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Digital Media Dr. Jim Rowan ITEC 2110 Vector Graphics II Manipulating objects AKA closed curves • Translation is a simple up/down side-to- side movement • Scaling: make bigger or smaller • Rotation about a point • Reflection about a line Object fills • Solid color • Patterns • Gradients – linear – radial 3-D... 3 dimensions • x, y and z • x & y form the ground plane • z is the height 3-D • Way more complex than 2-D • 3-D shapes (objects) are defined by their surfaces • Made even more complicated by the fact that a 3-D object inside the computer must be translated into 2-D to be rendered on a computer screen... – This results in the need to specify the viewpoint 3-D: additional complexity • lighting – natural – artificial • atmosphere • surface texture • rendering is extremely computationally expensive (demanding) Managing Complexity Structural hierarchy • Things in the real world are compositions of smaller things • Things in the 3-D graphics world are also compositions of smaller things • Hierarchical structure is an excellent way of coping with complexity • Also seen in object-oriented programming like Java and Squeak! Structural hierarchy Car – Wheels (4) • tire • wheel • hubcap – Doors (2) • handles – inside » lever – outside » button » handle • window(s) – Lights • headlights (2) • tail lights (2+) • stop lights (2+) 3-D: additional complexity • rendering is extremely computationally expensive (demanding) – lighting • natural • artificial • reflections off other objects in the scene • shadows cast by other objects in the scene – surface texture affects appearance 3D Models 3-D models Building things from known shapes • Constructive solid geometry – uses geometric solids: cube, cylinder, sphere and pyramid – objects build by squishing and stretching those objects – objects joined using union, intersection and difference 3-D models constructive solid geometry • Union – new object is made from the space occupied by both objects • Intersection – new object is made of the space that the two objects have in common • Difference new object is made from one object’s subtraction from another object 3-D models Free Form Building things one side at a time • Uses an object’s surface (it’s boundary with the world) to define it • Build surfaces from flat polygons or curved patches – flat polygons are easier to render and therefore frequently used in games where computational power is limited • Results in an object drawn as a “mesh” • Can be done using Bezier surface patch but have 16 control points • More tractable patch uses a surface called a non- rational B-spline 3-D models Free Form: Extrusion Building things using a paydoh factory • Draw a 2 dimensional shape through space along a line • The line can be straight or curved 3-D models Meat balls • Reacts like soft objects rather than hard, solid ones • Think of it as having surface tension • Kinda like an uncooked meatball, press two of them together and they “squish” 3-D models Procedural modeling • Best known is based on Fractals – Fractals – exhibit the same structure at all levels of detail – aka “self similar” – used to model natural objects – http://en.wikipedia.org/wiki/Fractal • Particle systems... many particles, few controls • Physics... distribution of mass, elasticity, optical properties, laws of motion 3-D Rendering • Rendering engine handles the complexity • Wire frames are used to preview objects and their position – can’t tell which surface is closer to us and which surface is hidden • To save computation time, hidden surfaces are removed before rendering – Why render what can’t be seen? 3-D rendering • Lighting – Added to scene much like an object – spot light, point source, floodlight... – position and intensity • Direct relationship between rendering quality and computational burden 3-D rendering • Shading... how light reacts with surface – Based roughly on physics but modified by heuristics (rules derived from experience) – Examples ===> • Texture mapping – An image is mathematically wrapped around the object 3-D rendering • Light reflecting off objects of one color affect the color and lighting of surrounding objects – Ray tracing Complex... must be repeated for pixel in the image... photo-realistic results – Wayne Wooton Pixar – Radiosity Questions?
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