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I'm trying to draw two curves and a surface, where one of the curves is to appear on the surface. Unfortunately the curves are drawn with very few points and appear extremely unclear. Is there a way to make them clear thick lines instead?

Here's the code: 

Manipulate[ ParametricPlot3D[{{Cos[[Phi]] Cos[[Theta]], Sin[[Phi]] Cos[[Theta]], Sin[[Theta]]}, {b0x + 2 brx Cos[[Phi]] + 2 bix Sin[[Phi]], b0y + 2 bry Cos[[Phi]] + 2 biy Sin[[Phi]], b0z + 2 brz Cos[[Phi]] + 2 biz Sin[[Phi]]}, {(b0x + 2 brx Cos[[Phi]] + 2 bix Sin[[Phi]])/ Norm[{b0x + 2 brx Cos[[Phi]] + 2 bix Sin[[Phi]], b0y + 2 bry Cos[[Phi]] + 2 biy Sin[[Phi]], b0z + 2 brz Cos[[Phi]] + 2 biz Sin[[Phi]]}], (b0y + 2 bry Cos[[Phi]] + 2 biy Sin[[Phi]])/ Norm[{b0x + 2 brx Cos[[Phi]] + 2 bix Sin[[Phi]], b0y + 2 bry Cos[[Phi]] + 2 biy Sin[[Phi]], b0z + 2 brz Cos[[Phi]] + 2 biz Sin[[Phi]]}], (b0z + 2 brz Cos[[Phi]] + 2 biz Sin[[Phi]])/ Norm[{b0x + 2 brx Cos[[Phi]] + 2 bix Sin[[Phi]], b0y + 2 bry Cos[[Phi]] + 2 biy Sin[[Phi]], b0z + 2 brz Cos[[Phi]] + 2 biz Sin[[Phi]]}]}}, {[Phi], 0, 2 [Pi]}, {[Theta], -[Pi], [Pi]}, PlotRange -> {-2, 2}, Mesh -> None, PlotStyle -> Thick, PlotStyle -> Opacity[0.6]], {{b0x, 0}, -5, 5}, {{b0y, 0}, -5, 5}, {{b0z, 1}, -5, 5}, {{brx, 1}, -5, 5}, {{bry, 0}, -5, 5}, {{brz, 0}, -5, 5}, {{bix, 0}, -5, 5}, {{biy, 1}, -5, 5}, {{biz, 0}, -5, 5}]

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  • $\begingroup$ Not sure but you can try PlotStyle -> Thickness[0.06]? $\endgroup$ Commented Mar 22, 2015 at 0:09

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You can use the option PlotStyle to style each of the three parts separately:

PlotStyle -> {Opacity[.6], EdgeForm[{Opacity[1], Thick, Blue}], EdgeForm[{Opacity[1], Thick, Red}]}

Since the three-argument form of ParametricPlot3D produces polygons (i.e., those lines are not Lines!), you need to set the styles using EdgeForm.

We get a much cleaner picture using the two-argument form of ParametricPlot3D for curves and the three-argument form for surfaces and combine the two with Show:

Manipulate[Show[ParametricPlot3D[{ {b0x + 2 brx Cos[ϕ] + 2 bix Sin[ϕ], b0y + 2 bry Cos[ϕ] + 2 biy Sin[ϕ], b0z + 2 brz Cos[ϕ] + 2 biz Sin[ϕ]}, {(b0x + 2 brx Cos[ϕ] + 2 bix Sin[ϕ])/ Norm[{b0x + 2 brx Cos[ϕ] + 2 bix Sin[ϕ], b0y + 2 bry Cos[ϕ] + 2 biy Sin[ϕ], b0z + 2 brz Cos[ϕ] + 2 biz Sin[ϕ]}], (b0y + 2 bry Cos[ϕ] + 2 biy Sin[ϕ])/ Norm[{b0x + 2 brx Cos[ϕ] + 2 bix Sin[ϕ], b0y + 2 bry Cos[ϕ] + 2 biy Sin[ϕ], b0z + 2 brz Cos[ϕ] + 2 biz Sin[ϕ]}], (b0z + 2 brz Cos[ϕ] + 2 biz Sin[ϕ])/ Norm[{b0x + 2 brx Cos[ϕ] + 2 bix Sin[ϕ], b0y + 2 bry Cos[ϕ] + 2 biy Sin[ϕ], b0z + 2 brz Cos[ϕ] + 2 biz Sin[ϕ]}]}}, {ϕ, 0, 2 π}, PlotRange -> {-2, 2}, BoxRatios -> 1, PlotStyle -> {Directive[Thickness[.01], Blue], Directive[Thickness[.01], Red]}], ParametricPlot3D[{Cos[ϕ] Cos[θ], Sin[ϕ] Cos[θ], Sin[θ]}, {ϕ, 0, 2 π}, {θ, -π, π}, PlotRange -> {-2, 2}, Mesh -> None, PlotStyle -> Opacity[0.3]]], {{b0x, 0}, -5, 5}, {{b0y, 0}, -5, 5}, {{b0z, 1}, -5, 5}, {{brx, 1}, -5, 5}, {{bry, 0}, -5, 5}, {{brz, 0}, -5, 5}, {{bix, 0}, -5, 5}, {{biy, 1}, -5, 5}, {{biz, 0}, -5, 5}]

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