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SpaceCurve2::usage="Parametric equations are indicated below. References: Hollis, Selwyn. CalcLabs with Mathematica, Multivariable Calculus. 4a Ed., Cengage Learning: p.46, 2010; Personal ";​​f[x_,y_]:=4-
2
x
-
2
y
;g[x_,y_]:=
2
x
+2
2
y
-xy;​​Show[surf1=Plot3D[f[x,y],{x,-3,3},{y,-3,3},ColorFunction"BlueGreenYellow",MeshFalse],surf2=Plot3D[g[x,y],{x,-3,3},{y,-3,3},ColorFunction"LightTemperatureMap",MeshFalse],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic]​​f[rCos[t],rSin[t]]==g[rCos[t],rSin[t]];​​roft=r/.First@Solve[%,r]//Simplify;​​z[t_]:=g[roftCos[t],roftSin[t]];​​γ[t_]:={roftCos[t],roftSin[t],z[t]};​​​​
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Animateγ[t_]:=-
2Cos[t]
2
2
Cos[t]
-Cos[t]Sin[t]+3
2
Sin[t]
,-
2Sin[t]
2
2
Cos[t]
-Cos[t]Sin[t]+3
2
Sin[t]
,
4
2
Cos[t]
2
2
Cos[t]
-Cos[t]Sin[t]+3
2
Sin[t]
-
4Cos[t]Sin[t]
2
2
Cos[t]
-Cos[t]Sin[t]+3
2
Sin[t]
+
8
2
Sin[t]
2
2
Cos[t]
-Cos[t]Sin[t]+3
2
Sin[t]
;ParametricPlot3D[γ[t],{t,0,θ1},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},MeshFalse,AxesTrue,ColorFunctionFunction[{x,y,z},Hue[z]],BoxedFalse,PlotRangeAll,PerformanceGoal"Quality"],​​{θ1,0.1,2π,0.1},AnimationRunningFalse
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