## Usted está aquí

Créditos
6
Tipos
Optativa
Requisitos
Esta asignatura no tiene requisitos
Departamento
CS
This course covers the techniques, algorithms and data structures used to acquire, represent and query geometric models of solids and surfaces. The course will cover various modeling techniques, including boundary representations, implicit representations, instantiation and Boolean combinations of shapes, as well as procedural modeling. We will also discuss effective data structures for representing various types of objects, as well as the process of acquiring models from real objects.

## Horas semanales

Teoría
2
Problemas
0
Laboratorio
1
Aprendizaje dirigido
0
Aprendizaje autónomo
5

## Contenidos

1. Foundations of 3D modeling
Elements of a geometric modeling system. Solid models. Closed, bounded and regular sets of points. Two-manifold surfaces. Abstraction levels in geometric modeling.
2. Boundary representation (BRep)
Polyhedra. Cells, shells, faces, loops, edges and vertices. Genus of a surface. Euler equation for polyhedra. Incidence relationships. Creation of BRep models. Sweep. Boolean operations.
3. Subdivision surfaces
Subdivision surfaces. Interpolation and approximation. Update rule. Classification. Catmull-Clark subdivision.
4. CSG models
Constructive Solid Geometry. CSG trees. Basic operations. Point-inside-CSG test.
5. Space decomposition models
Voxelizations. Octrees. Classic, Face and Extended octrees. Octree representation. Basic operations on octrees.
6. Implicit modeling
Scalar fields. Surface reconstruction from scalar fields. Blobby molecules, metaballs and soft objects.
7. Data structures for triangle meshes
Euler equation for triangle meshes. Face-based, Vertex-based and edge-based representations. The half-edge data structure. APIs for geometry processing.
8. Geometric tests and queries
Estimating normal and tangent planes at vertices of polygonal meshes. Discrete curvature at mesh vertices. Mesh quality. Non-selfintersection test.
9. Procedural modeling
Fractals. Lindenmayer systems (L-systems). Stochastic and parametric grammars. Shape grammars. Generative modeling.
10. Geometry acquisition
Pipeline for the acquisition of 3D models. Technologies. Registration and merge.

### Lectures

Material will be presented in lectures along the term. You are expected to conduct complementary readings and exercises will also be assigned on occasion, to be presented at a later date or turned in.

Teoría
39h
Problemas
0h
Laboratorio
0h
Aprendizaje dirigido
0h
Aprendizaje autónomo
36h

### Implementation of selected algorithms

A selection of relevant algorithms will be assigned to implement in Lab sessions and on your own. You may be required to present your solution to the class. You must turn in fully functional source code that runs in the indicated platform. Usual languages are C++ and Python.

Teoría
0h
Problemas
0h
Laboratorio
13h
Aprendizaje dirigido
0h
Aprendizaje autónomo
13h

### Final exam

At the end of the term you will have a final exam, which may be a take-home.

Semana: 17
Teoría
0h
Problemas
0h
Laboratorio
0h
Aprendizaje dirigido
0h
Aprendizaje autónomo
0h

### Partial exam

At the middle of the term you will have a partial exam, which may be a take-home.

Semana: 7
Teoría
2h
Problemas
0h
Laboratorio
0h
Aprendizaje dirigido
0h
Aprendizaje autónomo
0h

## Metodología docente

The teaching methodology will be based based on weekly theory classes and lab classes. Course concepts will be introduced in the theory classes. Exercises will be used to consolidate these concepts, which will be further developed in the lab sessions.

The lab sessions basically involve the teacher presenting the guidelines for the practical work (split by sessions) and the concepts bearing on the software to be used. Students will complete the design and programming of the various applications bearing on the course contents. The exercises will be carried out individually.

## Método de evaluación

Partial: mark based on the student's performance in the partial exam

Exam: mark based on the student's performance in the final exam

Lab: grade stem from the student's implementations of selected algorithms (including occasionally their presentation of their
solution in a laboratory class)

The final grade for the course will be computed as:

Final Grade = 0.4 Exam + 0.3 Partial + 0.3 Lab