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Toggle Main Navigation. Search Answers Clear Filters. Answers Support MathWorks. Search Support Clear Filters. Support Answers MathWorks. Search MathWorks. MathWorks Answers Support. Open Mobile Search. Trial software. You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. Plotting antenna field patterns in spherical coordinates.In mathematicsa spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.

It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the radius or radial coordinate. The polar angle may be called colatitudezenith anglenormal angleor inclination angle. The use of symbols and the order of the coordinates differs among sources and disciplines. Other conventions are also used, such as r for radius from the z- axis, so great care needs to be taken to check the meaning of the symbols.

According to the conventions of geographical coordinate systemspositions are measured by latitude, longitude, and height altitude. There are a number of celestial coordinate systems based on different fundamental planes and with different terms for the various coordinates.

The spherical coordinate system generalizes the two-dimensional polar coordinate system. It can also be extended to higher-dimensional spaces and is then referred to as a hyperspherical coordinate system. To define a spherical coordinate system, one must choose two orthogonal directions, the zenith and the azimuth referenceand an origin point in space. These choices determine a reference plane that contains the origin and is perpendicular to the zenith.

The spherical coordinates of a point P are then defined as follows:. The sign of the azimuth is determined by choosing what is a positive sense of turning about the zenith. This choice is arbitrary, and is part of the coordinate system's definition.

If the radius is zero, both azimuth and inclination are arbitrary. In linear algebrathe vector from the origin O to the point P is often called the position vector of P. Several different conventions exist for representing the three coordinates, and for the order in which they should be written. Some combinations of these choices result in a left-handed coordinate system.

Degrees are most common in geography, astronomy, and engineering, whereas radians are commonly used in mathematics and theoretical physics. The unit for radial distance is usually determined by the context. When the system is used for physical three-space, it is customary to use positive sign for azimuth angles that are measured in the counter-clockwise sense from the reference direction on the reference plane, as seen from the zenith side of the plane.

This convention is used, in particular, for geographical coordinates, where the "zenith" direction is north and positive azimuth longitude angles are measured eastwards from some prime meridian.

On the other hand, every point has infinitely many equivalent spherical coordinates. One can add or subtract any number of full turns to either angular measure without changing the angles themselves, and therefore without changing the point. If it is necessary to define a unique set of spherical coordinates for each point, one must restrict their ranges.

A common choice is. This is the standard convention for geographic longitude. To make the coordinates unique, one can use the convention that in these cases the arbitrary coordinates are zero.Use PlotPoints and MaxRecursion to control adaptive sampling:.

Use PlotRange to focus in on areas of interest:. Use Exclusions to remove points or split the resulting surface:. Provide an interactive Tooltip for each surface:. BoundaryStyle automatically matches MeshStyle :.

Boundaries are drawn where the surface is clipped by RegionFunction :. Boundaries are not drawn where the surface is clipped by Exclusions :.

The default BoxRatios preserves the natural scale of the surface:. Use specific BoxRatios :. Color a surface by,and parameters:.

Use ColorData for predefined color gradients:. Named color gradients color in the direction:. ColorFunction has higher priority than PlotStyle :. ColorFunction has lower priority than MeshShading :.

Use scaled coordinates in the direction and unscaled coordinates in the direction:. Show where RevolutionPlot3D samples a function in coordinates:. This uses automatic methods to compute exclusions, in this case from branch cuts:.

**Plotting Points Using Spherical Coordinates: Dynamic & Modifiable Illustrator**

Style the boundary with a red line and the surface in between with yellow:. Use an explicit list of values for the mesh in the parameter and no mesh in the parameter:.

## Using surf or equivalent with spherical coordinates

Use explicit value and style for the mesh:. Use a mesh evenly spaced in the,and directions:. Show five mesh levels in the direction red and ten in the direction blue :.In this tutorial, we will look at what is involved in creating the 3D graph with spherical coordinate data, as well as using X-Function sph2cart to convert data in a workbook or matrix from spherical coordinate to Cartesian coordinates.

It is important to go over the Converting Algorithm for sph2cartand notice that Origin use as the elevation and as the azimuth in the transform formula. Origin can create surface plot with data in virtual matrix spherical coordinate and add colormap for it. The following steps introduce the plot of a ellipsoid with colormap surface.

The azimuth and elevation can be unevenly spaced in space. Origin can construct a surface function under spherical coordinates.

The azimuth, elevation and radius are placed in the different matrix. The following steps shows how to construct multiple surfaces by using three matrix and use sph2cart to convert them into XYZ space.

Origin can create 3D space curve with unevenly spaced data in XYZ column spherical coordinates. The following steps introduce the plot of a non-isometric spiral with a sphere shape.

The azimuth and elevation in X and Y can be evenly or unevenly spaced in space. OriginLab Corp. All rights reserved. What will you learn Convert data in a worksheet virtual matrix from spherical coordinate to Cartesian coordinates and make a 3D surface plot. Convert data in a matrix object from spherical coordinate to Cartesian coordinates and make a 3D surface plot. Convert data in three matrix objects from spherical coordinate to Cartesian coordinate and make a discrete 3D surface plot.

