IIT Delhi Deformation http://www.cse.iitd.ac.in/
Deformation IIT Delhi http://www.cse.iitd.ac.in/
Deformation IIT Delhi Deformation causes change in the shape keeping typically the same topology Geometric deformation (does not account for any law of physics) Local or global deformation http://www.cse.iitd.ac.in/
Deformation IIT Delhi Deformation: A transformation/mapping of the positions of every particle in the original object to those in the deformed body Each particle represented by a point p is moved by φ ( • ): p → φ ( t , p ) where p represents the original position and φ ( t , p ) represents the position at time t . http://www.cse.iitd.ac.in/
Deformation IIT Delhi http://www.cse.iitd.ac.in/
Deformation IIT Delhi • Changing an object’s shape –Usually refers to non-simulated algorithms –Usually relies on user guidance • Easiest when the number of faces and vertices of a shape is preserved, and the shape topology is not changed either –Define the movements of vertices http://www.cse.iitd.ac.in/
Deformation IIT Delhi � � � sformation � � � (x,y,z) (x,y,z) � �� � �� http://www.cse.iitd.ac.in/
Deformation IIT Delhi � If vertex i is displaced by (x , y , z) units � Displace each neighbor, j , of i by � (x , y , z) * f (i , j) � f (i , j) is typically a function of distance � Euclidean distance � Number of edges from i to j � Distance along surface (i.e., geodesics) http://www.cse.iitd.ac.in/ � ��
� Deformation IIT Delhi of all vertices � control a few vertices wh http://www.cse.iitd.ac.in/ � ��
Deformation IIT Delhi http://www.cse.iitd.ac.in/ � ��
� Deformation � � � IIT Delhi � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1 k � � i � � � ( ) 1 . 0 � � ; 0 � f i k � � 1 � n � � 1 k � � � � i � � � � � � ( ) 1 . 0 � � ; 0 i f k � � � � 1 � � � n ST � NY BR �� K STATE UNIVERSITY OF NEW YORK http://www.cse.iitd.ac.in/ � ��
Deformation IIT Delhi Assumption � �� http://www.cse.iitd.ac.in/
Deformation IIT Delhi � �� http://www.cse.iitd.ac.in/
Deformation IIT Delhi � �� http://www.cse.iitd.ac.in/
Deformation IIT Delhi CSE528 � �� http://www.cse.iitd.ac.in/
Deformation IIT Delhi � �� http://www.cse.iitd.ac.in/
Deformation IIT Delhi !"#$%$&'"&%()) ST � NY BR �� K CSE528 STATE UNIVERSITY OF NEW YORK http://www.cse.iitd.ac.in/
Deformation IIT Delhi � � compute � � � � � http://www.cse.iitd.ac.in/ � ��
Deformation IIT Delhi http://www.cse.iitd.ac.in/
Local Deformation IIT Delhi Hierarchical B-Spline Surfaces http://www.cse.iitd.ac.in/
Local Deformation IIT Delhi Hierarchical B-Spline Surfaces http://www.cse.iitd.ac.in/
Local Deformation IIT Delhi Hierarchical B-Spline Surfaces http://www.cse.iitd.ac.in/
Local Deformation IIT Delhi Hierarchical B-Spline Surfaces http://www.cse.iitd.ac.in/
Local Deformation IIT Delhi Hierarchical B-Spline Surfaces http://www.cse.iitd.ac.in/
Local Deformation IIT Delhi Hierarchical B-Spline Surfaces http://www.cse.iitd.ac.in/
Local Deformation IIT Delhi Hierarchical B-Spline Surfaces http://www.cse.iitd.ac.in/
Global Deformation IIT Delhi A Barr SIGGRAPH 1984 http://www.cse.iitd.ac.in/
Global Deformation IIT Delhi http://www.cse.iitd.ac.in/
Global Deformation IIT Delhi http://www.cse.iitd.ac.in/
Global Deformation IIT Delhi http://www.cse.iitd.ac.in/
Global Deformation IIT Delhi http://www.cse.iitd.ac.in/
Global Deformation IIT Delhi http://www.cse.iitd.ac.in/
Global Deformation IIT Delhi http://www.cse.iitd.ac.in/
