More Object RepresentationsParametric InstancingRendering InstancesOpenGL SupportDisplay Lists (2)Display Lists (3)Hierarchical ModelingHierarchical Model ExampleSlide 9Regularized Set OperationsConstructive Solid Geometry (CSG)CSG ExampleRendering CSGCSG SummarySweep ObjectsGeneral SweepsRendering SweepsSpatial EnumerationOctrees (and Quadtrees)Quadtree ExampleRendering OctreesSpatial Data StructuresMore Object Representations•Parametric instancing•Hierarchical modeling•Constructive Solid Geometry•Sweep Objects•Octrees•Blobs and Metaballs and other such things•Production rulesParametric Instancing•Many things, called primitives, are conveniently described by a label and a few parameters–Cylinder: Radius, length, does it have end-caps, …–Bolts: length, diameter, thread pitch, …–Almost anything you buy from a catalogue•This is a modeling format:–Provide something that knows how to draw the object given the parameters–Depends on the rendering style–Can be an exact representationRendering Instances•Generally, provide a routine that takes the parameters and produces a polygonal representation–May include texture maps, normal vectors, colors, etc–OpenGL utility library (GLu) defines routines for cubes, cylinders, disks, and other common shapes–Renderman does similar things, so does POVray, …•The procedure may be dynamic–Adjust the polygon resolution according to distance from the viewerOpenGL Support•OpenGL defines display lists for encapsulating commands that are executed frequentlylist_id = glGenLists(1);glNewList(list_id, GL_COMPILE);glBegin(GL_TRIANGLES);draw some stuffglEnd();glEndList();And laterglCallList(list_id);Display Lists (2)•The list can be:–GL_COMPILE: things don’t get drawn, just stored–GL_COMPILE_AND_EXECUTE: things are drawn, and also stored•The list can contain almost anything:–Useful for encapsulating lighting set-up commands•The list cannot be modified after it is compiled–The whole point is that the list may be internally optimized, which precludes modification–For example, sequences of transformations may be composited into one transformationDisplay Lists (3)•When should you use display lists:–When you do the same thing over and over again•Advantages:–Can’t be much slower than the original way–Can be much much faster•Disadvantages:–Doesn’t support real parameterized instancing, because you can’t have any parameters!–Can’t use various commands that would offer other speedups•For example, can’t use glVertexPointer()Hierarchical Modeling•A hierarchical model unites several parametric instances into one object–For example: a desk is made up of many cubes•Generally represented as a tree, with transformations and instances at any node•Rendered by traversing the tree, applying the transformations, and rendering the instances•Particularly useful for rigid-body animation–Human is a hierarchy of body, head, upper arm, lower arm, etc…–Animate by changing the transformations at the nodesHierarchical Model Examplebodyleft armxarmlrotate about shoulderupper armtranslate (l,0,0)rotate about (0,0,0)lower armVitally Important Point:•Every node has its own local coordinate system.•This makes specifying transformations much much easier.OpenGL Support•OpenGL defines glPushMatrix() and glPopMatrix()–Takes the current matrix and pushes it onto a stack, or pops the matrix off the top of the stack and makes it the current matrix–Note: Pushing does not change the current matrix•Rendering a hierarchy (recursive):RenderNode(tree)glPushMatrix()Apply node transformationDraw node contentsRenderNode(children)glPopMatrix()Regularized Set Operations•Hierarchical modeling is not good enough if objects in the hierarchy intersect each other–Transparency will reveal internal surfaces that should not exist–Computing properties like mass counts the same volume twice•Solution is to define regularized set operations:–Just a fancy name–Every object must be a closed volume (mathematically closed)–Define mathematical set operations (union, intersection, difference, complement) to the sets of points within the volumeConstructive Solid Geometry (CSG)•Based on a tree structure, like hierarchical modeling, but now:–The internal nodes are set operations: union, intersection or difference (sometimes complement)–The edges of the tree have transformations associated with them–The leaves contain only geometry•Motivated by computer aided design and manufacture–Difference in particular is like drilling or milling–Other operations reduce the number of primitives required–A common format in CAD productsCSG Example--cubescaletranslatecylinder cylinderscaletranslatescaletranslateFill it in!Rendering CSG•Normals and texture coordinates typically come from underlying primitives (not a big deal with CAD)•Some rendering algorithms can render CSG directly–Raytracing (later in the course)–Scan-line with an A-buffer–Can do 2D with tesselators in OpenGL•For OpenGL and other polygon renderers, must convert CSG to polygonal representation–Must remove redundant faces, and chop faces up•Basic algorithm: Split polygons until they are inside, outside, or on boundary. Then choose appropriate set for final answer.–Generally difficult, messy and slow–Numerical imprecision is the major problemCSG Summary•Advantages:–Good for describing many things, particularly machined objects–Better if the primitive set is rich•Early systems used quadratic surfaces–Moderately intuitive and easy to understand•Disadvantages:–Not a good match for polygon renderers–Some objects may be very hard to describe, if at all•Geometric computations are sometimes easy, sometimes hard•A volume representation (hence solid in the name)–Boundary (surface representation) can also workSweep Objects•Define a polygon by its edges•Sweep it along a path•The path taken by the edges form a surface - the sweep surface•Special cases–Surface of revolution: Rotate edges about an axis–Extrusion: Sweep along a straight lineGeneral Sweeps•The path maybe any curve•The polygon that is swept may be transformed as it is moved along the path–Scale, rotate with respect to path orientation, …•One common way to specify is:–Give a poly-line (sequence of line segments) as the path–Give a poly-line as the shape to sweep–Give a transformation to apply at the vertex of
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