Plot sphere mathematica Provide details and share your research! But avoid Asking for help, clarification, or responding to other The Bloch class was designed from the outset to generate animations. plots several functions. Graph a Cartesian surface or space curve. 完整的 Wolfram 语言和笔记本体验. Sunita Sunita. com/s/xosww45vr183msh/sphere. Of course, we The demo allows the user to rotate the unit sphere from the pole aligned with the z-axis to a sphere with a pole aligned with the eigenvector corresponding to the singular value $0$. Provide details and share your research! But avoid Asking for $\begingroup$ @user64494 He wan to draw a portrait onto a sphere instead of a vector fields on sphere,so we need not consider vector field. ) are not the graphs of functions of two variables. Polar plots can be drawn using SphericalPlot3D[r, {phi, phimin, Sep 10, 2016 · Here is an attempt to draw a 3D Bloch sphere, on which we can select a point by simply clicking on it with the mouse and obtaining the corresponding qubit representation. That is possible unless the variable z does not $\begingroup$ @User The syntax for the second Table argument in general is {start,end,stepsize}. Modified 8 years, 5 months ago. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site The default PlotRange setting for SliceVectorPlot3D is {Full, Full, Full} (see the Details and Options section). g. The second hit will be ContourPlot. The projection obtained is generated by projecting points lying on a sphere from the sphere’s north pole to a plane tangent to the south pole of the sphere and plotting the intersection of the projection segment with the plane. jpg"]; (* Pretend this is $\begingroup$ While I'm a huge proponent of OPs editing their question to update with more info, here, the question went from 1) "What's the logic behind CountryData" to 2) "How to make a Simple way to draw sphere with list plot 3D function . The I am wondering if there is a way to plot a squashed sphere in Mathematica by manipulating the above command; namely a sphere that has two points that shrink like the one that is shown below. Actually, there is a special command in Mathematica that can be used to plot circles and ellipses: Circle[{x,y},r] gives a circle of radius r centered at {x,y}. $\endgroup$ – cvgmt sphere(___) plots the sphere without returning the coordinates. Cabin):. equator[θ_] := {Cos[θ], Sin[θ], 0} A function and a Oct 20, 2018 · I want to draw a solid or partially transparent hemisphere above a partially transparent cuboid object in Graphics3D. About; sphere in same 3D plot. Generally, you can combine all kinds of graphics with Mathematica. Is there a function that I can get to operate on How to make 3D plots. Stack Exchange network consists of 183 Q&A communities What about instead of curling the vector are I'm totally new at graphing with Mathematica, and my general knowledge of Mathematica is not so good either. Provide details and share your research! But avoid Asking for How to make 3D plots. 1} ]; ListAnimate[plots] {min,max}]] where Circle[{x, y}, r] represents a circle of radius r centered at {x, y}. ContourPlot3Dsph[{f[r,theta,phi]==0}, {phi,. Wolfram|One. It automates many details of plotting such as sample rate, aesthetic choices, and focusing on the region of interest. Here's the code: (Gravitational Constant) Thanks for contributing an answer to Mathematica Stack Sphere[p, r] 点 p を中心とした半径 r の球を表す． Sphere[{p1, p2, }, r] 半径 r の球の集合を表す．製品. r -> 200], Axes -> True], coordinate planes at the back of the plot "XStackedPlanes" coordinate planes stacked along axis "YStackedPlanes" coordinate planes stacked along axis "ZStackedPlanes" coordinate planes How do I plot for example a plane and a line in same 3D plot? Skip to main content. For example in ViewCenter->{0. ; Plot initially evaluates f at a number of equally spaced sample points specified by PlotPoints. To plot the result, we use GraphicsComplex with its VertexColors and VertexNormals options. using cartesian equations. following an answer to a previous gives the positions of n uniformly distributed points on the surface of a unit sphere. ; SphericalPlot3D [r, θ, ϕ] 中，的范围从 0 到，的范围从 PlotLegends->"Expressions" は凡例テキストとして f i を使う．; Plot は，まず， f を PlotPoints で指定された等間隔のサンプル点の数で評価する．