Global Deformation IIT Delhi http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi • Physical Analogy: A clear, flexible plastic parallelepiped with one or more objects embedded in it. • The embedded objects are also flexible so that they deform with the object. http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi Parametric surfaces are free-form surfaces. The flexibility in this technique of deformation allows us deform the model in a free-form manner. Any surface patches Global or local deformation Continuity in local deformation Volume preservation http://www.cse.iitd.ac.in/
� � Free Form Deformation IIT Delhi � � v w i x i i x x x x 0 3 1 2 v � �� http://www.cse.iitd.ac.in/
� � Free Form Deformation IIT Delhi � � v w i x i � i x x � x x 0 3 1 2 v � � �� is functions � � d � � � � � � � � ( 1 ) d i i v w x x t t � � i i i � i � i i x x x x http://www.cse.iitd.ac.in/ � ��
Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi � 2 2 ( 1 ) � 2 2 ( 1 ) 2 v 2 � u v u uv u 4 u 5 � 2 � � v 4 , 3 2 5 3 � 2 � 2 � 2 ( 1 ) ( 1 ) 2 ( 1 ) u v v u v v � � 4 ( 1 ) ( 1 ) u u v v � 2 � 2 � � 2 2 � 2 ( 1 ) ( 1 ) 2 ( 1 ) ( 1 ) ( 1 ) u v u u v u v http://www.cse.iitd.ac.in/ � ��
Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi Basic idea: deform space by deforming a lattice around an object •The deformation is defined by moving the control points of the lattice •Imagine it as if the object were enclosed by rubber •The key is how to define –Local coordinate system –The mapping http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi Can enforce C k continuity • Surface (s, t, u) = (s(v, w), t(v, w), u(v, w)) • Two adjacent FFDs X 1(s1, t1, u1) & X 2(s2, t2, u2) with common boundary s1= s2= 0 • Conditions for first derivative continuity – ∂ X 1(0, t, u) / ∂ s = ∂ X 2(0, t, u) / ∂ s – ∂ X 1(0, t, u) / ∂ t = ∂ X 2(0, t, u) / ∂ t – ∂ X 1(0, t, u) / ∂ u = ∂ X 2(0, t, u) / ∂ u http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi Can enforce Ckcontinuity http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi Can enforce Ckcontinuity http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi Volume Preservation http://www.cse.iitd.ac.in/
Extended Free Form Deformation IIT Delhi Non Parallelopiped Lattice http://www.cse.iitd.ac.in/
Extended Free Form Deformation IIT Delhi Non Parallelopiped Lattice http://www.cse.iitd.ac.in/
Extended Free Form Deformation IIT Delhi Non Parallelopiped Lattice http://www.cse.iitd.ac.in/
Extended Free Form Deformation IIT Delhi Some Results http://www.cse.iitd.ac.in/
Animation Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Animation Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Animation Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Animation Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Direct Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Direct Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
Direct Free Form Deformation IIT Delhi http://www.cse.iitd.ac.in/
References IIT Delhi 1. Hirearchical B-spline refinement, DR Forsey and RH Bartels, SIGGRAPH 88, Computer Graphics, Vol 22, No 4, August 1988 2. Fee form deformation of solid geometric models, TW Sederberg, SR Parry, SIGGRAPH 86, Computer Graphics, Vol 20, No 4, August 1986 3. Extended free form deformation: A sculpting tool for 3D geometric modeling, S Coquillart, SIGGRAPH 90, Computer Graphics, Vol 24, No 4, Aug 1990 4. Direct manipulation of free form deformations, WM Hsu, JF Hughes, H Kaufman, SIGGRAPH 92, Computer Graphics, Vol 26, No 2, July 1992 http://www.cse.iitd.ac.in/
References IIT Delhi http://www.pmp-book.org/download/slides/Deformation.pdf http://www.cs.sunysb.edu/~qin/courses/graphics/graphics-deformation.pdf http://caig.cs.nctu.edu.tw/course/CA/Lecture/deformation.pdf http://www.cse.iitd.ac.in/
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