Object representation

Object representation

Geri s Game Pixar 1997 Subdivision surfaces Polhemus 3d scan Over 700 controls 2 Computer Graphics

Quick test #1 Describe the picture Graphical systems, visualization and multimedia 3

Quick test #1 Describe the picture Graphical systems, visualization and multimedia 4

Quick test #2 Volunteers: Describe the image to others Others: Reproduce the image Graphical systems, visualization and multimedia 5

Semantic vs. numeric Humans semantic representation concepts, notions, meanings, emotions... imprecise, ambiguous Computers numeric representation exact, mathematical, straightforward Graphical systems, visualization and multimedia 6

Detailed representation Graphical systems, visualization and multimedia 7

Object properties basic What object properties there are? Graphical systems, visualization and multimedia 8

Object properties - advanced Physical object properties mass, stiffness, elasticity Material properties shininess, roughness light behavior friction etc. We ll deal with materials later Graphical systems, visualization and multimedia 9

Object definition Geometry plus model transformation (local global) Material color, shininess, index of refraction Body properties weight, elasticity... Graphical systems, visualization and multimedia 10

2D objects Let s define these objects Graphical systems, visualization and multimedia 11

2D objects Let s define these objects Graphical systems, visualization and multimedia 12

Shapes vs. bitmaps We ll deal with bitmaps later Shapes, vectors, curves, parametric, implicit Bitmaps, raster, pixels, explicit Graphical systems, visualization and multimedia 13

2D geometry

Polygons Control vertices x,y coordinates in order CCW Edges width shape style (solid, dotted etc.) Graphical systems, visualization and multimedia 15

Curves Primitives circle, ellipse General parametric curves Graphical systems, visualization and multimedia 16

Parametric curves Bezier curves Spline curves Graphical systems, visualization and multimedia 17

Remember: line equation Line P-Q where P = [x 1,y 1 ], Q = [x 2,y 2 ] x = x 1 + t * (x 2 x 1 ) } y = y 1 + t * (y 2 y 1 ) L = P + t*(q-p) Graphical systems, visualization and multimedia 18

Parametric curve Generalization x = f 1 ( t ) y = f 2 ( t ) } C(x,y) = f(t) Example Circle x c x r.cos( t) y c y r.sin( t), t 0,2 Graphical systems, visualization and multimedia 19

Cubic Bezier curves 4 control points C 0, C 1, C 2, C 3 C 0 and C 3 endpoints C 1 and C 2 define shape Can be expressed in matrix form Graphical systems, visualization and multimedia 20

Approximation / interpolation http://lubovo.misto.cz/curves/ Graphical systems, visualization and multimedia 21

Interpolation curves Control vertices + tangent vectors corner (cusp) smooth symmetrical Usually cubic splines good manipulation Graphical systems, visualization and multimedia 22

Parametric polygonal C(x,y) = f(t) t = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 Graphical systems, visualization and multimedia 23

3D geometry

From polygons to polyhedra Graphical systems, visualization and multimedia 25

From curves to surfaces Graphical systems, visualization and multimedia 26

Boundary representation Only the surface of the object is described No information about the inside Point cloud Wireframe Polygonal mesh Parametric surfaces Subdivision surfaces Implicit surfaces Graphical systems, visualization and multimedia 27

Point cloud Set of points located on object s surface Usually obtained by 3D scanning Connectivity information? http://www.photomodeler.com Graphical systems, visualization and multimedia 28

Wireframe Set of vertices V(x,y,z) Edges E(V i,v j ) Graphical systems, visualization and multimedia 29

Real wireframe Benedict Radcliffe s Toyota Corolla 30 Computer Graphics

Polygonal representation Polygonal mesh Vertices V(x,y,z) Faces F(V 1, V 2,... V n ) (Edges) E(V i, V j ) Graphical systems, visualization and multimedia 31

Example winged edge Data structure for mesh representation Fast mesh traversal Splitting / merging operations Graphical systems, visualization and multimedia 32

Polygon orientation normal Remember right-hand coordinate system Surface normal Graphical systems, visualization and multimedia 33

Parametric surfaces 3D generalization of parametric curves m n control points parameters u,v C(x,y,z) = f(u,v) http://cadauno.sourceforge.net/ Graphical systems, visualization and multimedia 34

Parametric surfaces e.g. Cubic Bezier surface, NURBS Graphical systems, visualization and multimedia 35

Parametric vs. polygonal Parametric smooth, reparametrizable harder rendering precise rendering Polygonal discrete, hard to reparametrize faster rendering or rasterization approximative rendering Graphical systems, visualization and multimedia 36

Parametric polygonal C(x,y,z) = f(u,v) u = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0, v = 0.0, 0.33, 0.66, 1.0 Graphical systems, visualization and multimedia 37

Subdivision surfaces Recursive subdivision of a polygonal model Limit surface - continuous Easy modeling, small data size http://www.holmes3d.net/graphics/subdivision/ Graphical systems, visualization and multimedia 38

Subdivision example Graphical systems, visualization and multimedia 39

Implicit surfaces F(x,y,z) = 0 sphere: metaballs: Examples: http://iat.ubalt.edu/summers/math/platsol.htm Graphical systems, visualization and multimedia 40 0 2 2 2 2 r z y x 0 ) ) ( ) ( ) /(( 2 2 2 c z z y y x x R m m m m

Video http://www.youtube.com/watch?v=k27zvop1pw4 Graphical systems, visualization and multimedia 41

Question What happens if we turn F(x,y,z) = 0 into F(x,y,z) 0? surface volume Graphical systems, visualization and multimedia 42

Volumetric representation not only boundary but also the insides of the object Medicine Physics Simulations Animation Graphical systems, visualization and multimedia 43

Voxels Volume elements, 3D pixels Discrete Binary values Float values Graphical systems, visualization and multimedia 44

Video Prof. Miloš Šrámek http://www.viskom.oeaw.ac.at/~milos/ Mpeg animation of 615 images, rendered from a segmented MRI data set. Graphical systems, visualization and multimedia 45

Constructive solid geometry Primitives + Boolean operators on sets AND, OR, NOT singularities manifolds Graphical systems, visualization and multimedia 46

CSG continued Hierarchy Leaves = primitives Nodes = operators Volume-rep good Boundary-rep difficult Graphical systems, visualization and multimedia 47

Functional representation F-rep ~ generalization of CSG More node functions operators e.g. object blending Graphical systems, visualization and multimedia 48

Special objects

Particle systems Emitter + physics + elementary particle Water, snow, rain Smoke, fog, clouds Swarms, crowds Multi-agent systems 50 Computer Graphics

Billboards Complex objects faked by a picture Trees, grass Fire, smoke Light effects Distant objects Can be animated Animated Sprite Pack http://www.thegamecreators.com/?m=view_product&id=2154 51 Computer Graphics

Billboard Tree 52 Computer Graphics

Multiple sprites 53 Computer Graphics

Summary Boundary vs. Volume representation Parametric vs. Polygonal representation Parametric Polygonal Sprites / Billboards 54 Computer Graphics