Object representation
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- Kristin Stone
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1 Object representation
2 Geri s Game Pixar 1997 Subdivision surfaces Polhemus 3d scan Over 700 controls 2 Computer Graphics
3 Quick test #1 Describe the picture Graphical systems, visualization and multimedia 3
4 Quick test #1 Describe the picture Graphical systems, visualization and multimedia 4
5 Quick test #2 Volunteers: Describe the image to others Others: Reproduce the image Graphical systems, visualization and multimedia 5
6 Semantic vs. numeric Humans semantic representation concepts, notions, meanings, emotions... imprecise, ambiguous Computers numeric representation exact, mathematical, straightforward Graphical systems, visualization and multimedia 6
7 Detailed representation Graphical systems, visualization and multimedia 7
8 Object properties basic What object properties there are? Graphical systems, visualization and multimedia 8
9 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
10 Object definition Geometry plus model transformation (local global) Material color, shininess, index of refraction Body properties weight, elasticity... Graphical systems, visualization and multimedia 10
11 2D objects Let s define these objects Graphical systems, visualization and multimedia 11
12 2D objects Let s define these objects Graphical systems, visualization and multimedia 12
13 Shapes vs. bitmaps We ll deal with bitmaps later Shapes, vectors, curves, parametric, implicit Bitmaps, raster, pixels, explicit Graphical systems, visualization and multimedia 13
14 2D geometry
15 Polygons Control vertices x,y coordinates in order CCW Edges width shape style (solid, dotted etc.) Graphical systems, visualization and multimedia 15
16 Curves Primitives circle, ellipse General parametric curves Graphical systems, visualization and multimedia 16
17 Parametric curves Bezier curves Spline curves Graphical systems, visualization and multimedia 17
18 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
19 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
20 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
21 Approximation / interpolation Graphical systems, visualization and multimedia 21
22 Interpolation curves Control vertices + tangent vectors corner (cusp) smooth symmetrical Usually cubic splines good manipulation Graphical systems, visualization and multimedia 22
23 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
24 3D geometry
25 From polygons to polyhedra Graphical systems, visualization and multimedia 25
26 From curves to surfaces Graphical systems, visualization and multimedia 26
27 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
28 Point cloud Set of points located on object s surface Usually obtained by 3D scanning Connectivity information? Graphical systems, visualization and multimedia 28
29 Wireframe Set of vertices V(x,y,z) Edges E(V i,v j ) Graphical systems, visualization and multimedia 29
30 Real wireframe Benedict Radcliffe s Toyota Corolla 30 Computer Graphics
31 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
32 Example winged edge Data structure for mesh representation Fast mesh traversal Splitting / merging operations Graphical systems, visualization and multimedia 32
33 Polygon orientation normal Remember right-hand coordinate system Surface normal Graphical systems, visualization and multimedia 33
34 Parametric surfaces 3D generalization of parametric curves m n control points parameters u,v C(x,y,z) = f(u,v) Graphical systems, visualization and multimedia 34
35 Parametric surfaces e.g. Cubic Bezier surface, NURBS Graphical systems, visualization and multimedia 35
36 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
37 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
38 Subdivision surfaces Recursive subdivision of a polygonal model Limit surface - continuous Easy modeling, small data size Graphical systems, visualization and multimedia 38
39 Subdivision example Graphical systems, visualization and multimedia 39
40 Implicit surfaces F(x,y,z) = 0 sphere: metaballs: Examples: Graphical systems, visualization and multimedia r z y x 0 ) ) ( ) ( ) /(( c z z y y x x R m m m m
41 Video Graphical systems, visualization and multimedia 41
42 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
43 Volumetric representation not only boundary but also the insides of the object Medicine Physics Simulations Animation Graphical systems, visualization and multimedia 43
44 Voxels Volume elements, 3D pixels Discrete Binary values Float values Graphical systems, visualization and multimedia 44
45 Video Prof. Miloš Šrámek Mpeg animation of 615 images, rendered from a segmented MRI data set. Graphical systems, visualization and multimedia 45
46 Constructive solid geometry Primitives + Boolean operators on sets AND, OR, NOT singularities manifolds Graphical systems, visualization and multimedia 46
47 CSG continued Hierarchy Leaves = primitives Nodes = operators Volume-rep good Boundary-rep difficult Graphical systems, visualization and multimedia 47
48 Functional representation F-rep ~ generalization of CSG More node functions operators e.g. object blending Graphical systems, visualization and multimedia 48
49 Special objects
50 Particle systems Emitter + physics + elementary particle Water, snow, rain Smoke, fog, clouds Swarms, crowds Multi-agent systems 50 Computer Graphics
51 Billboards Complex objects faked by a picture Trees, grass Fire, smoke Light effects Distant objects Can be animated Animated Sprite Pack 51 Computer Graphics
52 Billboard Tree 52 Computer Graphics
53 Multiple sprites 53 Computer Graphics
54 Summary Boundary vs. Volume representation Parametric vs. Polygonal representation Parametric Polygonal Sprites / Billboards 54 Computer Graphics
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