An expression of the form P ( x, y, z ) = P means that a point P ( x, y, z ) has cylindrical coordinates r, θ, and z. To distinguish them readily from Cartesian coordinates, the cylindrical coordinates of points in this notebook are in square brackets. The cylindrical coordinate system is just the hybrid that results from crossing polar coordinates in the xy -plane with the ordinary vertical Cartesian coordinate z. This notebook discusses cylindrical-coordinate plotting. The standard package Graphics`ParametricPlot3D` contains commands for 3-dimensional plotting of regions with cylindrical-coordinate descriptions. Hurley, Department of Mathematics, University of Connecticut, Unit 3009, Storrs, CT 06269-3009. Note that Sage has many other transformations built in, and lets you define your own transformations however you Cylindrical Coordinates in MathematicaĬopyright © 1995, 1997, 2003 by James F. For example, try this: T = Spherical('radius', ) # matches Mathematica ordering
Polar plot mathematica how to#
Read the documentation to Spherical to see how to change the coordinate system to match Mathematica's order. So according to many calculus textbook, and according to the Wolfram Mathworld website, Mathematica has the names backwards (i.e., Mathematica uses theta for inclination angle and phi for azimuth angle, whereas typical mathematical convention is to use theta for azimuth angle and phi for inclination angle). Note that in mathematica, the SphericalPlot3d "phi" corresponds to the PolarPlot "theta" (that's the azimuth angle) and the SphericalPlot3d "theta" is the inclination angle (which in lots of calculus textbooks is called "phi"). This is consistent with calculus textbooks, for example, and provides a natural extension of the polar plot commands (where the single parameter is the azimuth angle). The spherical_plot3d function adopts the convention that the first argument is the azimuth angle and the second angle is the inclination angle (or "polar angle"). In Sage, you can define the coordinates however you choose. See mathworld for many ways in which spherical coordinates are phrased in different disciplines. In Sage, we use "azimuth", "elevation", and "inclination", rather than "phi" and "theta". In different disciplines, phi and theta mean different things. What command should I give in sage to get a plot like the one we get from Mathematica? The following plot is what I wanted using spherical3d plotīut in sage, giving the same command is giving me this plot instead. I shall also give another example with pictures. I want to do a 3d polar plot of this to get a doughnut shape Or Another Example: polar_plot of cos(theta) I wanted to plot this sin(2*theta) function as a 3d plot, by revolving it around by it's vertical axis.īut the command spherical_plot3d(sin(2*theta),(theta,0,2*pi),(x,0,pi)) I tried spherical_plot but it is not giving me the plot which I expect to be equivalent to the revolution surface I get from rotating the 2d polar plot along vertical axis.Įxample: show(polar_plot(sin(2*theta),theta,0,2*pi)) The polar plot is of the form r=f(theta).īut the polar_plot function in sage gives me only 2d plot. I have to make a 3d plot by rotating a 2d polar plot along the vertical axis.
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