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### 15.1.2 Three-Dimensional Plotting

The function `mesh` produces mesh surface plots. For example,

 ```tx = ty = linspace (-8, 8, 41)'; [xx, yy] = meshgrid (tx, ty); r = sqrt (xx .^ 2 + yy .^ 2) + eps; tz = sin (r) ./ r; mesh (tx, ty, tz); ```

produces the familiar “sombrero” plot shown in fig:mesh. Note the use of the function `meshgrid` to create matrices of X and Y coordinates to use for plotting the Z data. The `ndgrid` function is similar to `meshgrid`, but works for N-dimensional matrices.

Figure 15.5: Mesh plot.

The `meshc` function is similar to `mesh`, but also produces a plot of contours for the surface.

The `plot3` function displays arbitrary three-dimensional data, without requiring it to form a surface. For example

 ```t = 0:0.1:10*pi; r = linspace (0, 1, numel (t)); z = linspace (0, 1, numel (t)); plot3 (r.*sin(t), r.*cos(t), z); ```

displays the spiral in three dimensions shown in fig:plot3.

Figure 15.6: Three dimensional spiral.

Finally, the `view` function changes the viewpoint for three-dimensional plots.

Function File: mesh (x, y, z)

Plot a mesh given matrices x, and y from `meshgrid` and a matrix z corresponding to the x and y coordinates of the mesh. If x and y are vectors, then a typical vertex is (x(j), y(i), z(i,j)). Thus, columns of z correspond to different x values and rows of z correspond to different y values.

Function File: meshc (x, y, z)

Plot a mesh and contour given matrices x, and y from `meshgrid` and a matrix z corresponding to the x and y coordinates of the mesh. If x and y are vectors, then a typical vertex is (x(j), y(i), z(i,j)). Thus, columns of z correspond to different x values and rows of z correspond to different y values.

Function File: meshz (x, y, z)

Plot a curtain mesh given matrices x, and y from `meshgrid` and a matrix z corresponding to the x and y coordinates of the mesh. If x and y are vectors, then a typical vertex is (x(j), y(i), z(i,j)). Thus, columns of z correspond to different x values and rows of z correspond to different y values.

Function File: hidden (mode)
Function File: hidden ()

Manipulation the mesh hidden line removal. Called with no argument the hidden line removal is toggled. The argument mode can be either 'on' or 'off' and the set of the hidden line removal is set accordingly.

Function File: surf (x, y, z)

Plot a surface given matrices x, and y from `meshgrid` and a matrix z corresponding to the x and y coordinates of the mesh. If x and y are vectors, then a typical vertex is (x(j), y(i), z(i,j)). Thus, columns of z correspond to different x values and rows of z correspond to different y values.

Function File: surfc (x, y, z)

Plot a surface and contour given matrices x, and y from `meshgrid` and a matrix z corresponding to the x and y coordinates of the mesh. If x and y are vectors, then a typical vertex is (x(j), y(i), z(i,j)). Thus, columns of z correspond to different x values and rows of z correspond to different y values.

Function File: surfl (x, y, z)
Function File: surfl (z)
Function File: surfl (x, y, z, L)
Function File: surfl (x, y, z, L, P)
Function File: surfl (…,"light")

Plot a lighted surface given matrices x, and y from `meshgrid` and a matrix z corresponding to the x and y coordinates of the mesh. If x and y are vectors, then a typical vertex is (x(j), y(i), z(i,j)). Thus, columns of z correspond to different x values and rows of z correspond to different y values.

The light direction can be specified using L. It can be given as 2-element vector [azimuth, elevation] in degrees or as 3-element vector [lx, ly, lz]. The default value is rotated 45° counter-clockwise from the current view.

The material properties of the surface can specified using a 4-element vector P = [AM D SP exp] which defaults to p = [0.55 0.6 0.4 10].

`"AM" strength of ambient light`
`"D" strength of diffuse reflection`
`"SP" strength of specular reflection`
`"EXP" specular exponent`

The default lighting mode "cdata", changes the cdata property to give the impression of a lighted surface. Please note: the alternative "light" mode, which creates a light object to illuminate the surface is not implemented (yet).

Example:

 ```colormap(bone); surfl(peaks); shading interp; ```

Function File: surfnorm (x, y, z)
Function File: surfnorm (z)
Function File: [nx, ny, nz] = surfnorm (…)
Function File: surfnorm (h, …)

Find the vectors normal to a meshgridded surface. The meshed gridded surface is defined by x, y, and z. If x and y are not defined, then it is assumed that they are given by

 ```[x, y] = meshgrid (1:size(z, 1), 1:size(z, 2)); ```

If no return arguments are requested, a surface plot with the normal vectors to the surface is plotted. Otherwise the components of the normal vectors at the mesh gridded points are returned in nx, ny, and nz.

The normal vectors are calculated by taking the cross product of the diagonals of each of the quadrilaterals in the meshgrid to find the normal vectors of the centers of these quadrilaterals. The four nearest normal vectors to the meshgrid points are then averaged to obtain the normal to the surface at the meshgridded points.

