Hierarchical Models Josef Pelikán & Alexander Wilkie CGG MFF UK Praha

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1 Hierarchical Models Josef Pelikán & Alexander Wilkie CGG MFF UK Praha 1 / 16

2 Hierarchies for 3D Modeling Bottom-up modeling Complex models are assembled from simpler ones During modeling, components are often re-used (building components, standardised parts) Databases of 3D objects In mechanical and civil engineering, standardised parts are frequently used Parametric models Individual object instances can be customised 2 / 16

3 Hierarchical Models A scene consists of objects Objects contain of components» Components are made up of parts Parts consist of... Hierarchical modeling is simple and effective Entire ready-made model components can be stored in a database, and combined by the designer / user Other features:» Attribute hierarchy (inheritance, parametrisation)» Relative transformation matrices (movement only relative to parent node) 3 / 16

4 Robot: Hierarchical Model robot modeling head body arm le g hand shoe thumb finger 4 / 16

5 Robot: Scene Graph robo t rendering hea d bod y ar m ar m le g le g... finger han d finger finger han d sho e thumb finger finger finger shoe 5 / 16

6 Object Storage in Database Global (implicit) attributes and parameters Colour, material, curve approximations,... Custom 3D elements Objects, polygons, surfaces,... (according to object type) Coordinate system Local values of attributes and parameters References to sub-objects Transformation matrices (relative!) Parameter and attribute modifications 6 / 16

7 Models in Memory Conversion of DAG to a tree node = object instance Geometrical data is no longer shared Coordinates of vertices, control nodes, surfaces,.. After 3D transformations and projections ~ Relative object coordinates - 3D ~ World coordinates - 3D ~ Projection coordinates - 2D or 3D (z = depth) ~ Display coordinates - 2D (integer) 7 / 16

8 Relative Transformations Transformation of scene leaves (triangle meshes) to world coordinates defined by a sequence of transformations Combination of matrices computed on the GPU robot head body hand hand leg leg eye eye shoulder elbow wrist T 5 T 7 T 9 T 9 T 7 T 5 thumb finger1 finger2 8 / 16

9 Coordinate Systems Model coordinates (Object space) Modeling transform World space [x,y,z,w] Camera coordinates (Eye space) -z View transform Projection transform -z Clip space xy xy n f [x,y,z,w] -z xy -z xy OpenGL / 31

10 Coordinate Systems II Clip space Perspective divide Normalized device space [x,y,z,w] [x,y,z] Viewport transform -z Window space [x,y,z] xy OpenGL: [-1,-1,-1] to [1,1, DirectX: [-1,-1, 0] to [1,1,1 [x,y] z actual fragment size on screen depth compatible with the z buffer OpenGL / 31

11 Coordinate Systems III Model coordinates Database of objects that comprise the scene Source: 3D modeling applications (3DS, Maya,..) World coordinates Absolute coordinates of the 3D world The relative coordinates of object instances are given there Camera coordinates 3D world relative camera coordinates Projection center: origin, view direction: -z (or z) OpenGL / 31

12 Coordinates (vertices, nodes,..) Objects on disc World coordinates Different scene views Display devices object A object B creation of object instances 3D or homogeneous projection, (clipping) 3D (z=depth) 3D (z=depth)... (clipping), visibility... memory 2D (integer) 2D (integer) / 16

13 Hierarchical 3D Formats PHIGS(+) (ANSI, ISO) Programmer s Hierarchical Interactive Graphics System OpenInventor, Performer (both SGI) Object-oriented OpenGL front-ends VRML ( Virtual Reality Modeling Language ) WebSpace (World-Wide Web) OpenSG, X3D, Input formats of rendering programs PoV Ray, RayShade, Radiance, 13 / 16

14 Scene Graph Scenes are represented by a tree (or DAG) Internal nodes transformations, attribute changes, groups, selection, time dependencies leaves geometry (vertices, normals), lights, materials, DAG some leaves or geometry can be shared (e.g. common geometry) Result is defined by an in-order graph traversal Internal nodes modify parameters & state Leaves contribute to the actual result (scene primitives) 14 / 16

15 Scenegraph Images SGI 15 / 16

16 End Further information: J. Foley, A. van Dam, S. Feiner, J. Hughes: Computer Graphics, Principles and Practice, / 16

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