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3D objects representation and data structure

This lecture discusses the representation and data structure of 3D objects, including internal and external data structures, vertex and edge lists, winged-edge structure, and plane equations. It emphasizes the need for a suitable data structure for both display and application purposes.

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3D objects representation and data structure

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  1. 3D objects representation and data structure Dr Nicolas Holzschuch University of Cape Town e-mail: holzschu@cs.uct.ac.za Modified by Longin Jan Latecki latecki@temple.edu Sep. 18, 2002

  2. Map of the lecture • Object representations in 3D • internal/external • Data structure • vertex list, edge list, winged edge • Plane equation • computing the plane equation

  3. Objects representation • In application model • Will be modified by the application • Ultimately, will be send for display • Must be adapted for both tasks

  4. Sending to display • Need the list of faces, with list of vertices for each face • Redundant information not a problem • one vertex may appear several times • Neighboring information not needed • Data structure: • list of faces • list of vertices for each face

  5. Access by the application • Modification of the application model • moving vertices • adding new faces • adding new vertices • redundant information is excluded • Needs neighboring information • for coloring • for computing average normals (shading)

  6. Internal vs. external • External data structure: • used for display • can be very simple • Internal data structure • will have complex manipulations • must provide for these manipulations

  7. Vertex list • List of faces • For each face: • list of pointers to vertices • Good points: • redundancy removed. Space saved. • Bad points: • find which polygons share an edge, or a given vertex?

  8. Edge list • For each face: • list of pointers to edges • For each edge: • the two polygons sharing it • the two vertices • Neighboring information available • faces adjacent to an edge

  9. Edge list: shortcomings • List of polygons sharing a vertex? • I move a vertex: • I need to find which edges share this vertex • must go through the whole list • I add a face, an edge: • must go through the whole list

  10. Winged-edge data structure E2 Polygon 1 V1 E4 Edge 1 V2 E3 Polygon 2 E5

  11. Winged-edge data structure • Each vertex also has a pointer to one of its edges • Each face has a pointer to one of its edges • Efficient: • faces adjacent to one vertex • edges adjacent to one vertex

  12. Plane equation • Each face is a planar polygon • Plane equation: ax+by+cz+d = 0 • Normal to the plane: (a,b,c) • Finding the equation?

  13. Finding a plane equation • Plane defined by three points: P1,P2,P3 • First, find the normal: n = P1P2 ^ P1P3 • If n=0? then it isn’t a plane • n gives a,b and c • Find d using P1

  14. Using a plane equation • n is fundamental: • defines a front and a back • M is in front of the plane: P1M•n³ 0 • M is behind the plane: P1M•n£ 0 • Same classification using the equation: ax+by+cz+d ³ 0

  15. 3D objects: conclusion • Data structure essential • must be adapted to the task • trivial data structure sufficient for display • more complex data structure required for application • Plane equation

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