# Fill between 3D curves in ParametricPlot3D

I have a pair of 3D parametric curves:

ParametricPlot3D[
{{x*Sin[x], x*Cos[x], -((2*x)/3)}, {1.15*x*Sin[x], 1.15*x*Cos[x], -((2*x)/3)}},
{x, 0, (11/4)*Pi},
PlotStyle -> {Darker[Blue], Darker[Blue]}
] I would like to fill the 2D region between the two curves, in order to create a locally flat 'solid'. How do I go about this?

I'm guessing the the best bet might be ParametricRegion - but I can't figure out how to make it work...

ParametricPlot3D[{v x Sin[x], v x Cos[x], -2 x /3},
{x,  0, (11/4)*Pi}, {v, 1, 1.15},
PlotStyle -> Darker[Blue],  Mesh -> None,  PlotPoints -> 100] ParametricPlot3D[{v x Sin[x], v x Cos[x], -2 x /3},
{x, 0, (11/4)*Pi}, {v, 0, 1.15},
PlotStyle -> None, PlotPoints -> 100,
MeshFunctions -> {#5 &}, Mesh -> {{1}}, MeshShading -> {None, Darker@Blue}]


same picture

ParametricPlot3D[{v x Sin[x], v x Cos[x], -2 x /3},
{x, 0, (11/4)*Pi}, {v, 0, 1.15},
PlotStyle -> Darker[Blue],  PlotPoints -> 100, Mesh -> None,
RegionFunction -> (1 <= #5 <= 1.15 &)]


same picture

• With thanks to you both, I am ticking the second answer, as this produces a smoother curve. I appreciate both replies, thank you. – Richard Burke-Ward Jun 3 at 16:21

One easy way is to let ParametricPlot linearly interpolate between the two curves:

f1 = {x*Sin[x], x*Cos[x], -((2*x)/3)};
f2 = {1.15*x*Sin[x], 1.15*x*Cos[x], -((2*x)/3)};
ParametricPlot3D[{
lambda f1 + (1 - lambda) f2
},
{x, 0, (11/4)*Pi},
{lambda, 0, 1},
PlotStyle -> Darker[Blue],
Mesh -> None
] 