repara.mw Set preferences for plotting About this worksheet Author and Date Content, Purpose and Use Updates and log of modifications. Shifts in time "Cheating" with periodic functions Example: A usual quarter-circle Same quarter-circle paramterized with a different interval The full 3D-view in xyt-space The side views xt and yt projections - exhibiting the trick The xt-view alone The yt-view alone Arbitrary shifting in (time) t An arbitray, true shift (xy-view) The full 3D-view in xyt-space The xt-view alone The yt-view alone Scaling time -- changing the speed Covering a circle in unit time The full 3D-view in xyt-space The xt-view The yt=view Any line segment in unit time The usual paramterization Automating this paramterization Any curve in any time given time-interval An example Using a specified time interval, the data given Look at the data and make a plan! Some college algebra, finding the equation of a line through two given points The picture for the change of time intervals: t_old to t_new [Untitled Section] [Untitled Section] Back to the example - the substitutions Plot the re-paramaterized curve The full 3D-views of the original and re-parameterized curves The top = xy-view The xt-view alone The yt-view alone A general position of the full 3D-view Reparameterization by arc-length (later) Background The idea Try your own examples in this template. Three dimensions