Slice Curves
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) Text We can describe a slice curve with x = x_{0} as a
parametric curve x(t) = x_{0}, y(t) = t, so f(x(t),y(t)) = f(x_{0},t).
Similarly the slice curve with y = y_{0} can be given as (x(t),y(t),f(x(t),y(t))) = (t, y_{0},f(t,y_{0})).
The slice curve through (x_{0},y_{0}) with slope m can be
described as (x_{0} + t. y_{0} + mt, f((x_{0} + t. y_{0} + mt).
In polar coordinates, this can be written (x_{0} + tcos(θ_{0}), y_{0} + tsin(θ_{0}),f(x_{0} + tcos(θ_{0}), y_{0} +
tsin(θ_{0}), where m = tan(θ_{0}).
In general the slice curve over the parametric curve (x(t),y(t))
in the domain of a function f is the curve (x(t),y(t),f(x(t),y(t))).
Demos
Parametric Slice Curves
 
Define an interval for t, and two functions x(t), y(t).
Show this curve on the domain of the function. In another window, show
(x(t), y(t), 0),(x(t), y(t), f(x(t),y(t))) and (0,0,f(x(t),y(t))), with
the option of showing the "fence" connecting the first of these points
to
the second.