次に，適応的アルゴリズムを使用し，指 Just for further information, I tried to plot the sphere S first, instead of the plane R and that still made no difference $\endgroup$ – Nok. Sep 26, 2023 · We give a procedure to plot parametric curves on the sphere whose advan-tages over classical graphs in the Cartesian plane are obvious whenever the graph involves infinite Plot the textured Riemann sphere and its equator, which is the projection of the unit circle in the complex plane. All the functions etc. Show[{ Graphics3D[Sphere[{0, 0, 0}, r /. I am interested in something So if you're used to writing Plot[f[t], {t, 0, 10}, PlotStyle->something, otheroptions->othervalues] then that something is probably a directive. About the rotation Opacity runs from 0 to 1, with 0 representing perfect transparency. rose-hulman. Coloring should include two colors depending on whether Feb 14, 2018 · Here is a static solution to the problem. Then it uses an adaptive algorithm to subdivide at most MaxRecursion times to Plot geodesics on a sphere: In[6]:= Out[6]= Gray, A. Then it uses an adaptive algorithm to How can I generate the Bloch dynamical evolution on a 3D plot (using fourth order Runge-Kutta method)? That is the curve given by the solution of above equation in a Bloch sphere? plotting; differential-equations; This peculiar method works in Mathematica versions 7 (thanks, Mr. I have no restrictions on the triangle's kind or on the sphere in And, the plot should be without a box (easy to do) but with coordinate axis that are centered on the sphere itself. , Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. I wish to create a nice data representation of three nested spherical sections, with Nov 17, 2024 · covert your spherical parametrized curve into cartesian parametrized curve with formulas: $$\begin{cases} x&=r\sin\theta\cos\varphi\\ y&=r\sin\theta\sin\varphi\\ z&=r\cos\theta Jun 10, 2020 · I really want to know how to plot the Cartesian grid lines on a 2D plane onto a sphere in the context of stereographic projection. Plot a revolution around an axis. For example, the parameter function is sin(t) and cos(t) and a point starts DensityPlot3D is also known as volume map. Stack Overflow. Circle[{x, Mathematica. The data is a text file of N rows by 3 How to plot an octahedron inside a sphere and the same sphere inside a cube in 3d? plotting; Share. On I am trying to plot a velocity field over a sphere where the velocity vector is u has magnitude 1/sin \theta and it is in theta direction. Jan 17, 2017 · I recently need to plot a 3d function that satisfies certain constraints, like . If you'd like to Mathematica. With Graphics3D those coordinate axis are outside of the sphere as if they were labeling 3 edges of You can move the sphere as well by shifting the origin. $\endgroup$ – MMA13 Commented Aug 8, 2020 at 13:58 Parametric Equations can be a little tricky to think about at first glance. In Simple Question: I want to create beautiful density plots like those on a Wikipedia page: Mathematica has a lot of built-in color functions but none of them is as good as I have a function with variables (theta,phi) the spherical coordinates. A plot of a function expressed in spherical coordinates, with radius r as a function of angles theta and phi. However, I do not know how to do this such that only half the sphere is drawn. Wolfram言語とWolframノートブックの決定的な経験. I have spherical datas (function depending on $\theta$ and $\phi$ that I want to I am new to Mathematica and I tried to make a superimposed plot of a curve on a half sphere and need help with some graphics. Let's put it at {0, 0, 3/4 n3} with a larger radius for the points. Use spherical coordinates. plotting; Share. Jul 17, 2014 · Currently, I have a matrix containing a list of spherical coordinates. How can I get this picture in Mathematica? Jan 7, 2015 · Plot two non-intersecting semi-transparent spheres whose centers lie on the plane P defined by x + y + z = 1, as well as P restricted to the interiors of the spheres, all in the positive octant. The arrows are colored by default Wolfram Mathematica. Circle[{x, y}, {rx, ry}] gives an axis-aligned ellipse with semiaxes lengths rx and ry. Also add a labeled arrow from the Feb 11, 2016 · The basic parametric plot code for a sphere is: ParametricPlot3D[{Cos[ϕ]*Sin[θ], Sin[ϕ]*Sin[θ], Cos[θ]}, {ϕ, 0, 2 π}, {θ, 0, π}] I essentially want to apply the above inequality to Aug 15, 2014 · Add coordinate axes to a 3D plot of concentric spheres (2 answers) Closed 10 years ago . Archives About We give a procedure to plot parametric curves on the sphere whose This part of tutorial demonstrates tremendous plotting capabilities of Mathematica for three-dimensional figures. 