1. COMPUTER AIDED GEOMETRY DESIGN AND MODELING
What is the course about ???
Title
*One of the 1rst post doc at HU, in 1928!
CAG Design and Simulation

2. COMPUTER AIDED GEOMETRY DESIGN AND MODELING
What is the course about ???
Title
*One of the 1rst post doc at HU, in 1928!
CAG Design and Simulation

3. COMPUTER AIDED GEOMETRY DESIGN AND MODELING
What is the course about ???
Title
*One of the 1rst post doc at HU, in 1928!
CAG Design and Simulation

4. COMPUTER AIDED GEOMETRY DESIGN AND MODELING
What is the course about ???
Title
*One of the 1rst post doc at HU, in 1928!
CAG Design and Simulation

5. COMPUTER AIDED GEOMETRY DESIGN AND MODELING
SYLLABUS OUTLINE
Design, Modeling and Simulation
Functions,Curves and Surfaces
Construction of Curves and Surfaces by Means of Basis Functions
Bezier Curves
B-splines ( Basis Splines , I-J Schoenberg* 1946 )
Bezier , B-splines surfaces, Volumes.
Basis Functions revisited, Hierarchy, Knot insertion
1rst Applications to Design and Simulation, Data Organisation, Sparce matrices
Relation to the Finite Element Method
NURBS(Non Uniform B- Splines), curves, surfaces and volumes.
Applications: Free Form Design, Simulation, Optimisation ( and time permits Animation)
Title
*One of the 1rst post doc at HU, in 1928!
CAG Design and Simulation

6. COMPUTER AIDED GEOMETRY DESIGN AND MODELING
Bibliography, Web (re)Sources, Software Tools
BOOKS ON CAGD
(Fundamentals of ) Computer Aided Geometric Design , Hoschek Lasser -AK Peters 1993
Curves and Surfaces for CAGD A Practical Guide 5th edition Gerald Farin- Morgan-Kaufmann 2002
Geometric Modeling with Splines, Cohen, Riesenfeld Elber - AK Peters 2001
The Nurbs Book,2nd ed. Peigl,Tiller Springer 1997
BOOKS on Numerical Methods- Simulation
Computational Science and Engineering 1rst Edition G. Strang Wellesleycambridge press 2007
An Analysis of the Finite Element Method, 2nd ed. by G. Strang and George Fix† Wellesleycambridge (2008)
Isogeometric Analysis J.A. Cottrell, T.J.R. Hugues, Y. Bazilevs
WEB Resources:
Tom Sederberg
Title
*One of the 1rst post doc at HU, in 1928!
CAG Design and Simulation

7. COMPUTER AIDED GEOMETRY DESIGN AND MODELING
Bibliography, Web (re)Sources, Software Tools
WEB Resources:
Tom Sederberg
Wikipedia ( but you may have to correct-modify it)
My own notes :
Strang courses MIT (videos and books website
Software:
Matlab
Poor man’s matlab :
Poor man’s 3D creation:
Visualisation : Tcl/Tk, OpenGL
Title
*One of the 1rst post doc at HU, in 1928!
CAG Design and Simulation

8. TENSOR PRODUCT SURFACES
CAG Design and Simulation

9. TENSOR PRODUCT SURFACES
CAG Design and Simulation

10. TENSOR PRODUCT SURFACES
CAG Design and Simulation

11. TENSOR PRODUCT SURFACES
The two-dimensional basis functions are shown as wireframe surfaces. Since the control points are on the same row, the basis function in the u-direction is fixed while the basis functions in the v-direction change. Since B-spline basis functions are in general non-zero only on a few consecutive knot spans (i.e., the local modification scheme), the two-dimensional B-spline basis functions are non-zero on the product of two knot spans on which at least one one-dimensional basis function is non-zero. This fact is shown in the above figures clearly.
CAG Design and Simulation

12. TENSOR PRODUCT SURFACES
Bezier surface
CAG Design and Simulation

13. TENSOR PRODUCT SURFACES
Schematic illustration of NURBS paraphernalia for a one-patch surface model. Open knot vectors and quadratic C1-continuous basis functions are used. Complex multi-patch geometries may be constructed by assembling control meshes as in standard finite element analysis. Also depicted are C1-quadratic (p = 2) basis functions determined by the knot vectors. Basis functions are multiplied by control points and summed to construct geometrical objects, in this case a surface in R3. The procedure used to define basis functions from knot vectors will be described in detail in Chapter 2.
CAG Design and Simulation

14. TENSOR PRODUCT SURFACES
CAG Design and Simulation

15. TENSOR PRODUCT SURFACES
CAG Design and Simulation

16. TENSOR PRODUCT SURFACES
Definition de domaines…..2d -> 2d, 2d-> 3d, 3d->3d
CAG Design and Simulation