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## 02585 Computational Geometry Processing

### Danish title:

Beregninger på geometrisk data

5

### Course type:

 Advanced course Taught under open university

E3A

### Scope and form:

Lectures and databar exercises.

13 weeks

E3A

,

### Participants restrictions:

Minimum  5, Maximum:  60

### General course objectives:

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.

### Learning objectives:

A student who has met the objectives of the course will be able to:
• 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

### Content:

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.

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

### Responsible:

J. Andreas Bærentzen, 324, 110, (+45) 4525 3414,
Jens Gravesen, 303B, 152, (+45) 4525 3064,
Henrik Aanæs, 321, 224, (+45) 4525 3417,

### Department:

02 Department of Informatics and Mathematical Modeling

### Department involved:

01 Department of Mathematics

http://www2.imm.dtu.dk/courses/02585