5} the 0. takes variables {x, y} to be in the geometric region reg. There will be holes in the final surface anywhere at which etc. In this case we want to get from 0 to 2Pi in 20 steps, but since we also use $\begingroup$ The actual data points I am interested in are not a sphere or an ellipsoid. Thanks for contributing an answer to Mathematica Stack Exchange! Please be sure to answer the question. Other customizations are possible. Thanks for contributing an answer to Mathematica coordinate planes at the back of the plot "XStackedPlanes" coordinate planes stacked along axis "YStackedPlanes" coordinate planes stacked along axis "ZStackedPlanes" coordinate planes Thanks for contributing an answer to Mathematica Stack Exchange! Please be sure to answer the question. For example in sphere's case $x^2+y^2+z^2=1$ I tried to use Plot3D but it doesn't wo SphericalPlot3D[r, \[Theta], \[Phi]] generates a 3D plot with a spherical radius r as a function of spherical coordinates \[Theta] and \[Phi]. Here I used SphericalPlot3D to create the sphere instead (I put all the other Graphics PlotLegends->"Expressions" uses the f i as the legend text. Commented Sep 13, 2021 at 8:40 Suppose I have some vector field equations $(f(\theta,\phi), g(\theta,\phi))$. Sphere[{p1, p2, }, r] 表示半径为 r 的球体集合. example. I guess something similar can be done to plot a spherical polygon. I want to represent it as a density plot over the surface of a sphere. Plain plotting was given in the first part of tutorial. RevolutionPlot3D[fz, {t, tmin, tmax}, {\[Theta], \[Theta]min, \[Theta]max}] takes the I want to plot this matrix in spherical coordinate system such that each point is colored according to the first element of the six element arraysay red for 2/3, green for 1/3 That example was chosen to yield a simple expression in Cartesian coordinates. So I wonder how to plot the part that only lies within the constraints? An example surface can be . Graphics3D[{CapForm["Round"], Tube[{{0, 0, 0}, {0, 0, 0}}, {0, Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. Use this syntax with any of the input arguments in previous syntaxes. Column 1 is r; r=1 for all points. News about products and events. Hi all, Kinda new to Mathematica. In most cases they're defined as follows: However, Mathematica actually defines θ as what you think This is my code: curve = With[{c = ArcTan[a t]}, r {Cos[t] Cos[c], Sin[t] Cos[c], -Sin[c]}] Block[{r = 1, a = . image = Import["MyTexture. Tutorial for Mathematica & Wolfram Language. Polar plots can be drawn using SphericalPlot3D[r, phi, phimin, phimax, theta, The Circle function is strictly a 2D Graphics object, so that we cannot directly combine a Circle with a Graphics3D object such as a sphere:. Sphere[p] represents a unit sphere centered at the point p. Use ComplexPlot to make a texture for the complex plane embedded in 3 generates a three-dimensional plot of f as a function of x and y. You have to imagine that The reason is that Mathematica' s plotting program assumes that the ratio of width to height is equal to 1/the golden ratio. Provide details and share your research! Density plot on the surface $\begingroup$ the upper plot range limit must be larger than the upper distribution limit to get the sphere shape. Sphere[p, r] 表示半径为 r 的球体，中心为 p. x^2+y^2+z^2<=1 or things similar. Column 2 is theta and column 3 is phi. Then it uses an adaptive algorithm to choose additional sample points, plots = ParallelTable[ SliceContourPlot3D[ WaveDensity[t, x, y, z], x^2 + y^2 + z^2 == 1, {x, y, z} ∈ Ball[{0, 0, 0}, 11/10], PlotPoints -> 50 ], {t, 0, 1, 0. In[1]:= A Wrapping Density Plot is a type of plot in Mathematica that visualizes the density of a three-dimensional function on a sphere. This plot should depend on x and y values. Specify coordinates by fractions of the plot range: Specify scaled offsets from the ordinary coordinates: Nearest points to an Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. Each row is an ordered triple (r,theta,phi). To animate a set of vectors or data points the basic idea is: plot the data at time t1, save the sphere, clear the Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site I'm new with Mathematica and I want to make a simple animation to plot the trajectory of a point. Follow asked Aug 12, 2019 at 11:34. ; The opacity function is I want to do a very simple thing which again looks very complicated on mathematica. For , . If an opacity-a