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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 Figure 15.5. 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.

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 Figure 15.6.

Finally, the `view`

function changes the viewpoint for
three-dimensional plots.

- Function File:
**mesh***(*`x`,`y`,`z`) - Function File:
**mesh***(*`z`) - Function File:
**mesh***(…,*`c`) - Function File:
**mesh***(…,*`prop`,`val`, …) - Function File:
**mesh***(*`hax`, …) - Function File:
`h`=**mesh***(…)* Plot a 3-D wireframe mesh.

The wireframe mesh is plotted using rectangles. The vertices of the rectangles [

`x`,`y`] are typically the output of`meshgrid`

. over a 2-D rectangular region in the x-y plane.`z`determines the height above the plane of each vertex. If only a single`z`matrix is given, then it is plotted over the meshgrid

. Thus, columns of`x`= 1:columns (`z`),`y`= 1:rows (`z`)`z`correspond to different`x`values and rows of`z`correspond to different`y`values.The color of the mesh is computed by linearly scaling the

`z`values to fit the range of the current colormap. Use`caxis`

and/or change the colormap to control the appearance.Optionally, the color of the mesh can be specified independently of

`z`by supplying a color matrix,`c`.Any property/value pairs are passed directly to the underlying surface object.

If the first argument

`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a graphics handle to the created surface object.**See also:**ezmesh, meshc, meshz, trimesh, contour, surf, surface, meshgrid, hidden, shading, colormap, caxis.

- Function File:
**meshc***(*`x`,`y`,`z`) - Function File:
**meshc***(*`z`) - Function File:
**meshc***(…,*`c`) - Function File:
**meshc***(…,*`prop`,`val`, …) - Function File:
**meshc***(*`hax`, …) - Function File:
`h`=**meshc***(…)* Plot a 3-D wireframe mesh with underlying contour lines.

The wireframe mesh is plotted using rectangles. The vertices of the rectangles [

`x`,`y`] are typically the output of`meshgrid`

. over a 2-D rectangular region in the x-y plane.`z`determines the height above the plane of each vertex. If only a single`z`matrix is given, then it is plotted over the meshgrid

. Thus, columns of`x`= 1:columns (`z`),`y`= 1:rows (`z`)`z`correspond to different`x`values and rows of`z`correspond to different`y`values.The color of the mesh is computed by linearly scaling the

`z`values to fit the range of the current colormap. Use`caxis`

and/or change the colormap to control the appearance.Optionally the color of the mesh can be specified independently of

`z`by supplying a color matrix,`c`.Any property/value pairs are passed directly to the underlying surface object.

If the first argument

`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a 2-element vector with a graphics handle to the created surface object and to the created contour plot.**See also:**ezmeshc, mesh, meshz, contour, surfc, surface, meshgrid, hidden, shading, colormap, caxis.

- Function File:
**meshz***(*`x`,`y`,`z`) - Function File:
**meshz***(*`z`) - Function File:
**meshz***(…,*`c`) - Function File:
**meshz***(…,*`prop`,`val`, …) - Function File:
**meshz***(*`hax`, …) - Function File:
`h`=**meshz***(…)* Plot a 3-D wireframe mesh with a surrounding curtain.

The wireframe mesh is plotted using rectangles. The vertices of the rectangles [

`x`,`y`] are typically the output of`meshgrid`

. over a 2-D rectangular region in the x-y plane.`z`determines the height above the plane of each vertex. If only a single`z`matrix is given, then it is plotted over the meshgrid

. Thus, columns of`x`= 1:columns (`z`),`y`= 1:rows (`z`)`z`correspond to different`x`values and rows of`z`correspond to different`y`values.The color of the mesh is computed by linearly scaling the

`z`values to fit the range of the current colormap. Use`caxis`

and/or change the colormap to control the appearance.Optionally the color of the mesh can be specified independently of

`z`by supplying a color matrix,`c`.Any property/value pairs are passed directly to the underlying surface object.

If the first argument

`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a graphics handle to the created surface object.**See also:**mesh, meshc, contour, surf, surface, waterfall, meshgrid, hidden, shading, colormap, caxis.

- Command:
**hidden** - Command:
**hidden***"on"* - Command:
**hidden***"off"* - Function File:
`mode`=**hidden***(…)* Control mesh hidden line removal.

