3D Computer Graphics in a Nutshell

3D Computer Graphics in a Nutshell Guillaume Caumon, January 2002

Introduction • Computer graphics is concerned with all the aspects of “drawing” on computers • Performance is critical • 3D Computer Graphics deals with the generation images from 3D objects.

The Rendering Pipeline Pipeline = Linear succession of operations Rendering speed = speed of the slowest step (bottleneck) Application Geometry Rasterization

meshing decimation collision detection animation … Application Software-based processing / modifications Rendering primitives 3D Model

Geometry Transforms Lightning Projection Clipping

Geometry : Transforms Model Transform Model Coordinates World Coordinates Scaling, etc. View Transform Viewing Coordinates

Geometry: lighting and shading Simulate interaction of light with matter: - Emission - Absorption - Reflection

L α N β IR(l) Ambient light coefficient Ex: (.1, .1, .1) Material color Ex: (1, 0, 0) Specular Coeficient Ex: (1, 1, 1) ν : r, g or b Shininess (s > 1) Geometry: A Lightning Equation

Geometry: Shading Flat shading: each triangle has the same color Gouraud shading: colors are interpolated between vertices Phong shading: normal are interpolated and colors computed for each pixel

Geometry: Projection normalization Viewing Coordinates Virtual Device Coordinates Perspective/ parallel

Geometry: Clipping

Geometry: Device Coordinates My Window Unit Cube

Rasterization Screen = matrix Per-pixel operations: ray-tracing Scan conversion of lines: naive version Bresenham algorithm Scan conversion of polygons Aliasing / antialiasing Texturing

Graphics Hardware Quickly evolving Main principle: use of buffers Color buffer : 1 byte per pixel (256) + lookup tables 2 bytes per pixel (65 536) “high color” 3+1 bytes per pixel bpp (16 millions) “true color” + alpha channel Depth buffer : 16 to 32 bit per pixel

Graphics Hardware (II) • Double buffering : • show the front buffer while rasterizing the back buffer • swap buffers in synchronization with the screen refresh • to get the new frame Stencil buffer : allows high-level operations (antialiasing, filtering, etc.) See OpenGL programmer’s reference for more details

Conclusion 3D Graphics require intensive computations Yet, 3D Graphics are time-critical Bottlenecks Display lists Only low-level graphics have been described. } Scene Graphs Selection and tools See OpenInventor, VTK, etc.

References and further reading • Foley, van Dam, Feiner, Hughes, Computer Graphics Principle and practice,2nd edition. Addisson Wesley, 1997 • Moller, Haines, Real-Time Rendering. AK Peters, 1999 (http://www.realtimerendering.com) • The Graphic Gems series, Academic Press. • Neider, Davis, Woo, OpenGL Programming Guide. Addisson Wesley, 1993 • Wernecke, The Inventor Mentor, release 2, Addisson Wesley,1994 • Schroeder, Martin, Lorensen, The Visualization Toolkit, 2nd edition. Prenctice Hall, 1998 • Proceedings of Siggraph, Visualization, Eurographics, etc.

3D Computer Graphics in a Nutshell