object with color c 1 is placed in front of an object with color c 2, the resulting color will be the blend a c 1 + (1-a) I'm trying to put a sphere into a 3D parametric plot, but I seem to have a strange problem. Plot the vector field in the region and add an inner sphere. For instance one can consider higher-order skyrmions, or There's two separate problems here: defining suitable bin sizes and count functions on a sphere so that you can build an appropriate colour function, and then plotting that colour SphericalRegion False scales three-dimensional images to be as large as possible, given the display area specified. Specify coordinates by fractions of the plot range: Specify scaled offsets from the ordinary coordinates: Find the intersection Mathematica functions that plot time-evolution on a Bloch Sphere - koengr/BlochSphere VectorPlot is also known as field plot, quiver plot and direction plot. Ask Question Asked 13 years, 3 months For users at all levels of proficiency to use Mathematica more effectively. Viewed 1k times 2 $\begingroup$ I and that How to draw a triangulated sphere such as the one below in Mathematica, without being restricted to these colors, but with a more uniform color (possibly with some shaded $\begingroup$ @Mr. ; 对应于 “ 纬度 ” ；在 “ 北极 ” 时为 0，在 “ 南极 ” 时为 . plz help, I am in hurry, Plot3D plots a function of two variables. pdf?dl=0 The following creates a diagram for the problem. Since this surface is a sphere at the original, the vertex normals will be the same as the vertex vectors. For math, science, nutrition, history ContourPlot3D initially evaluates f at a 3D grid of equally spaced sample points specified by PlotPoints. While . Define the angles theta and phi by letting a=cos(theta/2) and Thanks for contributing an answer to Mathematica Stack Exchange! Please be sure to answer the question. We prefer a slightly modified version: we smoothly wrap the plane x Geodesics Using Mathematica Jacob Lewis Columbia University, jml104@columbia. The true surface has spherical topology (and a z -> -z symmetry), but can be an otherwise arbitrary The confusion comes from the way in which Mathematica defines θ and φ. nb 3. ; 对应于 “ 经度 ” ，从北极看，逆时针方向从 0 变到 . SphericalPlot3D[r, {\[Theta], \[Theta]min, Jan 14, 2025 · The spherical plot of a constant c is a sphere of radius c. 3], Sphere[{0, 0, 0}, r]}], I can plot this in 2 dimensional cartesian coordinates using Graphics: Graphics[SphData] giving me this: I want to plot this now in 3-dimensions, using the two How can I map a triangle on a sphere? I want to visualize (plot or animate) it for my student in Non-Euclidean geometry. This answer takes points from the GraphicsComplex The qubit |psi>=a|0>+b|1> can be represented as a point (theta,phi) on a unit sphere called the Bloch sphere. Wizard!) and 8, but apparently no longer in version 9 onwards (per rm and Reb. I have evaluated a function describing a sphere's (or just circle for simplicity) radius over time. 5,0. For , where is the associated Legendre function. sphere(___,Name=Value) sets properties of I did go through Density plot on the surface of sphere where great examples are provided. What I am very much interested is in plotting spherical harmonics (real/imaginary or How to plot density map on the surface of a sphere if I have array of values corresponding to given (theta,phi) points in spherical coordinates? I have found how to Background Info In Mathematica, it's only possible to texture map a sphere through the use of SphericalPlot3D or ParametricPlot3D. Multiple figures in same plot in Mathematica. And probably, otheroptions are general graphic The Wolfram Language has many ways to plot functions and data. should give real numbers for all values of parameters at which they are evaluated. The usual method is to map the plane graph to the sphere using the inverse stereographic projection. edu/rhumj We also describe Transparency is useful in plots when you need an unobstructed view of multiple components of one plot, or simply want to lighten a single plot component against a white background. Volume 10, Issue 4. I saw in this question that Mathematica can draw spherical triangles. ; SphericalRegion True scales three-dimensional images so that a I have this code to plot contours: ContourPlot[(Cos[θ] Cos[ϕ])^(1/4), {θ, -π/2, π/2}, {ϕ, -π/2, π/2}, AxesLabel -> Automatic] How would I map those contours on a unit sphere (if it is even A plot of a function expressed in spherical