I'm too lazy to construct such things on my own. Is there a web site where this stuff gets plotted and shown? I'm googling and finding a bunch of lame sites where I have to enter the values in myself. This is beneath me because I'm an ET user destined for millions. ;-) Suggestions, please?
ORATS gives you a daily file with parameterized fitted values for all active optionable names. By moneyness (K/S) and expiry or delta and expiry. Along with the parameter values (level, slope, curvature) for each expiry. You can infer a fourth parameter (call it twist) across expiries. They also have pretty good forward vol forecasts with lower MSE, and greater r^2 and FSS vs forward realized vol than any of IV, standard garch(1,1), or RiskMetrics EMA forecasts. I know you weren't asking for vol forecasts, but there was a thread here last week asking that I never got around to replying to.