width.
-PH-curves (curves where the arc-length is a polynomial in the parameter).
-Geodesics.
-Classical constructions in geometry (evolute, involute, cycloids, surfaces of revolution, ruled surfaces,...)
-Numerical solutions of the Frenet-Serret equations.
-Subdivision. |
| Contact: Jens Gravesen, building 303, (+45) 4525 3064, j.gravesen@mat.dtu.dk |
| Department: 001 Department of Mathematics |
| Course URL: http://www.mat.dtu.dk/courses/01243 |
| Keywords: differential geometry, design, motion planning |
| Updated: 04-05-2001 |
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