Shape Modeling

Instructor

• Vladimir SAVCHENKO

Goal and Theme

The objective of the lectures is to study basic methods related to
shape modeling, in particular we will consider:
parametric representations, spline approximation and interpolation, differential geometry, and topology of curves and surfaces.

Abstract

Curves and surfaces arise in many applications such as art, industrial design, mathematics, architecture, and engineering, and numerous computer drawing packages and computer-aided design packages have been developed to facilitate the creation of geometric shapes.

The objective of the lectures is to study basic geometric methods, in particular we will consider:

• Differential Geometry of Curves and Surfaces
• Elements of computational geometry
• Preliminary mathematics and methods of parametric representation of curves and shapes
• Representational schemes in geometric modeling for Solids- CSG, Boundary representation, sweeps

Schedule

1^st week: Introduction to Shape modeling and geometry modeling

2^nd week: Basic graphics: Curves

3^rd week: Differential Geometry of Curves and Surfaces (I)

4^th week: Differential Geometry of Curves and Surfaces (II)

5^th week: Elements of Computational Geometry

6^th week: Parametric representation for curves (I): the Bezier Curves

7^th week: Parametric representation for curves (II): the Bezier Curves

8^th week: Parametric representation for curves (III): the B-spline curves.

9^th week: Parametric representation for surfaces ( IV)

10^th Basics of Topology

11^th week: Representational Schemes in Geometric Modeling For Solids, CSG

12^th week: Boundary representation

13^th week: Sweep representation

14^th week: Fractals and their Applications, Gramma-Based models, L-systems

15^th week: Principels of Genetic Algorithms and their applications to Shape modeling

Materials

Lecture notes

References

Given in lecture notes

Evaluation Method

According to exam