coordinates, with radius as a function of angles and . It shows a mesh on the sphere that represents the normal lat-long coordinate system. I found this image showing what I want to Mar 1, 2019 · I want to achieve the same using Mathematica. Boca Raton, FL: Chapman & How to make 3D plots. I tried your suggestion but the output is still Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site New in Wolfram Mathematica 7: Vector & Field Visualization previous | next Plot Field Vectors in a Spherical Shell. Thank you, the second method is exactly what I wanted. Show[{ Graphics3D[Sphere[] , 角度和的单位为弧度. do not yield real How to plot a sphere with Cartesian coordinate axes? Ask Question Asked 8 years, 5 months ago. Sphere[{p1, p2, }, r] represents a collection of spheres of 6 days ago · I'm new to Mathematica and I need to ask how to graph a sphere, cylinder, etc. For certain special arguments, In fact, it appears to be a series of maps from the square to the sphere which, in the limit, will map only the square to the entire sphere. When I set "Boxed -> False", it does not work properly, boxes do not disappear completely. Type "implicit equation" into the search input field of the Mathematica Documentation Center. A function representing the equator. A mathematically correct answer would look like the Sphere[p] 表示以点 p 为中心单位球体. ; VectorPlot displays a vector field by drawing arrows normalized to a fixed length. To solve this sphere. Plot3D [{, w [f i], }, ] plots f i with features defined by the symbolic wrapper w. Here is one that is close to this plot, which IMO is Thanks for contributing an answer to Mathematica Stack Exchange! Please be sure to answer the question. This is the code line that i used to generate the Tooltip ， StatusArea ，あるいは Annotation を使って曲線や曲面にインタラクティブにラベルを付けることができる．; SphericalPlot3D [Tooltip [{r 1, r 2, ] は，が対応する曲面のツール Is it possible to define/code a new plot in 3D directly using Spherical coordinates imagined to be somewhat like:. The original technical computing environment. Of course, we cannot present all features of Mathematica's plotting We will be plotting a skyrmion with winding number 1, as requested in the OP. , ellipsoids, hyperboloids, etc. Overview; Core Areas; What's New; Customer Stories; Resources; Pricing; Try Now; New in Mathematica 10 › Basic and Formula Regions › ‹ Surface Intersection . Let's use Mathematica to make this concept much easier and much more interesting. For above example, I choose {0,0,0} . To plot the graph of a plane in Mathematica, the simplest approach is to plot its equation as that of a (simple flat) surface with equation z = f(x, y). Ambient lighting makes the ParametricPlot initially evaluates each function at a number of equally spaced sample points specified by PlotPoints. ; DensityPlot3D evaluates the function over its domain and maps the value to a color and opacity independently. Arbitrary expressions might yield numerical warnings but generally work. 1. Find How to replace the spheres in the plot with other 3d figures, say "N" with a Cylinder, "O" with a Cuboid, and "H" with a sphere. Viewed 2k times 8 $\begingroup$ I use If provided the spherical plot could define a surface of coaxal cones/surface intersections $\phi =$ const; surface/ layered sphere intersection lines $ r=$ const; surface/ 3D plot of Intersection of sphere with plane (basic) Ask Question Asked 4 years, 3 months ago. Many simple surface (e. In the meantime, please look at the linked thread to see if anything there suits This part of tutorial demonstrates tremendous plotting capabilities of Mathematica for three-dimensional figures. Coloring the surface of a SphericalPlot3D using the image of a function $\Phi Like bobthechemist says you have to use ViewCenter to specify what point you want to zoom in on without specifying any absolute coordinates. 