When called with no argument the hidden line removal state is toggled. When called with one of the modes

`"on"`

or`"off"`

the state is set accordingly.The optional output argument

`mode`is the current state.Hidden Line Removal determines what graphic objects behind a mesh plot are visible. The default is for the mesh to be opaque and lines behind the mesh are not visible. If hidden line removal is turned off then objects behind the mesh can be seen through the faces (openings) of the mesh, although the mesh grid lines are still opaque.

**See also:**mesh, meshc, meshz, ezmesh, ezmeshc, trimesh, waterfall.

- Function File:
**surf***(*`x`,`y`,`z`) - Function File:
**surf***(*`z`) - Function File:
**surf***(…,*`c`) - Function File:
**surf***(…,*`prop`,`val`, …) - Function File:
**surf***(*`hax`, …) - Function File:
`h`=**surf***(…)* Plot a 3-D surface mesh.

The surface mesh is plotted using shaded rectangles. The vertices of the rectangles [

`x`,`y`] are typically the output of`meshgrid`

. over a 2-D rectangular region in the x-y plane.`z`determines the height above the plane of each vertex. If only a single`z`matrix is given, then it is plotted over the meshgrid

. Thus, columns of`x`= 1:columns (`z`),`y`= 1:rows (`z`)`z`correspond to different`x`values and rows of`z`correspond to different`y`values.The color of the surface is computed by linearly scaling the

`z`values to fit the range of the current colormap. Use`caxis`

and/or change the colormap to control the appearance.Optionally, the color of the surface can be specified independently of

`z`by supplying a color matrix,`c`.Any property/value pairs are passed directly to the underlying surface object.

`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a graphics handle to the created surface object.Note: The exact appearance of the surface can be controlled with the

`shading`

command or by using`set`

to control surface object properties.**See also:**ezsurf, surfc, surfl, surfnorm, trisurf, contour, mesh, surface, meshgrid, hidden, shading, colormap, caxis.

- Function File:
**surfc***(*`x`,`y`,`z`) - Function File:
**surfc***(*`z`) - Function File:
**surfc***(…,*`c`) - Function File:
**surfc***(…,*`prop`,`val`, …) - Function File:
**surfc***(*`hax`, …) - Function File:
`h`=**surfc***(…)* Plot a 3-D surface mesh with underlying contour lines.

The surface mesh is plotted using shaded rectangles. The vertices of the rectangles [

`x`,`y`] are typically the output of`meshgrid`

. over a 2-D rectangular region in the x-y plane.`z`determines the height above the plane of each vertex. If only a single`z`matrix is given, then it is plotted over the meshgrid

. Thus, columns of`x`= 1:columns (`z`),`y`= 1:rows (`z`)`z`correspond to different`x`values and rows of`z`correspond to different`y`values.The color of the surface is computed by linearly scaling the

`z`values to fit the range of the current colormap. Use`caxis`

and/or change the colormap to control the appearance.Optionally, the color of the surface can be specified independently of

`z`by supplying a color matrix,`c`.Any property/value pairs are passed directly to the underlying surface object.

`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a graphics handle to the created surface object.Note: The exact appearance of the surface can be controlled with the

`shading`

command or by using`set`

to control surface object properties.**See also:**ezsurfc, surf, surfl, surfnorm, trisurf, contour, mesh, surface, meshgrid, hidden, shading, colormap, caxis.

- Function File:
**surfl***(*`z`) - Function File:
**surfl***(*`x`,`y`,`z`) - Function File:
**surfl***(…,*`lsrc`) - Function File:
**surfl***(*`x`,`y`,`z`,`lsrc`,`P`) - Function File:
**surfl***(…, "cdata")* - Function File:
**surfl***(…, "light")* - Function File:
**surfl***(*`hax`, …) - Function File:
`h`=**surfl***(…)* -
Plot a 3-D surface using shading based on various lighting models.

The surface mesh is plotted using shaded rectangles. The vertices of the rectangles [

`x`,`y`] are typically the output of`meshgrid`

. over a 2-D rectangular region in the x-y plane.`z`determines the height above the plane of each vertex. If only a single`z`matrix is given, then it is plotted over the meshgrid

. Thus, columns of`x`= 1:columns (`z`),`y`= 1:rows (`z`)`z`correspond to different`x`values and rows of`z`correspond to different`y`values.The default lighting mode

`"cdata"`

, changes the cdata property of the surface object to give the impression of a lighted surface.**Warning:**The alternative mode`"light"`

mode which creates a light object to illuminate the surface is not implemented (yet).The light source location can be specified using

`lsrc`. It can be given as a 2-element vector [azimuth, elevation] in degrees, or as a 3-element vector [lx, ly, lz]. The default value is rotated 45 degrees counterclockwise to 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

