INFO4216 : Géométrie Computationnelle et Images Digitales

This course will focus on algorithms and data structures for geometric objects (segments, polygons, surfaces, volumes, …) and digital images. We will focus on various ways such
data can be generated, processed and used. After introducing the classical data structures to store 2D and 3D shapes, we will cover how these data structures are used depending on
the way the data is generated or processed. Typical algorithms include nearest neighbor search or ray tracing queries, surface reconstruction from point sets, parameterization for
texture mapping, rasterization and image synthesis.

Detailed Notions

Image processing

• Colors
• Histograms
• Fourrier analysis
• Shannon theorem
• Local descriptor

3D Geometry basics

• Vectors, Matrices, Perspective transformations
• Triangles meshes
• Normals
• Parameterization
• Splines

Rendering

• Camera
• Visibility
• Rasterization
• Ray tracing
• Depth
• Lighting
• Shadows

Geometry processing

• Differential operators on meshes
• Curvature
• Mesh quality
• Compression

Computational geometry

• Convex hulls
• Delaunay /Voronoi
• Spatial acceleration structures
• Predicates and robustness