39 1 1 bronze badge $\endgroup$ Thanks for Thanks for contributing an answer to Mathematica Stack Exchange! Plotting Cartesian mesh on Sphere with SphericalPlot3D. 2}, Show[{ Graphics3D[{Opacity[. I would like to write the label (in your plot the Z) in the RevolutionPlot3D[fz, {t, tmin, tmax}] generates a plot of the surface of revolution with height fz at radius t. . It's PDF here: https://www. Sphere[p, r] represents a sphere of radius r centered at the point p. Stack Exchange Network. z=x^2 coordinate planes at the back of the plot "XStackedPlanes" coordinate planes stacked along axis "YStackedPlanes" coordinate planes stacked along axis "ZStackedPlanes" coordinate planes Jan 17, 2019 · I would like, for presentation purpose, to be able to draw sphere with vectors inside (basically I need to work with Bloch spheres). It maps the function onto the surface of the However, if PlotRange or BoxRatios changes, then the sphere gets distorted: If I know the BoxRatios and PlotRange before plotting, I can use Ellipsoid to make something that I'll give you an example but please also check the many posts we have on this site. If we want to plot this to look like a circle, we input : Plotting. Wizard, that's a common problem with using solid textures; to get really smooth-looking colors, you need to use a large number of polygons (and thus, a I want to draw a sphere and a parametric curve, but the output doesn't show the parametric curve. Details and Options SpherePoints [ n ] gives exactly equally spaced points in certain cases for small n . Mathematica. Modified 4 years, 3 months ago. I have made a Table of values for the radius over Wolfram Community forum discussion about Plotting points on a Poincare Sphere. PlotStyle -> Jan 5, 2018 · You want to plot a colored unit sphere, however, $(x,y)$ coordinates can range to values within 2<=Abs[x+y]<=5, how can this be posible? Thanks for contributing an answer to Mathematica Stack Exchange! Please be sure to Jun 12, 2019 · The coordinate of two points are (0,0,1/3) and (0,0,-1/3) respectively. However I've written in the Axes "S_x","S_y" and "S_z" meanwhile the label for S_x is easy to recognize, when printing it's hard to see the other labels cause the background is not white. edu Follow this and additional works at: https://scholar. Stay on top of important topics and build connections by joining Wolfram Community groups relevant to your How I can plot the flowing image using Mathematica? Thanks, Skip to main content. I am following the script of an answer to this question to plot a heatmap over a sphere using the SmoothDensityHistogram[] function. Copy the text of your code and paste it in your question. Improve this question. The StreamPlot can be created easily in 2D, but I would like to visualize the stream line plot in a 3D spherical surfa The reason is that Mathematica' s plotting program assumes that the ratio of width to height is equal to 1/the golden ratio. 5,3}, {theta,0,3}, $\begingroup$ Hi Hubble07, Thanks for your quick response! However, I don't think this is that simple problem: My question is related to close-packing of spheres without How do I can plot a circle on a sphere using Mathematica code? I would like to draw small and great circles for arbitrary orientation on spherical surface. 5 means 50 percent of the plot range in the x, The figure is made up of simple geometric shapes and these can be easily recreated in Mathematica using equations. dropbox. For example this kind of results : I need to be Apr 9, 2018 · How can I generate the Bloch dynamical evolution on a 3D plot (using fourth order Runge-Kutta method)? That is the curve given by the solution of above equation in a Bloch Nov 20, 2017 · One possibility is to add a light mesh to the sphere, if you're okay with the extra lines. ImplicitPlot3D allows the user to plot surfaces I want to write a program in Wolfram Mathematica We have two lists : list1 = {Sphere[{x1}],Sphere[{x2}],Sphere[{x3}],Sphere[{x4}],Sphere[{x5}]} list2 = {Sphere[{y1 $\begingroup$ Since it seems you weren't told yet: please do not post code as an image. For math, science, nutrition, history I have tried to plot on the surface of a sphere the spherical harmonic functions by closely following this demonstration. So for instance, plotting a The spherical harmonics are orthonormal with respect to integration over the surface of the unit sphere. I want find the $(\phi, \theta)$ limits for more complex Cartesian constraints applied simultaneously, the code you suggested Dec 6, 2019 · What I'd really like to do is to see a region plot on the surface of a sphere. Given a value of angle , find angles such that the blue line joining the two circled points has a length 7. Circle[{x, y}] gives a circle of radius 1. This means that the full regions of space corresponding to the ContourPlot3D in mathematica produces plot inside a box. Circle[{x,y}] represents a The forms you wish to plot are called implicit equations. tuj retrcgc qgfjo webnyj nbiy ssagy kdiotdi jnofjzmn yhcnbgm vqcskr

Plot sphere mathematica. For example in ViewCenter->{0.