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  1. Assignment OrthographicWireframeElevation OrthographicWireframeEnd-Elevation OrthographicWireframePlan PerspectiveView

  2. Assignment (cont…) • Your application must include the following: • Four different views of a scene: • An orthographic wireframe elevation of the scene which does not change • An orthographic wireframe plan of the scene which does not change • An orthographic wireframe end-elevation of the scene which does not change • A perspective view of the scene in which the user should be able to move the camera • A scene composed of at least the following: • 1 teapot • Ten different objects • One animating object

  3. Assignment (cont…) • At least one light source • At least one bitmap textured surface • Controls (using whatever modality you see fit, e.g. keyboard, mouse etc) that allow a user to: • Turn on and off the lights in the scene • Navigate around the perspective view of the scene • Reset the view of the scene to the initial position • A representation in each of the orthographic views of the camera position used in the 3-D perspective view • Correct resizing of the window

  4. Assignment (cont…) • JAZZ! A considerable portion of the marks (20%) for this assignment will be awarded for doing something interesting in the application beyond what is given as the minimum requirements. Examples might include: • Using models designed in 3DS max/Milkshape/Maya • Adding interesting effects such as particle systems • Adding clever use of lighting – for example have the light source appear to be the lamp in the scene in figure 1 • Add a sky box

  5. Assignment (cont…) • Assignment submission deadline: 8th December, 2006 • Submission of the assignment will be through WebCT • Any Questions?

  6. CGames • The 9th International Conference on Computer Games: AI, Animation, Mobile, Educational & Serious Games will be held at DIT from the 22nd – 24th of November • All DIT students are allowed attend all sessions free of charge – graphics labs/lectures will be rearranged to accommodate this – more to follow • For more:

  7. Computer Graphics 10:3D Object Representations

  8. Contents • In today’s lecture we are going to start to look at how objects are modelled in 3D • Polyhedra • Quadric surfaces • Sweep representations • Constructive solid geometry methods

  9. Polyhedra • Objects are simply a set of surface polygons that enclose an object interior • Simplest and fastest way to render objects • Often referred to as standard graphics objects • In many cases packages allow us to define objects as curved surfaces etc but actually convert these to polygon meshes for display • To define polyhedra we simply define the vertices of the polygons required

  10. Polyhedra (cont…) Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)

  11. Quadric Surfaces • A frequently used class of objects are quadric surfaces • These are 3D surfaces described using quadratic equations • Quadric surfaces include: • Spheres • Ellipsoids • Tori • Paraboloids • Hyperboloids

  12. Quadric Surfaces - Spheres • A spherical surface with radius r centred on the origin is defined as the set of points (x, y, z) that satisfy the equation • This can also be done in parametric form using latitude and longitude angles

  13. Quadric Surfaces – Spheres (cont…) z axis P ( x, y, z ) r φ θ x axis y axis

  14. Sweep Representations • Sweep representations are useful for constructing 3 dimensional objects that possess translational, rotational or other symmetries • Objects are specified as a 2 dimensional shape and a sweep that moves that shape through a region of space

  15. Sweep Representations - Examples Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)

  16. Constructive Solid Geometry Methods • Constructive Solid Geometry (CSG) performs solid modelling by generating a new object from two three dimensional objects using a set operation • Valid set operations include • Union • Intersection • Difference

  17. Constructive Solid Geometry Methods (cont…) Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004) Difference Intersection

  18. Constructive Solid Geometry Methods (cont…) • CSG usually starts with a small set of primitives such as blocks, pyramids, spheres and cones • Two objects re initially created and combined using some set operation to create a new object • This object can then be combined with another primitive to make another new object • This process continues until modelling complete

  19. Constructive Solid Geometry Methods (cont…) CSG Object oper1 oper3 obj1 obj2 obj4 oper2 obj2 obj3 • CSG models are usually represented as CSG trees

  20. Constructive Solid Geometry Methods (cont…)

  21. Ray-Casting • Ray-casting is typically used to implement CSG operators when objects are described with boundary representations • Ray casting is applied by determining the objects that are intersected by a set of parallel lines emanating from the xy plane along the z axis • The xy plane is referred to as the firing plane

  22. Ray-Casting (cont…) Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)

  23. Ray-Casting (cont…) • Surface intersections along each ray are calculated and these are sorted according to distance from the firing plane • The surface limits for the composite object are then determined by the specified set operation

  24. Ray Casting Example Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)

  25. Summary • In today’s lecture we began to look at how objects are modelled in 3D • Polyhedra are by far the most common modelling technique, but there are many others • Often more exotic modelling techniques are used in a modelling phase, but the resultant models are converted to polyhedra before rendering • Next time we will look at more modelling techniques