01999 Geometric Operations in Plane and Space
Geometriske operationer i plan og rum
Point( ECTS )
Taught under open university
E4B (fri 8-12)
Scope and form:
Lectures and exercises including computer experiments. Project exercises at the end of the semester.
Duration of Course:
Date of examination:
Type of assessment:
General course objectives:
To provide the student with a solid framework for understanding and applying a number of geometric shapes and techniques as they are used in engineering and architectural design contexts as exemplified below.
For mechanical engineers: Geometric construction of screws, screw pumps, hydraulic pumps, gear wheels, and roller bearings (helices, helicoids, cycloids, hypocycloids, spherical forms).
For ship building engineers: Propeller geometries via deformations of standard profiles and the construction of ship hulls.
For architectural engineers: Classical geometric concepts and basic operations for shape design and form description in plane and space.
To apply 2x2 and 3x3 matrices and their properties to analyze simple geometric constructions in plane and space and thereby obtain and practice the essential understanding of coordinate transformation techniques.
To define and to calculate precise modifications of a given geometric object.
To apply computer experiments as an integrated part of the course for illustrations, learning, and calculations.
A student who has met the objectives of the course will be able to:
Calculate on a vectorial basis the area and volume
Apply matrix calculus to construct and and analyze deformations of basic objects and explain the induced change in area and volume
Find parametrizations of simple geometric objects in plane and space
Calculate and explain the notions of area and volume for parametrized objects
Apply simple parametrizations or other representations to construct triangulations of surfaces and domains in space and compare the respective areas and volumes
Apply basic kinematic concepts to analyse simple motions in the plane
Calculate and explain the notions of arclength and curvature for curves in the plane
Apply extrudition, offsetting, and projection to construct new geometric objects from old ones
Apply twisting, tapering, shearing, bending, and inversion on simple domains in space
Analyse these deformations concerning surface area, volume, isoperimetry, curvature, etc.
Recognize and suggest applications of geoemtric methods in architectural engineering, mechanical constructions, etc.
Apply the respective methods and concepts in an individually chosen project exercise - possibly from a wide window of offered projects - and present the findings in a report
Vectors in plane and space.
2x2 and 3x3 matrices.
Triangles and tetrahedra as basic objects.
Topological combinations in plane and space.
Triangulations, parametrizations, splines, and other representations.
Simple kinematic analysis concerning controlled motions along curves in plane and space.
Frenet-Serret basis, curvature and torsion for curves.
Various types of extruditions.
Construction and deformation of surfaces and solids.
Gaussian and mean curvature of surfaces.
Project exercises from applications within e.g. architecture, mechanical constructions, and 3D printing.
H. Pottmann et al.: Architectural Geometry, Bentley Institute Press 2007.
Fabricius Bjerre [Geometri] i udvalg.
S. Markvorsen, [Notes].
The course provides a basic foundation for the understanding of the geometric operations which are applied in FEM modelling, machine element design, architectural engineering, and sculptural design.
Green challenge participation:
Please contact the teacher for information on whether this course gives the student the opportunity to prepare a project that may participate in DTU´s Study Conference on sustainability, climate technology, and the environment (GRØN DYST). More infor
, Building 303 B, room 160, Ph. (+45) 4525 3049
01 Department of Applied Mathematics and Computer Science
Registration Sign up:
Last updated: 02. maj, 2013