Memo rial Luiz V elho Overview Education B.S. Degree - - PDF document

Memo rial Luiz V elho

Overview Education � B.S. Degree - ESDI { M.S. Degree - MIT Media Lab { Ph.D. Degree - U. T o ronto { Resea rch � Image Dithering { Multiresolution P ainting { Mo deling with Implicit Objects { P olygonization Metho ds { Exp erience � F AM { Glob o {

B.S. Degree - ESDI Computer Graphics and Design Investigation of T echnology and Applications of CG Field Study { CAD in Brazil � Exp eriment with Designers { P attern Creation � (Simmetry Groups) Computer Animation { Wireframe 3D System � (Development and Pro duction)

Exp eriment with Graphic Designers Simmetry Groups �

3D Wireframe Animation First Computer Generated Animation in Brazil

M.S. Degree - MIT Media Lab Computer Animation Pro cedural Animation System Animation Abstractions { Scripts � T racks � System Architecture { Extension Language � Distributed Computation � Multiple Windo ws (X11) � Di�erent Levels { Autho ring � Interaction �

Scripts System T ypical w o rking con�guration �

Animation Example Inverse Kinematics � F o rw a rd Dynamics � Collision Detection �

Ph.D. Degree - U. of T o ronto Geometric Mo deling Mo deling F ramew o rk based on Piecewise Implicit Descriptions Cha racterization of Implicit Mo dels � T ubula r Neigb o rho o d { Smo oth Implicit F unction Mo del � Multiscale Edge Analysis / Synthesis { Hiera rchical Implicit Rep resentation � Multiscale B-Spline Basis { Adapted Simplicial Decomp osition � Physics-Based Simulation { Complete F ramew o rk * Decomp osition + Adaptation Conversion of Rep resentations Implicit $ P a rametric - . V olumetric

Smo oth Implicit F unction Cha racteristic F unction W avelet Maxima V alues V olumetric Implicit F unction

Hiera rchical Rep resentation B-spline Pyramid of the Implicit F unction B-spline F unctions

App ro ximate Conversion Initial and Final Mesh fo r Solid Shap e Final Mesh fo r Hollo w Shap e Bounda ry derived from the Mesh

Image Dithering Pyramid Dither � Dither with Space Filing Curves � Basic { Adaptive { Colo r { Graphic E�ects {

Pyramid Dither Image Pyramid � Recursive Quantization � P W = w i Distribution of Intensities � w = d + r i i i Deterministic Comp onent { d = b ( v =V )) W c i i Probabilistc Comp onent { r = 1 with Probabilit y e i i Analysis � Optimal Lo cal and Global Quantization { Deterministic T erm Dominates Globally { Probabilistic T erm Dominates Lo cally {

Example Photographic Image � Computer Generated Image �

Space Filling Curve Dither SF C Dither � Ap erio dic { V a riable Cluster { Anisotropic { * Fills T echnology Gap * Reop ened the a rea

SF C: Basic Metho d Image Scan � Image P a rtition � P attern Generation �

SF C: Adaptation Pixel Centering � V a riable Cluster Size � Adaptation F unction (image gradient) �

SF C: Colo r Co rrelated Cluster P ositioning �

Algo rithm 1. Sub division of Image into Cells 2. Computation of Average Intensit y 3. Generation of Dot P atterns

Examples Photograph � Ca rto on �

2D P aint W avelet P aint � Multiresolution T extures � op ened the a rea

W avelet P aint Multiresolution P ainting Pro cess mo dify image at level x # " move up o r do wn a level Computational Supp o rt � P ainting over Multiple Levels { Multiresolution Comp ositing { B-Spline W avelets of degree n { Advantages � Quick Changes (la rge a reas) { Unlimited Detail {

Example P ainting and Zo oming �

Multiresolution T extures Pro cedural P aint-Brushes � New T o ol, designed fo r MPS � Complex P atterns { Automatic Generation of Detail { Mechanisms Pro cedural Bandpass Pyramid: f ( u; v ; s ) � Base Pro cedure { inital app ea reance � Called during P ainting � Detail Pro cedure { add detail � Called During Magni�cation � T exture Alpha Channel: � � f T exture Propagation { Lazy Evaluation {

Example Ro ck T exture � Mixture of T extures �

Implicit Surfaces Multiscale Rep resentation � Surface Defo rmation � and Animation T exture Mapping �

Multiscale Rep resentation of Implicit Surfaces Multiscale B-Spline Mo del � Piecewise { Structured { Hiera rchical { Rep resentation � 0 1 X X X @ A f = g = a � ( x ) j i;j j 2 ;k i j j i where e a = < F ; � > i;j j;k i Computation � Laplacian Decomp osition { Data Structure � Spatial Hash T able { H = f a ; � g i;j i Applications Conversion V olumetric - Implict { V a riable Level of Detail Mo del { F ast Ra y T racing / V olume Rendering {

Example: Noisy Sphere Slices of the Densit y F unction � B-Spline Pyramid � 32 � 32 16 � 16 8 � 8 Surface Ra y-T raced �

Surface Defo rmation and Animation System Pip eline � IMPLICIT OBJECT MESH GENERA TION SPRING-MASS MESH USER D YNAMICS SIMULA TION INPUT GEOMETRIC D A T A VISUALIZA TION Mesh Adaptation Algo rithm �

Example: Cylinder Mesh Adaptation � Initial and Defo rmed Meshes Dynamics Simulation �

T exture of Implicit Surfaces 2D T exture Mapping with P a rticle Systems Projection � T exture Supp o rt Object # Implicit Object Mapping F unction � F o rce Field { 2 d x dx + � + r F = 0 2 dt dt Computation � P a rticle System { Control � Global { Relative P ositioning � Blending of Gradient Fields � Lo cal { A ttracto rs / Repulso rs �

Example: Cok e Bottle Source T exture � P a rticle T rajecto ries and T extured Object �

P olygonization P olygonization of Implicit Surfaces � using Simplicial Decomp ositions Physics-Based P olygonization � of Implicit Surfaces Uni�ed P ath-Based P olygonization � of P a rametric and Implict Surfaces

Simplicial P olygonization Adaptive P olygonization � Metho d � Recursive Simplicial Decomp osition { Bounda ry Constraints { Sub division of the Cub e � F ace and Edge Constraints �

Example: Blobb y P olygonization � Detail �

Physics-Based P olygonization Quasi-Regula r T riangulation � F at T riangles { Optimal Sample Placement { Physics-Based Metho d � Sp ring-Mass Meshes { Mesh Adaptation { Internal F o rces � (mesh) External F o rces � (gradient �eld) Induced P olygonal Mesh � Dual {

Example: Cylinder Mesh Adaptation � P olygonal Mesh �

P ath-Based P olygonization Uni�ed F ramew o rk � P a rametric { Implicit { Adaptive T riangulation � Consistent T op ology { Hiera rchical Mesh � Multiresolution { Progressive { Op erations � Multiresolution P ath Sampling { 0 2 1 2 0 p q 0 S t L R 1 t t 2 Cell Structuring { o 3 n 1 n 2 n n 1 n 2 o 1 o 2 o 1 o 2 n 3 o � �

Example: T o rus P a rametric � Implicit �