Steps 3D Surface plot with colormap for data in virtual matrix Origin can create surface plot with data in virtual matrix spherical coordinate and add colormap for it. Open the Tutorial Data. Open the virtual matrix data spheriPlot in tutorial data, the structure of the virtual matrix is shown in graph below: In this example, the azimuth is from 0 toand the elevation is from to The unit used for angle is degree. Open the Script Window, type in code below and run: sph2cart -d; Setting the sph2cart dialog follows graph below, then click OK.

Three new matrix objects will be created which are corresponded to XYZ. Then add an extra matrix object after the matrix Z in Matrix Layer to act as the colormap.

Copy the data in colormap matrix in Spherical Coordinates folder, paste the data to the new added matrix object. Set the Parametric Surface in dialog follows graph below, and click OK to apply the settings.

You graph may looks like this: Next we will apply the colormap to the ellipsoid, double click the surface to open the Plot Details dialog, go to the Fill tab, change the Contour fill from matrix into Mat 4.

Go to the Mesh tab, deselect the Enable checkbox to close the mesh line, click OK to close the dialog. All Books. User Guide. Quick Help. Origin Help.Use PlotPoints and MaxRecursion to control adaptive sampling:. Use PlotRange to focus in on areas of interest:.

Use Exclusions to remove points or split the resulting surface:. Provide an interactive Tooltip for each surface:. BoundaryStyle automatically matches MeshStyle :.

Boundaries are drawn where the surface is clipped by RegionFunction :. Boundaries are not drawn where the surface is clipped by Exclusions :. The default BoxRatios preserves the natural scale of the surface:. Use specific BoxRatios :.

Color a surface by,and parameters:. Use ColorData for predefined color gradients:. Named color gradients color in the direction:. ColorFunction has higher priority than PlotStyle :. ColorFunction has lower priority than MeshShading :. Use scaled coordinates in the direction and unscaled coordinates in the direction:. Show where RevolutionPlot3D samples a function in coordinates:. This uses automatic methods to compute exclusions, in this case from branch cuts:.

Style the boundary with a red line and the surface in between with yellow:. Use an explicit list of values for the mesh in the parameter and no mesh in the parameter:. Use explicit value and style for the mesh:. Use a mesh evenly spaced in the,and directions:.

### Spherical coordinate system

Show five mesh levels in the direction red and ten in the direction blue :. Alternate red and blue arcs in the direction:. Use None to remove segments:. MeshShading has higher priority than PlotStyle for styling:. MeshShading can be used with ColorFunction :.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. It only takes a minute to sign up.

I just learned 3d rectangular graphs in pgf-plots, and now I need to graph in spherical coordinates. Ive been reading the manual and cant find an answer.

Thank you for the help. For further complications, basically, you have to either make a mini parser or send it to a more powerful syntax handler for which gnuplot is a very good alternative. You have to make sure that gnuplot is on the system path and your editor calls TeX with -shell-escape or -enable-write18 on Windows option to communicate with gnuplot. Sign up to join this community.

The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 3 years, 9 months ago. Active 3 years, 9 months ago. Viewed times. Tony Mau.

Tony Mau Tony Mau 3 3 silver badges 10 10 bronze badges. Does that help? Ive been using addplot3[] with pgf-plots and i was wondering if i could use the same command. What do you want to plot? Can you try and give us your code even if its bugged?

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Linked Related Hot Network Questions. Question feed.Create a new matplotlib. Figure and add a new axes to it of type Axes3D :. New in version 1. Prior to version 1. Other arguments are passed on to plot. Source codepngpdf. Keyword arguments are passed on to scatter. Returns a Patch3DCollection. The rstride and cstride kwargs set the stride used to sample the input data to generate the graph. If either is 0 the input data in not sampled along this direction producing a 3D line plot rather than a wireframe plot.

They are now superseded by rcount and ccount. Will raise ValueError if both stride and count are used. These arguments will determine at most how many evenly spaced samples will be taken from the input data to generate the graph.

Will raise ValueError if both stride and count are specified. If either is zero, then the input data is not sampled along this direction, producing a 3D line plot rather than a wireframe plot.

Added in v2. Keyword arguments are passed on to LineCollection. Returns a Line3DCollection. By default it will be colored in shades of a solid color, but it also supports color mapping by supplying the cmap argument.

If 1k by 1k arrays are passed in, the default values for the strides will result in a x grid being plotted. Defaults to Raises a ValueError if both stride and count kwargs see next section are provided.

The rcount and ccount kwargs supersedes rstride and cstride for default sampling method for surface plotting. Other arguments are passed on to Poly3DCollection. See Triangulation for a explanation of these possibilities. The positional and other keyword arguments are passed on to contour. Returns a contour. The positional and keyword arguments are passed on to contourf.

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