.. _plot3D: 3-D Plots ==================================== .. include:: ../replace.txt .. index:: 3-D plots, axis right hand rule, meshgrid |M| has several functions for plotting data in three dimensions. Try this code. The ``membrane`` data is built into |M|. +---------------------+--------------------------+ | | | | :: | | | | .. image:: membrane.png | | >> m = membrane; | | | >> surf(m) | | | >> xlabel('x') | | | >> ylabel('y') | | | >> zlabel('z') | | | | | +---------------------+--------------------------+ .. .. image:: membrane.png :width: 40% :align: center Do you recognize the shape of the data? Given only a matrix as input, the 3-D surface plotting functions will show the matrix values as the :math:`z`--axis values and use the matrix indices for the :math:`x`-- and :math:`y`--axis. The ``meshgrid`` function is used to create matrices of the :math:`x`-- and :math:`y`--axis values that cover the range of data. Using data created from ``meshgrid``, the :math:`z`--axis values are simple to create from an equation. :: >> x = -3:3; >> y = -3:3; >> [X, Y] = meshgrid(x,y); >> X X = -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 >> Y Y = -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 >> Z = X.^2 + Y.^2 Z = 18 13 10 9 10 13 18 13 8 5 4 5 8 13 10 5 2 1 2 5 10 9 4 1 0 1 4 9 10 5 2 1 2 5 10 13 8 5 4 5 8 13 18 13 10 9 10 13 18 3-D Plot Functions --------------------- Here are descriptions of some of the 3-D plots available in |M|. Examples of the plots are shown in :numref:`plots3D1` and :numref:`plots3D2`. The data for the plots is from the following code. Except for the ``plot3`` function, the ``X``, ``Y``, and ``Z`` data is a two dimension grid of values, such as produced by the ``meshgrid`` function. :: x = -8:0.25:8; y = -8:0.25:8; y1 = 8:-0.25:-8; t = x.^2 + y1.^2; z = (y1-x).*exp(-0.12*t); % for plot3 [X, Y] = meshgrid(x,y); T = X.^2 + Y.^2; Z = (Y-X).*exp(-0.12*T); % for surface plots .. _plots3D1: .. figure:: plots3D1.png :align: center :width: 90% Three Dimensional Plots: (a) surf, (b) surfc, (c) mesh, (d) plot3. .. describe:: surf ``surf(X, Y, Z)``: A three-dimensional surface plot. Probably the most often used 3-D plot function. Example shown in :numref:`plots3D1` (a). ``_ .. index:: surf .. describe:: surfc ``surfc(X, Y, Z)``: A contour plot under a surface plot. Example shown in :numref:`plots3D1` (b). ``_ .. index:: surfc .. describe:: mesh ``mesh(X, Y, Z)``: A wireframe mesh with color determined by Z, so color is proportional to surface height. Example shown in :numref:`plots3D1` (c). ``_ .. index:: mesh .. describe:: plot3 ``plot3(x, y, z)``: A line plot, like the ``plot`` function, but in 3 dimensions. Example shown in :numref:`plots3D1` (d). ``_ .. index:: plot3 .. _plots3D2: .. figure:: plots3D2.png :align: center :width: 90% Three Dimensional Plots: (a) contour, (b) contour3, (c) meshz, (d) waterfall. .. describe:: contour ``contour(X, Y, Z)``: A contour plot displays isolines to indicate lines of equal :math:`z`--axis values, like found on a topographic map. Example shown in :numref:`plots3D2` (a). ``_ .. index:: contour .. describe:: contour3 ``contour3(X, Y, Z)``: A 3-D contour plot. Not all data shows well with contour type plots. Example shown in :numref:`plots3D2` (b). ``_ .. index:: contour3 .. describe:: meshz ``meshz(X, Y, Z)``: Like a mesh plot, with a curtain around the wireframe mesh. Example shown in :numref:`plots3D2` (c). ``_ .. index:: meshz .. describe:: waterfall ``waterfall(X, Y, Z)``: A mesh similar to the meshz function, but it does not generate lines from the columns of the matrices. Example shown in :numref:`plots3D2` (d). ``_ .. index:: waterfall .. describe:: surfl ``surfl(X, Y, Z)``: A shaded surface based on a combination of ambient, diffuse, and specular lighting models. Color is required for this plot to look right and the effect will vary depending on the data. An example plot is not shown. ``_ .. index:: surfl .. topic:: Tip Sometimes a 3-D plot will at first look like as a 2-D plot. Before concluding that you made a mistake, use the rotate tool to move the plot around. Sometimes 3-D plots first show a view of the plot that make it look a 2-D plot when it is actually a 3-D plot. Axis Orientation ----------------- .. index:: right hand rule, axis right hand rule If the axes are not labeled, it may be hard to remember which is the :math:`x`--axis and the :math:`y`--axis. Use the right hand rule to help with this. Point your right index finger in the direction of the :math:`x`--axis. Hold your middle finger at 90 degrees, which will be in the direction of the :math:`y`--axis. Your thumb will be in the direction of the :math:`z`--axis. See :numref:`fig:right-hand-rule` for the correct 3-D coordinate frame layout. A physical model is also helpful to visualize the 3-D coordinate frame axes. One can be printed on a 3-D printer. For a paper model, Peter Corke's web-site has a PDF file that can be printed, cut, folded, and glued. The PDF file is available at ``_ .. _fig:right-hand-rule: .. figure:: axis_right_hand_rule.png :align: center :width: 80% 3-D coordinate frame and the right hand rule. .. figure:: index_rhr.jpg :align: center :width: 30% Right hand rule