Dr. Jim Rowan ITEC 2110 Vector Graphics II 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)

3-D models 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

3-D models Free Form 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 Draw a 2 dimensional shape through space along a line The line can be straight or curved

3-D models Procedural modelling Objects are defined by formulas Best known is based on Fractals Fractals exhibit the same structure at all levels of detail aka “self similar” used to model natural objects Meatballs model soft objects 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

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 Texture mapping An image is mathematically wrapped around the object Light reflecting off objects of one color affect the color and lighting of surrounding objects Two methods Ray tracing Complex... must be repeated for pixel in the image... photo-realistic results Radiosity

3-D texture mapping An image is mathematically wrapped around the object

Questions?