1. 1 of 25 Assignment Orthographic Wireframe Elevation Orthographic Wireframe Plan Orthographic Wireframe End-Elevation Perspective View

2. 2 of 25 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. 3 of 25 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. 4 of 25 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. 5 of 25 Assignment (cont…) Assignment submission deadline: 8th December, 2006 Submission of the assignment will be through WebCT Any Questions?

6. 6 of 25 CGames The 9 th International Conference on Computer Games: AI, Animation, Mobile, Educational & Serious Games will be held at DIT from the 22 nd – 24 th 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: www.comp.dit.ie/cgames

7. Course Website: http://www.comp.dit.ie/bmacnameehttp://www.comp.dit.ie/bmacnamee Computer Graphics 10: 3D Object Representations

8. 8 of 25 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. 9 of 25 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. 10 of 25 Polyhedra (cont…) Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)

11. 11 of 25 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. 12 of 25 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. 13 of 25 Quadric Surfaces – Spheres (cont…) y axis z axis x axis P ( x, y, z ) θ φ r

14. 14 of 25 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. 15 of 25 Sweep Representations - Examples Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)

16. 16 of 25 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. 17 of 25 Constructive Solid Geometry Methods (cont…) Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004) Difference Intersection

18. 18 of 25 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. 19 of 25 Constructive Solid Geometry Methods (cont…) CSG Object oper 1 obj 1 obj 2 oper 3 obj 4 oper 2 obj 2 obj 3 CSG models are usually represented as CSG trees

20. 20 of 25 Constructive Solid Geometry Methods (cont…)

21. 21 of 25 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. 22 of 25 Ray-Casting (cont…) Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)

23. 23 of 25 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. 24 of 25 Ray Casting Example Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)

25. 25 of 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