Many engineering disciplines require methods for handling geometry via a computer. For instance, this is the case in the fields of computer graphics, physical simulation, medical science, image analysis, and signal analysis. The aim of this course is to teach methods for the handling and processing geometry. The teaching is on a level which enables the student to construct software for handling specific problems pertaining to the topics taught. It is furthermore the goal to give the student an understanding of the problems related to the discretization of continuous geometry as well as advantages and disadvantages of various methods for doing so.

Having followed this course, the student should be prepared to write a master s thesis within this area.

• Use and select surface representations for geometric tasks.
• Compute differential geometric properties of discrete and smooth surfaces.
• Form smooth surfaces from polygonal meshes.
• Form smooth surfaces from 2D and 3D point sets.
• Simplify polygonal meshes.
• Smooth and remove noise from polygonal meshes.
• Register and merge polygonal meshes.
• Triangulate 2D point sets.
• Parameterize 3D surfaces.
• Employ distance fields and the level set method.
• Compute convex hulls in 2D and 3D
• Index 2D and 3D data

The following topics are discussed:
- Several surface representations, for instance, meshes, distance fields (signed and unsigned), level sets, Non-uniform Rational B-Splines, and radial basis functions.
- Differential geometry properties of surfaces and how such properties are computed in the case of discrete representations.
- Subdivision surfaces.
- Primitive operations on meshes.
- Simplification and optimization of meshes.
- Registration and merging of meshes.
- Triangulation and manipulation of triangulations.
- Scanning.

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 information http://www.groendyst.dtu.dk/kursustilmelding.aspx