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Computer Graphics Modellering engels
 

Computer Graphics Modellering engels

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    Computer Graphics Modellering engels Computer Graphics Modellering engels Presentation Transcript

    • 8. Mathematic Modelling of Objects
      8.3. Modelling of Point clouds
    • 8.3. Mathematic Modelling of Objects
      8.3.1. Definition
      Point clouds are sets of discrete values clustered in a certain area.
      In Computer Graphics: unordered set of points in a catesian coordinate system
      • uncertain contextual relationship
      • No composition of points (no planes)
      • No predefined order
      Conclusion
    • 8.3. Mathematic Modelling of Objects
      8.3.2. Properties
      Objects don‘t have facettes
       Textures can‘t be used
      Objects don‘t have face normals
      • Lighting computation not possible
      • Color of each point must be defined
      Each point is rendered (no face culling because of absence of faces)
      Tight-packed points construct point clusters
      • Construction of solid objects possible
    • 8.3. Mathematic Modelling of Objects
      8.3.3. Application Domain
      Constuction of solid objects:
      medical computer graphics (Computer Assisted Surgery [CAS])
      automotive industry
      Point cloud visualization:
      voxel graphics (Voxel = Volume Pixel)
      particle systems
    • 8.3. Modellierung von Punktewolken
      8.3.4. Programmierung
      […]
      #define M 4 //Größe des Objekts
      #define ABSTAND 0.1 //Abstand der Einzelpunkte
      //Zeichne Punkte
      glBegin(GL_POINT);
      {
      intx,y,z;
      for(int i=0; i<100; i++)
      {
      // pro Durchgang: erhöhe den Tiefenwert; Baue Objekt erst Spalten-
      // dann Zeilenweise auf.
      z=i%M; x=((int)(i/M))%(M*M); y=(int)(i/(M*M));
      // Setze Farbwert
      glColor4f(0.0f, 0.12f, 0.75f, 0.8f);
      // Setze Position
      glVertex3f(ABSTAND*x, ABSTAND*y, ABSTAND*z);
      }
      }
      glEnd();
      […]
       Vorteil: Bewegung in das Objekt möglich
    • 8.3. Mathematic Modelling of Objects
      8.3.5. professional generationofpointcloudobjects
      manualgenerationofpointclouds time intensive / not applicable
      • Technical pointrecording:
      3D camerarecords
      Laser scansof solid objects
      MRI (MagneticResonance Imaging)
      X-raying
    • 8.3. Mathematic Modelling of Objects
      8.3.6. Conversion point cloud – polygonial net (Meshing)
      First approach for conversion: Triangulation (triangle construction)  Graham-Algorithmus
      2-dimensional: detect point with lowest y-value
      Afterwards: connection of the other points depending on the angle to seed point, beginning with the lowest
      interconnect environment points according to angle order
    • 8.3. Mathematic Modelling of Objects
      8.3.6. Conversion point cloud – polygonial net (Meshing)
      Last step: delete concave corner points
    • 8.3. Mathematic Modelling of Objects
      8.3.6. Conversion point cloud – polygonial net (Meshing)
      Second approach: construction of polygon according to human thinking  Two-Peasant – Graphs
      Detection of points with x-maximum and x-minimum
      seperation of cloud in upper and lower half
      order halfs
      interconnection of sequential points of upper half from min(x) to max(x)
      Interconnection of sequential points of lower half from max(x) to min(x)
    • 8.3. Modellierung von Punktewolken
      8.3.6. Umwandlung Punktewolke - Dreiecksnetz
      Übergang 2D-3D: Mustererkennung
      Anwendbar bei Wissen über geometrische Zusammensetzung der Szene (Beispiel: Billard-Tisch)
      Vergleich einzelner Punktehaufen mit mathematischer Objektbeschreibung
      Objekt modellieren wenn genügende Anzahl (Schwellwert) an Punkte auf Objektbeschreibung zutrifft
      Billard: Kugel definiert durch Mittelpunkt und Radius
      x−x02+y−y02+ z−z02= r2
       
    • 8.3. Modellierung von Punktewolken
      8.3.6. Umwandlung Punktewolke - Dreiecksnetz
      Suche von Minimum- und Maximum-Punkt für x-, y- und z-Werte
      Verbindung der Punkte; Halbierung der Strecken;
      Mittelwerte der Beträge halben Strecken  mgl. Radius
      P0= xPxMin+xPxMax−xPxMin2zPyMin+yPyMax−yPyMin2zPzMin+zPzMax−zPzMin2
      Test nach genannter Formel, ob Oberflächenpunkte zu Kugel zugehörig
       
    • 8.3. Mathematic Modelling of Objects
      8.3.6. Conversion point cloud – polygonial net (Meshing)
      Last presentedpossiblity: 3D-facettes byMarching Cubes
      weightingofcornerpoints
      Constructionofweightedvoxels
      Check per voxel: cornersexceedingcertainthreshold; indexcontatenationofincludingcorners
      check Look-Up Table forpolygonconfiguration
      compositionofvoxel-cuberesultstooneobjects
      facettenormalscanbesaved inLook-Up Table too
    • 8.3. Modellierung von Punktewolken
      8.3.6. Umwandlung Punktewolke - Dreiecksnetz
      1 Voxel; Bsp.-Wert: 105 = 1|4|6|7
      20+23+25+26=105
       
      105
    • 8.4. Constructive Solid Geometry (CSG)
      • cover: constructed (composed) objects
      • construction: compostion of multiple objects
      • Application:
      virtual objects for construction of real objects
      • solid: filled; closed
      • objects with matter
      • combination of geometric primitives
      • basic blocks
    • 8.4. Constructive Solid Geometry (CSG)
      8.4.1. Definition
      CSG is a technique for creation of solid objects. complex structures can be build via boolean combination of geometric primitives.
      CSG models are convex objects,
      build out of co-planar facettes.
      • ball
      • cube
      • cylinder
      • cone
      • torus
      • facette
    • 8.4. Constructive Solid Geometry (CSG)
      8.4.2. Properties
      CSG models:
      filledandclosed
      facettenormals existent
      • illuminationcomputationpossible
      convex: allcornerfacettesco-planar: all corners
      arefacing in opponentof a facetteare in one
      directionsplane
    • 8.4. Constructive Solid Geometry (CSG)
      8.4.3. Application Domain
      similarapplicationdomainsaspolygonialobjects
      Computer Aided Design (CAD) forRapid Prototypingand Manufacturing; Product- andJewellery design
      Spacecraft Simulation; ComponentPrototyping
      Mechanical Engineering: Modellingofnew Engine Components
      major CAD systems: Autodesk SolidWorks, Catia, ProEngineer
    • 8.4. Constructive Solid Geometry (CSG)
      8.4.3. Application Domain
    • 8.4. Constructive Solid Geometry (CSG)
      8.4.4. boolean object combination
      Union:
      united set of objects
      objects are into each other
      Difference:
      all points of a basic object,
      which are not included in the
      combined object
      Intersection:
      Points, included in all combined objects
    • 8.4. Constructive Solid Geometry (CSG)
      8.4.4. boolean object combination
      objectmodelling via treestructure
      Example… 

       

      U
      Ball
      Cube
      Ball
      Ball

    • 8.4. Constructive Solid Geometry (CSG)
      8.4.5. Programming
      forgeneration, storageandroughvisualization:
      • CSG Editor
      Programming via OpenGL-basedAPI OpenCSG