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Games, Movies and Virtual Worlds – An Introduction to Computer Graphics Ayellet Tal Department of Electrical Engineering Technion

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When you think about graphics, you envision

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Applications Science Art Engineering Medicine Entertainment Advertising Education

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Applications Science Art Engineering Medicine Entertainment Advertising Education

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Applications Science Art Engineering Medicine Entertainment Advertising Education

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Applications Science Art Engineering Medicine Entertainment Advertising Education

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Applications Science Art Engineering Medicine Entertainment Advertising Education

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Applications Science Art Engineering Medicine Entertainment Advertising Education

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Applications Science Art Engineering Medicine Entertainment Advertising Education

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Applications Science Art Engineering Medicine Entertainment Advertising Education Outside-In

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Why interesting? The world complex dynamic multi-dimensional continuous The screen simple static two-dimensional discrete

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Beauty Science – math and physics Engineering – software and hardware Artistic and aesthetic issues Fun!

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Issues in computer graphics Geometric modeling Rendering Animation Scientific visualization “The purpose of computing is insight, not numbers” Hamming Virtual reality Human-computer interaction

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Geometric modeling How do we represent objects?

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Wish list 1. Large domain 2. Unambiguous 3. Unique 4. Accurate 5. Impossible to create invalid representations 6. Easy to create and maintain 7. Closure under certain operations 8. Compact 9. Efficient

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Geometric modeling How do we represent objects? Voxels

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Geometric modeling How do we represent objects? Splines

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Geometric modeling How do we represent objects? Polyhedra

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Rendering 1. What pixels? 2. What ’ s in the pixel? 3. Which color?

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What pixels = scan conversion Given: A mathematical description of a two or a three dimensional “scene” Find: A value for each pixel in the frame buffer

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What pixels = scan conversion Given: A mathematical description of a two or a three dimensional “scene” Find: A value for each pixel in the frame buffer

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What ’ s in the pixel - visibility Goal: Hidden surface removal In object space or in image space? In software or in hardware?

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What color? Illumination and shading Transparency, reflection

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Issues - recap Modeling: Construct / represent objects Transform to construct scene Rendering: Project Scan convert Remove hidden surface Assign colors

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Animation How to define / represent complex time-dependent behavior of objects?

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Animation topics Automatic in-between Transformations Collision Motion Facial animation Morphing Physically-based simulation

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Animation topics Automatic in-between Transformations Collision Motion Facial animation Morphing Physically-based simulation

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Animation topics Automatic in-between Transformations Collision Motion Facial animation Morphing Physically-based simulation

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Animation topics Automatic in-between Transformations Collision Motion Facial animation Morphing Physically-based simulation

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Animation topics Automatic in-between Transformations Collision Motion Facial animation Morphing Physically-based simulation

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Animation topics Automatic in-between Transformations Collision Motion Facial animation Morphing Physically-based simulation 72 Frames - 5 Full Frames

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Animation topics Automatic in-between Transformations Collision Motion Facial animation Morphing Physically-based simulation

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Animation topics Automatic in-between Transformations Collision Motion Facial animation Morphing Physically-based simulation 1993, Apple Computer, Inc.

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Case study – Teaching dinos to dance

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Algorithm 1. Decomposition 2. Control skeleton extraction 3. Joint binding 4. Motion definition or “ copying ”

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Algorithm 1. Decomposition 2. Control skeleton extraction 3. Joint binding 4. Motion definition or “ copying ”

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Algorithm 1. Decomposition 2. Control skeleton extraction 3. Joint binding 4. Motion definition or “ copying ”

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Algorithm 1. Decomposition 2. Control skeleton extraction 3. Joint binding 4. Motion definition or “ copying ”

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Algorithm 1. Decomposition 2. Control skeleton extraction 3. Joint binding 4. Motion definition or “ copying ”

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Research topic: decomposition Let S be an orientable mesh. Goal: decompose S into connected sub-meshes S 1, S 2 … S k that are face-wise disjoint, and whose union gives S. S S1S1 S2S2 SkSk

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Key idea: two-phase algorithm 1. Find major components with fuzzy boundaries 2. Find exact boundaries

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Algorithm outline 1. Construct fuzzy decomposition a.Assign distances to pairs of faces b.Assign probabilities of belonging to patches c.Compute a fuzzy decomposition 2. Construct exact boundaries

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Algorithm outline 1. Construct fuzzy decomposition a.Assign distances to pairs of faces b.Assign probabilities of belonging to patches c.Compute a fuzzy decomposition 2. Construct exact boundaries

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Algorithm outline 1. Construct fuzzy decomposition a.Assign distances to pairs of faces b.Assign probabilities of belonging to patches c.Compute a fuzzy decomposition 2. Construct exact boundaries

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Algorithm outline 1. Construct fuzzy decomposition a.Assign distances to pairs of faces b.Assign probabilities of belonging to patches c.Compute a fuzzy decomposition 2. Construct exact boundaries

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Algorithm outline 1. Construct fuzzy decomposition a.Assign distances to pairs of faces b.Assign probabilities of belonging to patches c.Compute a fuzzy decomposition 2. Construct exact boundaries

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Problem: finding boundaries Given: G=(V,E) the dual graph of the mesh A,B,Fuzzy Goal: Partition V into V A ’ and V B ’ s.t. A A B B Fuzzy

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Algorithm for finding boundaries 1. Assign capacities 2. Construct a flow network on Fuzzy 3. Find the minimum cut

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The algorithm has 1. Geometry 2. Probability 3. Clustering 4. Graph theory

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Shuttle

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Dove

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Alien

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Camel

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Heart

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Venus

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Skeleton hand

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Skeleton extraction

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Help the dove fly

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So, Games, movies and virtual world?

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So, Games, movies and virtual world? Or Modeling, rendering, animations

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So, Games, movies and virtual world? Or Modeling, rendering, animations Math, physics, data structures, algorithms, software, hardware

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So, Games, movies and virtual world? Or Modeling, rendering, animations Math, physics, data structures, algorithms, software, hardware Science, education, medicine, engineering..

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THE END

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