An example of the use of `surfnorm` is

 ```surfnorm (peaks (25)); ```

Function File: diffuse (sx, sy, sz, l)

Calculate diffuse reflection strength of a surface defined by the normal vector elements sx, sy, sz. The light vector can be specified using parameter L. It can be given as 2-element vector [azimuth, elevation] in degrees or as 3-element vector [lx, ly, lz].

Function File: specular (sx, sy, sz, l, v)
Function File: specular (sx, sy, sz, l, v, se)

Calculate specular reflection strength of a surface defined by the normal vector elements sx, sy, sz using Phong's approximation. The light and view vectors can be specified using parameter L and V respectively. Both can be given as 2-element vectors [azimuth, elevation] in degrees or as 3-element vector [x, y, z]. An optional 6th argument describes the specular exponent (spread) se.

Function File: [xx, yy, zz] = meshgrid (x, y, z)
Function File: [xx, yy] = meshgrid (x, y)
Function File: [xx, yy] = meshgrid (x)

Given vectors of x and y and z coordinates, and returning 3 arguments, return three-dimensional arrays corresponding to the x, y, and z coordinates of a mesh. When returning only 2 arguments, return matrices corresponding to the x and y coordinates of a mesh. The rows of xx are copies of x, and the columns of yy are copies of y. If y is omitted, then it is assumed to be the same as x, and z is assumed the same as y.

Function File: [y1, y2, …, yn] = ndgrid (x1, x2, …, xn)
Function File: [y1, y2, …, yn] = ndgrid (x)

Given n vectors x1, … xn, `ndgrid` returns n arrays of dimension n. The elements of the i-th output argument contains the elements of the vector xi repeated over all dimensions different from the i-th dimension. Calling ndgrid with only one input argument x is equivalent of calling ndgrid with all n input arguments equal to x:

[y1, y2, …, yn] = ndgrid (x, …, x)

Function File: plot3 (args)

Produce three-dimensional plots. Many different combinations of arguments are possible. The simplest form is

 ```plot3 (x, y, z) ```

in which the arguments are taken to be the vertices of the points to be plotted in three dimensions. If all arguments are vectors of the same length, then a single continuous line is drawn. If all arguments are matrices, then each column of the matrices is treated as a separate line. No attempt is made to transpose the arguments to make the number of rows match.

If only two arguments are given, as

 ```plot3 (x, c) ```

the real and imaginary parts of the second argument are used as the y and z coordinates, respectively.

If only one argument is given, as

 ```plot3 (c) ```

the real and imaginary parts of the argument are used as the y and z values, and they are plotted versus their index.

Arguments may also be given in groups of three as

 ```plot3 (x1, y1, z1, x2, y2, z2, …) ```

in which each set of three arguments is treated as a separate line or set of lines in three dimensions.

To plot multiple one- or two-argument groups, separate each group with an empty format string, as

 ```plot3 (x1, c1, "", c2, "", …) ```

An example of the use of `plot3` is

 ``` z = [0:0.05:5]; plot3 (cos(2*pi*z), sin(2*pi*z), z, ";helix;"); plot3 (z, exp(2i*pi*z), ";complex sinusoid;"); ```

Function File: view (azimuth, elevation)
Function File: view (dims)
Function File: [azimuth, elevation] = view ()

Set or get the viewpoint for the current axes.

Function File: slice (x, y, z, v, sx, sy, sz)
Function File: slice (x, y, z, v, xi, yi, zi)
Function File: slice (v, sx, sy, sz)
Function File: slice (v, xi, yi, zi)
Function File: h = slice (…)
Function File: h = slice (…, method)

Plot slices of 3D data/scalar fields. Each element of the 3-dimensional array v represents a scalar value at a location given by the parameters x, y, and z. The parameters x, x, and z are either 3-dimensional arrays of the same size as the array v in the "meshgrid" format or vectors. The parameters xi, etc. respect a similar format to x, etc., and they represent the points at which the array vi is interpolated using interp3. The vectors sx, sy, and sz contain points of orthogonal slices of the respective axes.

If x, y, z are omitted, they are assumed to be `x = 1:size (v, 2)`, `y = 1:size (v, 1)` and `z = 1:size (v, 3)`.

Method is one of:

`"nearest"`

Return the nearest neighbor.

`"linear"`

Linear interpolation from nearest neighbors.

`"cubic"`

Cubic interpolation from four nearest neighbors (not implemented yet).

`"spline"`

Cubic spline interpolation—smooth first and second derivatives throughout the curve.

The default method is `"linear"`. The optional return value h is a vector of handles to the surface graphic objects.

Examples:

 ```[x, y, z] = meshgrid (linspace (-8, 8, 32)); v = sin (sqrt (x.^2 + y.^2 + z.^2)) ./ (sqrt (x.^2 + y.^2 + z.^2)); slice (x, y, z, v, [], 0, []); [xi, yi] = meshgrid (linspace (-7, 7)); zi = xi + yi; slice (x, y, z, v, xi, yi, zi); ```

Function File: ribbon (x, y, width)
Function File: ribbon (y)
Function File: h = ribbon (…)

Plot a ribbon plot for the columns of y vs. x. The optional parameter width specifies the width of a single ribbon (default is 0.75). If x is omitted, a vector containing the row numbers is assumed (1:rows(Y)). If requested, return a vector h of the handles to the surface objects.

Set the shading of surface or patch graphic objects. Valid arguments for type are

`"flat"`

Single colored patches with invisible edges.

`"faceted"`

Single colored patches with visible edges.

`"interp"`

Color between patch vertices are interpolated and the patch edges are invisible.

If ax is given the shading is applied to axis ax instead of the current axis.

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