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15

plot = StreamPlot[{y, -Sin[x]}, {x, -Pi, Pi}, {y, -3, 3}, Frame -> None, Epilog -> {PointSize -> Large, Point[{{0, 0}, {π, 0}, {-π, 0}}]}, StreamPoints -> Fine, AspectRatio -> 0.8] Try this: First[Normal@plot] /. a_Arrow :> ( a /. {x_Real, y_Real} :> {Cos[x], Sin[x], y} ...


10

You could use an image representation of the plot and map it onto the modified cylinder that I defined in the answer linked here. Just copy the definition of cyl from that answer, which includes the ability to add textures as follows: img = Image@StreamPlot[{y, -Sin[x]}, {x, -5, 5}, {y, -3, 3}, Frame -> None, PlotRange -> {{-5, 5}, {-3, 3}}, ...


10

Probably not that useful, but it turned out looking cool. temp[x_, y_, z_] := 10000 Exp[-Sqrt[4 + (z - 5)^2]/50]*40/(40 + x^2 + y^2); Graphics3D[{Opacity[0.5], Raster3D[ Table[Append[List @@ ColorData["BlackBodySpectrum"][#], Clip[(# - 6000) (10000 - #)^2/2.5*^10]] &@ temp[x, y, z], {x, -5, 5, 1/2}, {y, -5, 5, 1/2}, {z, 0, 30, 1/2}]] ...


8

1. The normal mesh functions are u (#4 &) and v (#5 &). So we can just use Mesh without special mesh functions. ParametricPlot3D[{Cos[u] Sin[v], Sin[v] Sin[u], Cos[v]}, {u, 0, 2 Pi}, {v, 0, Pi}, Mesh -> {{0, 2 Pi/3, 4 Pi/3}, {Pi/2}}, MeshShading -> Map[Directive[Opacity[0.6], #] &, {{Red, Green, Blue}, {Yellow, Yellow, Yellow}}, ...


7

Here's a way to get the plane of best fit: subtract the centroid of the data, and then plot the plane generated by the first two left singular vectors of the singular value decomposition of the resulting data: Y = # - Mean /@ # &[t1\[Transpose]] {U, S, V} = SingularValueDecomposition[Y]; Graphics3D[{InfinitePlane[{{0, 0, 0}, U[[;; , 1]], U[[;; , 2]]}], ...


6

Why do it this way? Well, (1) for fun and (2) because Mathematica can. There are infinitely many ways to interpolate a boundary and interior points. One way is to use the FEM functionality to do so. It might be the look the OP wants after all - who knows? :) We can create an element mesh containing the bounding curve and the xy locations of the ...


5

Firstly to use BSplineSurface an array of control points is required, in your case: Graphics3D[BSplineSurface[Partition[icir, 2]]] As Öskå commented you can simply use ListPlot3D[icir]. The RegionFunction option will limit the surface to a given region (see below) but your example points all fall within the unit circle so you won't see a circular ...


5

By adding axes labels to your plot we can see that the base of the cone is not in the zy plane as requested. You need to rework your inequality so that the radius is proportional to the distance from origo along the x-axis, i.e. $z^2+y^2\leq x^2$. RegionPlot3D[ (y^2 + z^2)^(1/2) <= x && 0 <= x <= 5, {x, 0, 5}, {y, -5, 5}, {z, -5, 5}, ...


5

Show[ ListPointPlot3D[t1, PlotStyle -> Red, Filling -> Bottom], Plot3D[ Evaluate@Fit[t1, {1, x, y}, {x, y}] , {x, Min[t1[[All, 1]]], Max[t1[[All, 1]]]} , {y, Min[t1[[All, 2]]], Max[t1[[All, 2]]]} ]]


5

Show[SphericalPlot3D[1, ##, Mesh -> None] & @@@ MapThread[{{s, Sequence @@ #1}, {t, Sequence @@ #2}, PlotStyle -> #3} &, {{{0, \[Pi]/2}, {0, \[Pi]/2}, {0, \[Pi]/ 2}, {\[Pi]/2, \[Pi]}}, {{0, (2 \[Pi])/3}, {(2 \[Pi])/3, ( 4 \[Pi])/3}, {(4 \[Pi])/3, 2 \[Pi]}, {0, 2 \[Pi]}}, {Red, Green, Blue, Yellow}}], PlotRange -> ...


4

I would be happy if I could get Mathematica to prefix each POV-Ray export (which Mathematica supports, by the way) with a preamble in which I specify camera, lighting, etc. But unfortunately I don't know to what extent it's possible to customize Mathematica's export facilities. Use ExportString for obtaining the output file as a String inside of ...


