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**Assignment**OrthographicWireframeElevation OrthographicWireframeEnd-Elevation OrthographicWireframePlan PerspectiveView**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**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**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**Assignment (cont…)**• Assignment submission deadline: 8th December, 2006 • Submission of the assignment will be through WebCT • Any Questions?**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: www.comp.dit.ie/cgames**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**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**Polyhedra (cont…)**Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)**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**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**Quadric Surfaces – Spheres (cont…)**z axis P ( x, y, z ) r φ θ x axis y axis**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**Sweep Representations - Examples**Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)**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**Constructive Solid Geometry Methods (cont…)**Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004) Difference Intersection**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**Constructive Solid Geometry Methods (cont…)**CSG Object oper1 oper3 obj1 obj2 obj4 oper2 obj2 obj3 • CSG models are usually represented as CSG trees**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**Ray-Casting (cont…)**Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)**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**Ray Casting Example**Images taken from Hearn & Baker, “Computer Graphics with OpenGL” (2004)**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