`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a graphics handle to the created surface object.Example:

colormap (bone (64)); surfl (peaks); shading interp;

**See also:**diffuse, specular, surf, shading, colormap, caxis.

- 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:rows (`z`), 1:columns (`z`));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`

issurfnorm (peaks (25));

- Function File:
*[*`fv`] =**isosurface***(*`val`,`iso`) - Function File:
*[*`fv`] =**isosurface***(*`x`,`y`,`z`,`val`,`iso`) - Function File:
*[*`fv`] =**isosurface***(…, "noshare", "verbose")* - Function File:
*[*`fvc`] =**isosurface***(…,*`col`) - Function File:
*[*`f`,`v`] =**isosurface***(*`x`,`y`,`z`,`val`,`iso`) - Function File:
*[*`f`,`v`,`c`] =**isosurface***(*`x`,`y`,`z`,`val`,`iso`,`col`) - Function File:
**isosurface***(*`x`,`y`,`z`,`val`,`iso`,`col`,`opt`) -
If called with one output argument and the first input argument

`val`is a three-dimensional array that contains the data of an isosurface geometry and the second input argument`iso`keeps the isovalue as a scalar value then return a structure array`fv`that contains the fields`Faces`and`Vertices`at computed points`[x, y, z] = meshgrid (1:l, 1:m, 1:n)`

. The output argument`fv`can directly be taken as an input argument for the`patch`

function.If called with further input arguments

`x`,`y`and`z`which are three–dimensional arrays with the same size than`val`then the volume data is taken at those given points.The string input argument

`"noshare"`

is only for compatibility and has no effect. If given the string input argument`"verbose"`

then print messages to the command line interface about the current progress.If called with the input argument

`col`which is a three-dimensional array of the same size than`val`then take those values for the interpolation of coloring the isosurface geometry. Add the field`FaceVertexCData`to the structure array`fv`.If called with two or three output arguments then return the information about the faces

`f`, vertices`v`and color data`c`as separate arrays instead of a single structure array.If called with no output argument then directly process the isosurface geometry with the

`patch`

command.For example,

[x, y, z] = meshgrid (1:5, 1:5, 1:5); val = rand (5, 5, 5); isosurface (x, y, z, val, .5);

will directly draw a random isosurface geometry in a graphics window. Another example for an isosurface geometry with different additional coloring

N = 15; # Increase number of vertices in each direction iso = .4; # Change isovalue to .1 to display a sphere lin = linspace (0, 2, N); [x, y, z] = meshgrid (lin, lin, lin); c = abs ((x-.5).^2 + (y-.5).^2 + (z-.5).^2); figure (); # Open another figure window subplot (2,2,1); view (-38, 20); [f, v] = isosurface (x, y, z, c, iso); p = patch ("Faces", f, "Vertices", v, "EdgeColor", "none"); set (gca, "PlotBoxAspectRatioMode", "manual", ... "PlotBoxAspectRatio", [1 1 1]); # set (p, "FaceColor", "green", "FaceLighting", "phong"); # light ("Position", [1 1 5]); # Available with the JHandles package subplot (2,2,2); view (-38, 20); p = patch ("Faces", f, "Vertices", v, "EdgeColor", "blue"); set (gca, "PlotBoxAspectRatioMode", "manual", ... "PlotBoxAspectRatio", [1 1 1]); # set (p, "FaceColor", "none", "FaceLighting", "phong"); # light ("Position", [1 1 5]); subplot (2,2,3); view (-38, 20); [f, v, c] = isosurface (x, y, z, c, iso, y); p = patch ("Faces", f, "Vertices", v, "FaceVertexCData", c, ... "FaceColor", "interp", "EdgeColor", "none"); set (gca, "PlotBoxAspectRatioMode", "manual", ... "PlotBoxAspectRatio", [1 1 1]); # set (p, "FaceLighting", "phong"); # light ("Position", [1 1 5]); subplot (2,2,4); view (-38, 20); p = patch ("Faces", f, "Vertices", v, "FaceVertexCData", c, ... "FaceColor", "interp", "EdgeColor", "blue"); set (gca, "PlotBoxAspectRatioMode", "manual", ... "PlotBoxAspectRatio", [1 1 1]); # set (p, "FaceLighting", "phong"); # light ("Position", [1 1 5]);

