Week 7: Basic Ideas for Physical Simulations in Computer Graphics Jack Tumblin CS 395 Advanced Computer Graphics Winter 2003

Recall Newton; New Notation Newtonian Physics: F = M a Notation: time derivative as a dot y == How does a spring work? F = -K(x-x0) . yt OpenGL, local shading, MOST ray tracing Make pictures ONLY from ‘single-bounce’ light: L->surf->eye + ‘ambient term’ for everything else. Uses separate approximations for ‘shadows’—which are still just 1st-bounce paths from light to eye Global Illum; Make pictures for ALL paths through the scene between light sources and eye,

1-D Spring-Mass Example Given initial position y0 at time t=0, What is y for time t>0? Position: y Velocity: y = v Accel: v = a Newton says: F = Ma Spring Force: F = GM -K(y - y0) solve.... y y0 . . K M G

'State Variable' Form 'State' == A vector that holds everything you know about a particle [or spring, or rigid object, or car, or body segment, or missile, or basketball or...]

How Do We Solve it? Explicit Integration Implicit Integration

Conclusion Physically accurate (geometric optics only) simulation of light transport. ‘Ultimate Realism’? perceptual, not physical Languished as tweak-hungry lab curiosity Gradual adoption for multitexturing source, for mixing real/synthetic images, Ph.Ds, theatre/architectural lighting, archaeology,… Growing interest for use in inverse rendering tasks: image-based rendering & modeling