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

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

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

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

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

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 http://tom.cs.byu.edu/~557/text/cagd.pdf http://graphics.cs.ucdavis.edu/~hamann/lectures.shtml http://people.bath.ac.uk/ensab/G_mod/FYGM/ http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/notes.html   Title *One of the 1rst post doc at HU, in 1928! CAG Design and Simulation

COMPUTER AIDED GEOMETRY DESIGN AND MODELING Bibliography, Web (re)Sources, Software Tools WEB Resources: Tom Sederberg http://tom.cs.byu.edu/~557/text/cagd.pdf Wikipedia ( but you may have to correct-modify it) My own notes : http://www.cs.huji.ac.il/course/2004/cagd/cagdnotes.pdf http://www.cs.huji.ac.il/course/2004/scicomp/VariationalMethods.pdf http://www.cs.huji.ac.il/course/2004/scicomp/finite_elements.pdf Strang courses MIT (videos http://ocw.mit.edu/OcwWeb/Mathematics/18-085Fall-2008/CourseHome/index.htm) and books website http://math.mit.edu/cse/ Software: Matlab Poor man’s matlab : http://www.scilab.org/ http://www.gnu.org/software/octave/ Poor man’s 3D creation: http://www.blender.org/ Visualisation : Tcl/Tk, OpenGL   Title *One of the 1rst post doc at HU, in 1928! CAG Design and Simulation

TENSOR PRODUCT SURFACES CAG Design and Simulation

TENSOR PRODUCT SURFACES CAG Design and Simulation

TENSOR PRODUCT SURFACES CAG Design and Simulation

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

TENSOR PRODUCT SURFACES Bezier surface CAG Design and Simulation

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

TENSOR PRODUCT SURFACES CAG Design and Simulation

TENSOR PRODUCT SURFACES CAG Design and Simulation

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