3

The region where $z$ is between $x$ and $y$ is bounded by the curves $z = x$ and $z = y$, or equivalently, $z-x=0$ and $z-y=0$. To draw these curves in the plot, the usual trick is to supply the left-hand sides of the equations to MeshFunctions and specify that Mesh lines be drawn only when they are zero. Plot3D[-4.53 + 2.67 x + 2.78 y - 1.09 x y, {x, 1.8, ...


3

It seems AxesOrigin property spoils everything. A bug maybe.. I can suggest 2 way outs: first, simply: Graphics3D[{arrowAxes[3], Sphere[{1, 1, 1}]}, Axes -> True, Boxed -> False, AxesEdge -> {{0, -1}, {0, -1}, {0, -1}}, AxesStyle -> Opacity[0], TicksStyle -> Opacity[1]] This gives what you want, but i don't know how to specify the ...


2

If the mesh lines are not needed, SphericalPlot can be used in a much simpler form: sp1 = SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, Mesh -> {1, 2}, MeshShading->Thread[{{Red, Blue, Yellow}, Green}], MeshStyle->None, Lighting->"Neutral"] If you do need the mesh lines, you can do sp2 = SphericalPlot3D[1, {θ, 0, π/2}, {ϕ, 0, 2 π}, ...


2

I changed your probabilities a bit to make them better match your sphere specification, and to get a more interesting color pattern, but you'll get the idea: probs = Table[1/84 Exp[-i*j*1.0/9000], {i, 1, 30}, {j, 1, 10}]; minprob = Min@probs; maxprob = Max@probs; probsScaled = Rescale[probs, {minprob, maxprob}, {0, 1}]; colors = ...


2

colors = Hue[100 #] & /@ Table[1/84 Exp[-i*i*1.0/9000], {i, 1, 300}]; spheres = Sphere[#, 2] & /@ Chop[Flatten[Table[R[i, j], {i, 1, 30}, {j, 1, 10}], 1]]; Graphics3D[Thread[{colors, spheres}]]


2

Using J.M.'s implementation of polyharmonic splines: points = {1, 1, 0.2} # & /@ Select[RandomReal[{-1, 1}, {20, 3}], f @@ Most@# > 0 &]; f[x_, y_] := 1 - x^2 - y^2 pointsByF = ({1, 1, 1/f @@ Most@#} # &) /@ points; zByF[x_, y_] := Evaluate@polyharmonicSpline[pointsByF, {x, y}]; z[x_, y_] := f[x, y] zByF[x, y] Show[Plot3D[z[x, y], {x, -1, ...


2

It seems you need more points, not recursion. If you increase the number of PlotPoints and add PerformanceGoal -> "Quality", the wiggles disappear! bicone = ParametricPlot3D[{(1 - Abs[z]) Cos[t], (1 - Abs[z]) Sin[t], z}, {z, -1, 1}, {t, 0, 2 \[Pi]}, Mesh -> None, Boxed -> False, Axes -> None, PlotStyle -> {Specularity[White, 15], ...


2

I don't know how much you have worked with POVRay, but there is no need to generate thousands of individual pov files. For animations you can use the built-in clock function. Include in the graphics primitives exported by Mathematica a dependence on the clock, and let POVRay do the work for you. The following is a very simple example of POVRay code which ...


1

Here's your code with fixes I've suggested in comments: DynamicModule[ {Location = {{0, 0, 0}, {0, 0, 0}}, pos10 = {{}, {}}, pos11 = {{0, 0, 0}, {0, 0, 0}}, pos12 = {{0, 0, 0}, {0, 0, 0}}, pos20, pos21 = {{0, 0, 0}, {0, 0, 0}}, pos22 = {{0, 0, 0}, {0, 0, 0}}, posInt, x, y, z, Chosen = 1}, posInt[] := ...


1

Your example works smoothly for me, but there are at least two ways to try faster rendering (possibly in combination): 1) Decrease the SpherePoints size (related post here, choose a value to your liking): Show[{q1, q2}, Method -> {"SpherePoints" -> 3}] 2) Use multi-primitive syntax: q1 = Graphics3D[{Red, Sphere[Chop@Table[R1[i], {i, 1, 500}], ...


1

I just changed your code a little bit, to TickStyle->None arrowAxes[arrowLength_] := Map[{Apply[RGBColor, #], Arrow[Tube[{{0, 0, 0}, #}]]} &, arrowLength IdentityMatrix[3]]; Graphics3D[{Sphere[{1, 1, 1}], arrowAxes[3]}, Axes -> True, Boxed -> False, AxesOrigin -> {0, 0, 0}, AxesStyle -> Opacity[0], TicksStyle -> None]


1

Here is a way of getting Mathematica’s 3D graphics into COLLADA format — e.g. for importing into iBooks Author on OS X — whilst preserving colour information. Unfortunately, this involves a manual intermediate step using Blender, but it is the only way that I have found that automatically preserves colour. The trick is to use the fact that Blender can ...



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