Computer Graphics Modellering engels
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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