Dottorato di Padova in Matematica Computazionale

From CAGD to virtual/augmented reality
A.A. 2011/2012

II ciclo


I week
Tuesday 15/05/2012 (11-13; 14-16); Thursday 17/05/2012 (11-13; 14-16)
CIRAM, via Saragozza 8, Bologna, piano terra AULA MUSEO
II week
Tuesday 22/05/2012 (11-13; 14-16); Thursday 24/05/2012 (11-13; 14-17)
CIRAM, via Saragozza 8, Bologna, piano primo AULA SEMINARI
Thursday 31/05/2012 Student seminars/Final Exam


The field of geometric modelling or Computer Aided Geometric Design (CAGD), which is mainly based on numerical analysis, analytic, projective and differential geometry as well as computer science, provides the necessary algorithms for the required curve and surface representations. CAGD also supplies the related discipline of Computer Graphics with many of its mathematical and geometrical foundations. Recently there are the first approaches of combining geometric modelling applications with the emerging fields of Virtual and Augmented Reality. The discipline of Virtual Reality (VR) completely immerses users inside a synthetic environment whereas Augmented Reality (AR) allows the user to see three-dimensional virtual objects superimposed upon the real world. The objective of this class is to introduce the mathematical foundations of the field of geometric modelling and computer aided geometric design as well as to give a general overview of the emerging fields of virtual and augmented reality.
Course contents:
Polynomial B\'ezier curves
Analytic versus geometric continuity
B-spline curves, Rational curves (projective geometry, properties, conic sections)
B\'ezier and B-Spline surfaces
Virtual and augmented reality: Introduction and applications,
3D-Viewing, Haptics, VR and AR devices
Geometric Modelling in VR/AR

Examination and grading:

The final examination can be either an oral presentation about a specific subject based on a research paper, or the completion of a project which involves computer modeling using X3D.


D.A. Bowman, E. Kruijff, J.J. LaViola,Jr., I. Poupyrev, 3D User Interfaces, Theory and Practice, Addison-Wesley 2005.
G. Farin, Curves and Surfaces for Computer Aided Geometric Design: a practical guide, 5th edition, Morgan Kaufmann 2001.
G. J. Kim, Designing Virtual Reality Systems - The Structured Approach, Springer 2005.
K. M. Stanney (ed.), Handbook of Virtual Environments - Design, Implementation, and Applications, Lawrence Erlbaum Associates, Inc. 2002.


Lezione (15/05/2012)
Lezione (15/05/2012)
Lezione (17/05/2012)
Lezione (17/05/2012)
Lezione (22/05/2012)
Lezione (22/05/2012)
Lezione (24/05/2012)


Esercitazione 1 (15/05/2012)
Esercitazione 1 (15/05/2012)
Database X3D models (17/05/2012)
KelpForestExhibit (17/05/2012)
Esercitazione 2 (22/05/2012)
Spline Tools (22/05/2012)