Last Time Intro to modeling Issues in evaluating modeling techniques How well does it represent objects What types of objects can it represent How easy is it to render How compact is it How easy is it to create modify How easy is it to perform geometric computations Polygonal modeling A multitude of ways to represent polygonal models and associated data 04 11 02 C 2002 University of Wisconsin Today A menagerie of other modeling techniques Homework 5 04 11 02 C 2002 University of Wisconsin More Object Representations Parametric instancing Hierarchical modeling Constructive Solid Geometry Sweep Objects Octrees Blobs and Metaballs and other such things Production rules 04 11 02 C 2002 University of Wisconsin Parametric 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 Other examples This is a modeling format Provide software that knows how to draw the object given the parameters or knows how to produce a polygonal mesh How you manage the model depends on the rendering style Can be an exact representation 04 11 02 C 2002 University of Wisconsin Rendering Instances Generally provide a routine that takes the parameters and produces a polygonal representation Conveniently brings parametric instancing into the rendering pipeline 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 For example adjust the polygon resolution according to distance from the viewer 04 11 02 C 2002 University of Wisconsin OpenGL Support OpenGL defines display lists for encapsulating commands that are executed frequently Not exactly parametric instancing because you are very limited in the parameters list id glGenLists 1 glNewList list id GL COMPILE glBegin GL TRIANGLES draw some stuff glEnd glEndList And later glCallList list id 04 11 02 C 2002 University of Wisconsin 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 Cannot contain vertex arrays and other client state 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 composed into one transformation 04 11 02 C 2002 University of Wisconsin Display 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 except transformations Can t use various commands that would offer other speedups For example can t use glVertexPointer 04 11 02 C 2002 University of Wisconsin Hierarchical Modeling A hierarchical model unites several parametric instances into one object For example a desk is made up of many cubes Other examples 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 animation Human is a hierarchy of body head upper arm lower arm etc Animate by changing the transformations at the nodes 04 11 02 C 2002 University of Wisconsin Hierarchical Model Example Draw body xarm l left arm Rotate about shoulder Draw upper arm Translate l 0 0 Rotate about origin of lower arm Draw lower arm 04 11 02 Vitally Important Point Every node has its own local coordinate system This makes specifying transformations much much easier C 2002 University of Wisconsin 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 transformation Draw node contents RenderNode children glPopMatrix 04 11 02 C 2002 University of Wisconsin 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 may count 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 volume 04 11 02 C 2002 University of Wisconsin Constructive 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 Allows complex shapes with only a few primitives Common primitives are cylinders cubes etc or quadric surfaces Motivated by computer aided design and manufacture Difference is like drilling or milling A common format in CAD products 04 11 02 C 2002 University of Wisconsin CSG Example Fill it in scale translate cube scale translate scale translate cylinder cylinder 04 11 02 C 2002 University of Wisconsin 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 problem 04 11 02 C 2002 University of Wisconsin CSG 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
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