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# Geometrical Modelling in Graphics (Course Materials)

Lecture Monday 9:00 MS Teams Exercise Tuesday 16:30 MS Teams

No make-up exams will be given for missed tests. All the assignments should be turn in by the designated due date. To pass this course all the course requirements must be SATISFACTORILY completed > 30% of each problem set. Programming, modelling projects and oral exam.

### What you Need to Pass

• Attend lessons. One missed +0 points. 2 missed 0 points, 3 and more is Fx.
• Programming, modelling project with production and exercise (mandatory, 50 points). Submission after deadline -50%.
• All programming is checked with deadlines during the exercises.
• Pass oral/written exam: (+50 points) If you feel you are better, convince me !
• Summary
• Attendance = 0 or -100 (Fx)
• Projects = +50..0
• Oral/written exam = +50..0
A = 92-100
B = 84-91
C = 76-83
D = 68-75
E = 60-67
Fx = 0-59
• VIEW RESULTS
• In case of online lecture, homework and homework results connect to MS Teams Team Code: rx0qlm4

### Oral Examination

To the oral examination all the above requirements must be SATISFACTORILY completed. Random lecture topic will be selected and presented by a student after written preparation.

• Mario Botsch, Leif Kobbelt, Mark Pauly, Pierre Alliez, Bruno Levy, "Polygon Mesh Processing" CRC Press
• Siu-Wing Cheng, Tamal K. Dey, Jonathan Shewchuk, "Delaunay Mesh Generation" CRC Press
• 3D printer modelling and best models to get the inspiration

### Lesson00 "Introduction to Geometry Modelling"

• Lecture schedule
• "Terms and conditions" of this lecture
• Lecture notes: lesson00.pdf

### Lesson01 "Polygonal meshes, Winged Edge, Quad Edge, DCEL"

• 2D manifold
• Polygonal meshes
• Winged Edge
• Double Connected Edge List
• Lecture notes: lesson01.pdf

### Lesson02 "Polygonal Mesh Properties"

• Normal, curvature, object interior
• Descriptors
• Bounded volume
• Lecture notes: lesson02.pdf

### Lesson03 "Polygonal Mesh Simplification"

• Mesh simplification algorithm
• Terrain visualisation
• Progressive meshes
• Lecture notes: lesson03.pdf

### Lesson04 "Polygonal Mesh Smoothing"

• Polygon and mesh smoothing with subdivision
• Catmull-Clark subdivision, Modified Butterfly subdivision
• Mesh Laplacian smoothing
• Lecture notes: lesson04.pdf

### Lesson05 "Polygonal Mesh Repairing"

• Polygon and mesh smoothing with subdivision
• Delaunay triangulation
• Triangulation in 3D
• Filling holes in meshes
• Volumetric mesh repair
• Lecture notes: lesson05.pdf

### Lesson06 "Curves"

• Polynomial curves
• Spline curves
• Rational curves
• Implicit curves
• Lecture notes: lesson06.pdf

### Lesson07 "Surfaces"

• Polynomial surfaces
• Spline surfaces
• Rational surfaces
• Implicit surfaces
• Lecture notes: lesson07.pdf

### Lesson08 "Volumes"

• Distance function
• Voxelization: Mesh voxelization, Implicit surface voxelization
• Distance transforms
• Fast marching method
• Visualization
• Lecture notes: lesson08.pdf

### Lesson09 "Point Clouds"

• Point cloud sources
• K-nearest neighbor search on Kd-tree
• Normal estimation
• Registration
• Visualization
• Lecture notes: lesson09.pdf

### Lesson10 "Surface Reconstruction"

• Implicit reconstruction
• Power crust mesh reconstruction
• Parameteric reconstruction
• Lecture notes: lesson10.pdf

# EXERCISES

Your presence at the seminar is mandatory. Exercise projects are done in Blender with Python language.

### Exercise 01 "Blender Scripting”

• Install [1]
• Using scripts reference page [2]
• Example mesh_script.blend
• to run in new Blender version,
• change line 31 and 32 to bpy.context.scene.collection.objects.link(obj)
• line 35 to obj.select_set(state=True)
• line 36 to bpy.context.view_layer.objects.active = obj
• Create tetrahedron [3]

### Exercise 06 "Triangle Mesh Edge Contraction”

Homework (13.4.)

• implement the edge contraction algorithm
• works on the quads and triangles simultaneously
• is able to extracts n shortest edges

### Exercise 09 "Butterfly subdivision - Triangular Meshes”

Homework (4.5.)

• implement modifed Butterfly subdivision scheme

### Exercise 10 "Polygonising a scalar field”

Homework (4.5.)

• create iso surface of a sphere, torus and cylinder
• determine a boolean union and intersection operator on the 3D shapes
• create an unique shape using all three iso surfaces and both operators