Tesis profesional presentada por Ricardo Pérez Águila

Doctorado en Ciencias de la Computación. Departamento de Computación, Electrónica, Física e Innovación. Escuela de Ingeniería y Ciencias, Universidad de las Américas Puebla.

Jurado Calificador

Presidente: Dra. Dolors Ayala Vallespí
Vocal y Director: Dr. Fernando Antonio Aguilera Ramírez
Secretario: Dr. Daniel Vallejo Rodríguez
Vocal: Dr. Isaac Juan Rudomín Goldberg
Vocal: Dr. Mauricio Javier Osorio Galindo

Cholula, Puebla, México a 13 de noviembre de 2006.

Resumen

The Extreme Vertices Model (3D-EVM) was originally presented, and widely described,

by Aguilera & Ayala for representing 2-manifold Orthogonal Polyhedra (1997) and later considering both Orthogonal Polyhedra (3D-OPs) and Pseudo-Polyhedra (3D-OPPs, 1998). This model has enabled the development of simple and robust algorithms for performing the most usual and demanding tasks on solid modeling, such as closed and regularized Boolean operations, solid splitting, set membership classification operations and measure operations on 3D-OPPs.

It is natural to ask...

Resumen (archivo pdf, 21 kb).

Índice de contenido

Portada (archivo pdf, 54 kb)

Agradecimientos y Dedicatorias (archivo pdf, 27 kb)

Índices (archivo pdf, 37 kb)

Capítulo 1. Introduction (archivo pdf, 50 kb)

Capítulo 2. Theoretical frame and previous work (archivo pdf, 223 kb)

  • 2.1 Terminology
  • 2.2 Schemes for the modeling of n-Dimensional Polytopes
  • 2.3 Topological properties of 4D Orthogonal Pseudo-Polytopes
  • 2.4 Conclusions

Capítulo 3. Configurations in the n-Dimensional Orthogonal Pseudo-Polytopes (archivo pdf, 285 kb)

  • 3.1 Introduction
  • 3.2 Configurations for the nD-OPP´s and the equivalence relation Rf
  • 3.3 The problem of determining the configurations for the nD-OPP´s (n > 4)
  • 3.4 Binary representation for the configurations in the nD-OPP´s
  • 3.5 Pólya´s countings and the number of configurations for the nD-OPP´s
  • 3.6 Four equivalence relations in the set Bn
  • 3.7 Fast comparison of combinations of nD hyper-boxes through relations Radj, RH & RE
  • 3.8 The ´Test-Box´ algorithm
  • 3.9 Conclusions

Capítulo 4. The odd edge characterization and its role in the combinatorial topology of the n-Dimensional Orthogonal Pseudo-Polytopes (archivo pdf, 336 kb)

  • 4.1 Local analysis over the nD-OPP´s
  • 4.2 Spivak´s k-chains fundamental Concepts
  • 4.3 Linking k-chains with Topological Local Analysis of Odd Edges
  • 4.4 Conclusions

Capítulo 5. Orthogonal polytopes modeling through the Extreme Vertices Model in the n-Dimensional Space (nD-EVM) (archivo pdf, 864 kb)

  • 5.1 Preliminary background
  • 5.2 Brinks and extreme vertices in the nD-OPP´s
  • 5.3 Local analysis over extreme vertices in the nD-OPP´s
  • 5.4 Global analysis over the nD-OPP´s and the extreme vertices model
  • 5.5 Relating sections and couplets
  • 5.6 Regularized boolean operations on the nD-EVM
  • 5.7 nD-EVM properties
  • 5.8 Conclusions

Capítulo 6. Algorithms in the nD-EVM and their performance (archivo pdf, 1 mb)

  • 6.1 Basic algorithms for the nD-EVM
  • 6.2 The boolean operations algorithm for the nD-EVM
  • 6.3 Computing the content of an nD-OPP
  • 6.4 Computing the content of the boundary of an nD-OPP
  • 6.5 Computing forward and backward differences of an nD-OPP
  • 6.6 Algorithms for converting the nD-EVM to and from other schemes
  • 6.7 Conclusions

Capítulo 7. Applications (archivo pdf, 2 mb)

  • 7.1 Application 1: Representing color 2D-animations through 4D-OPP´s and the EVM
  • 7.2 Application 2: A procedure for comparing color 2-dimensional images through their extrusions to the 5-dimensional colorspace
  • 7.3 Application 3: Incorporating the nD-EVM to image based reasoning
  • 7.4 Application 4: Manipulating "Real World" 3D datasets with the nD-EVM
  • 7.5 Application 5: Collision detection
  • 7.6 Conclusions

Capítulo 8. Conclusions and future work (archivo pdf, 71 kb)

  • 8.1 Main contributions
  • 8.2 Future work

Referencias (archivo pdf, 65 kb)

Apéndice A. The vector space Bn (archivo pdf, 43 kb)

Apéndice B. Configurations for the nD-OPP´s obtained by the ´Test-Box´ algorithms (archivo pdf, 46 kb)

Apéndice C. Some adjacencies´ properties of the configurations in the nD-OPP´s (archivo pdf, 38 kb)

Apéndice D. Some characterizations of odd and even edges in the nD-OPP´s (archivo pdf, 47 kb)

Apéndice E. Some characterizations of extreme and non-extreme vertices in the nD-OPP´s (archivo pdf, 85 kb)

Apéndice F. Characterization of extreme vertices according their incident odd/even edges and relating them with other edges´ characterizations (archivo pdf, 34 kb)

Apéndice G. Applying nD-EVM concepts together: an example in 4D space (archivo pdf, 56 kb)

Apéndice H. The "L-Shaped" nD polytopes family (archivo pdf, 43 kb)

Apéndice I. Extreme vertices countings for two color 2D-animations (archivo pdf, 49 kb)

Apéndice J. Properties of function (archivo pdf, 32 kb)

Pérez Águila, R. 2006. Orthogonal polytopes: study and application. Tesis Doctorado. Ciencias de la Computación. Departamento de Computación, Electrónica, Física e Innovación, Escuela de Ingeniería y Ciencias, Universidad de las Américas Puebla. Noviembre. Derechos Reservados © 2006.