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The students will learn and practice common modern approaches to geometric modelling in three dimensions. The course will cover an in-depth, yet wide, overview of the following stages in the geometry processing and modelling pipeline:
- Discrete representations of geometry: meshes, spline surfaces, points clouds, and more
- Acquisition and reconstruction
- Continuous curves and surfaces
- Mesh editing and deformation
- Continuous and discrete analysis of surfaces
- Remeshing and parametrization
- Maps between shapes, shape matching
- Space decomposition and collisions
In addition, the students will receive a concise, but necessary, background in linear algebra and calculus, comprising the following subjects:
- Vector spaces
- Linear maps and transformations
- Linear Equations and reductions
- Multivariate calculus
- Numerical optimization and approximation
Assessment
Deliverables, midterm exam, final exam.
The students will do six programming exercises in total. The subjects are as follows:
- MATLAB and linear systems
- Reconstruction from point clouds
- Bézier and B-Spline design
- Discrete shape analysis
- Mesh parameterization
- Mesh editing
For each deliverable, you will get a grade between 0 and 100, which will be weighted as follows. The practicals will amount to 5(the first)+9x5=50 points, the math home exam ("midterm") is 20 points, and the final home exam is 30 points.
To pass the course, the student must pass each deliverable (practical, midterm, or exam) by at least a 50, and the total (weighted) average must be at least a 55.
A repair test requires at least a 4 for the original test.
Prerequisites
- The course INFOGR Computer Graphics and courses in algorithms and programming are mandatory. The exercise will be performed on the Blender open-source 3D-modeling environment.
- The knowledge of linear algebra and basic calculus will be very helpful, but not entirely necessary; we will teach some of the basics in the context.
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3D Modeling pertains to all forms of creating, designing, synthesizing, acquiring, analyzing and deforming geometric shapes in space.
The applications are numerous: from computer graphics and the film industry, through computer-aided design (CAD/CAM) and architecture, to processing of point clouds and procedural modeling.
Course form
Lectures and practicals.
Literature
The course will draw material from the following textbooks. Note that they might have different notations or explanations, and in this case the lecture material is complete and the only source that counts.
- "Polygon Mesh Processing" by Botsch et al. Free available online.
- "Curves and surfaces for CAGD: a practical guide" by Gerald Farin. Electronic copy from the UU library.
- "A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics and Image Processing" by Cohen-Or et al. ISBN 9781498706285 Published July 1, 2015 by A K Peters/CRC Press
- "Mathematics for Computer Graphics Applicatons" by by Michael E Mortenson. ISBN: 9780831131111
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