Skip to main content

Three-dimensional plots

Most examples were adapted from the official pages of Wolfram Language Documentation Center.

The algorithms and implementations of those functions are the intellectual property of Wolfram Research. WLJS Team only reimplemented underlying low-level primitives such as `Line`, `Point`, `Polygon`, and etc.


Spherical Plot​

An example of Y2,0Y_{2,0}

Download original notebook 
(*SbB[*)Subscript[Y(*|*),(*|*)k_,q_](*]SbB*)[θ_, ϕ_] := SphericalHarmonicY[k,q, θ, ϕ]
SphericalPlot3D[(*SbB[*)Subscript[Y(*|*),(*|*)4,0](*]SbB*)[θ, ϕ], {θ,0,π}, {ϕ,0,2π}]
(*VB[*)(FrontEndRef["ca72fb9b-551b-4cc5-a054-efa9bdbee236"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKJyeaG6UlWSbpmpoaJumaJCeb6iYamJropqYlWialJKWmGhmbAQCUWRaL"*)(*]VB*)

Vector Plot 3D​

Visualize vector field in 3D

VectorPlot3D[{x, y, z}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}]
(*VB[*)(FrontEndRef["588f2ea9-afd7-45b4-8d86-be3c5106bb45"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKm1pYpBmlJlrqJqalmOuamCaZ6FqkWJjpJqUaJ5saGpglJZmYAgCLmBXg"*)(*]VB*)

Plot 3D​

Generates a three-dimensional plot

Plot3D[Im[ArcSin[(x + I y)^4]], {x, -2, 2}, {y, -2, 2}, 
	Mesh -> None, 
	PlotStyle -> Directive[Yellow, Opacity[0.8]], 
	ExclusionsStyle -> {None, Red}
]
(*VB[*)(FrontEndRef["abe5f76c-b695-4001-a747-28bddb668b90"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKJyalmqaZmyXrJplZmuqaGBgY6iaam5jrGlkkpaQkmZlZJFkaAACJ3hWp"*)(*]VB*)

Another example

NDSolve[{D[u[t, x], t] == D[u[t, x], x, x], u[0, x] == 0, u[t, 0] == Sin[t], u[t, 5] == 0}, u, {t, 0, 10}, {x, 0, 5}]; 

Plot3D[Evaluate[u[t, x] /. %], {t, 0, 10}, {x, 0, 5}, PlotRange -> All, ColorFunction -> "SunsetColors"]
(*VB[*)(FrontEndRef["1b3a992d-5c68-42ab-a966-b967f81c32c6"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKGyYZJ1paGqXomiabWeiaGCUm6SZampnpJlmamadZGCYbGyWbAQCCaxV/"*)(*]VB*)

A list version is also supporte

data = Table[Sin[j^2 + i], {i, 0, Pi, Pi/5}, {j, 0, Pi, Pi/5}];

ListPlot3D[data,  InterpolationOrder -> 3, 
 ColorFunction -> "SouthwestColors", BoxRatios->{1,1,0.5}]
(*VB[*)(FrontEndRef["d29a6ad5-357c-4485-a7da-ad735077e6ce"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKpxhZJpolppjqGpuaJ+uamFiY6iaapyTqJqaYG5samJunmiWnAgCG3BXc"*)(*]VB*)
Plot3D[Sin[Sqrt[x^2 + y^2]], {x, -6, 6}, {y, -6, 6}, 
 PlotRange -> All, 
 Mesh -> None, 
 ColorFunction -> "Rainbow"]
(*VB[*)(FrontEndRef["9910a721-a3a6-4be7-9538-5641b7f075f5"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKW1oaGiSaGxnqJhonmumaJKWa61qaGlvompqZGCaZpxmYm6aZAgB14hTt"*)(*]VB*)

Contour Plot 3D​

A 3D version of ContourPlot function

ContourPlot3D[x^3 + y^2 - z^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]
(*VB[*)(FrontEndRef["22b03336-28e2-470b-95c1-5add1a541cc8"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKGxklGRgbG5vpGlmkGumamBsk6VqaJhvqmiampBgmmpoYJidbAABy6hUw"*)(*]VB*)