**See also:**isonormals, isocolors.

- Function File:
*[*`n`] =**isonormals***(*`val`,`v`) - Function File:
*[*`n`] =**isonormals***(*`val`,`p`) - Function File:
*[*`n`] =**isonormals***(*`x`,`y`,`z`,`val`,`v`) - Function File:
*[*`n`] =**isonormals***(*`x`,`y`,`z`,`val`,`p`) - Function File:
*[*`n`] =**isonormals***(…, "negate")* - Function File:
**isonormals***(…,*`p`) -
If called with one output argument and the first input argument

`val`is a three-dimensional array that contains the data for an isosurface geometry and the second input argument`v`keeps the vertices of an isosurface then return the normals`n`in form of a matrix with the same size than`v`at computed points`[x, y, z] = meshgrid (1:l, 1:m, 1:n)`

. The output argument`n`can be taken to manually set`VertexNormals`of a patch.If called with further input arguments

`x`,`y`and`z`which are three–dimensional arrays with the same size than`val`then the volume data is taken at those given points. Instead of the vertices data`v`a patch handle`p`can be passed to this function.If given the string input argument

`"negate"`

as last input argument then compute the reverse vector normals of an isosurface geometry.If no output argument is given then directly redraw the patch that is given by the patch handle

`p`.For example:

function [] = isofinish (p) set (gca, "PlotBoxAspectRatioMode", "manual", ... "PlotBoxAspectRatio", [1 1 1]); set (p, "VertexNormals", -get (p,"VertexNormals")); # Revert normals set (p, "FaceColor", "interp"); ## set (p, "FaceLighting", "phong"); ## light ("Position", [1 1 5]); # Available with JHandles endfunction N = 15; # Increase number of vertices in each direction iso = .4; # Change isovalue to .1 to display a sphere lin = linspace (0, 2, N); [x, y, z] = meshgrid (lin, lin, lin); c = abs ((x-.5).^2 + (y-.5).^2 + (z-.5).^2); figure (); # Open another figure window subplot (2,2,1); view (-38, 20); [f, v, cdat] = isosurface (x, y, z, c, iso, y); p = patch ("Faces", f, "Vertices", v, "FaceVertexCData", cdat, ... "FaceColor", "interp", "EdgeColor", "none"); isofinish (p); ## Call user function isofinish subplot (2,2,2); view (-38, 20); p = patch ("Faces", f, "Vertices", v, "FaceVertexCData", cdat, ... "FaceColor", "interp", "EdgeColor", "none"); isonormals (x, y, z, c, p); # Directly modify patch isofinish (p); subplot (2,2,3); view (-38, 20); p = patch ("Faces", f, "Vertices", v, "FaceVertexCData", cdat, ... "FaceColor", "interp", "EdgeColor", "none"); n = isonormals (x, y, z, c, v); # Compute normals of isosurface set (p, "VertexNormals", n); # Manually set vertex normals isofinish (p); subplot (2,2,4); view (-38, 20); p = patch ("Faces", f, "Vertices", v, "FaceVertexCData", cdat, ... "FaceColor", "interp", "EdgeColor", "none"); isonormals (x, y, z, c, v, "negate"); # Use reverse directly isofinish (p);

**See also:**isosurface, isocolors.

- Function File:
*[*`cd`] =**isocolors***(*`c`,`v`) - Function File:
*[*`cd`] =**isocolors***(*`x`,`y`,`z`,`c`,`v`) - Function File:
*[*`cd`] =**isocolors***(*`x`,`y`,`z`,`r`,`g`,`b`,`v`) - Function File:
*[*`cd`] =**isocolors***(*`r`,`g`,`b`,`v`) - Function File:
*[*`cd`] =**isocolors***(…,*`p`) - Function File:
**isocolors***(…)* -
If called with one output argument and the first input argument

`c`is a three-dimensional array that contains color values and the second input argument`v`keeps the vertices of a geometry then return a matrix`cd`with color data information for the geometry at computed points`[x, y, z] = meshgrid (1:l, 1:m, 1:n)`

. The output argument`cd`can be taken to manually set FaceVertexCData of a patch.If called with further input arguments

`x`,`y`and`z`which are three–dimensional arrays of the same size than`c`then the color data is taken at those given points. Instead of the color data`c`this function can also be called with RGB values`r`,`g`,`b`. If input argumnets`x`,`y`,`z`are not given then again`meshgrid`

computed values are taken.Optionally, the patch handle

`p`can be given as the last input argument to all variations of function calls instead of the vertices data`v`. Finally, if no output argument is given then directly change the colors of a patch that is given by the patch handle`p`.For example:

function [] = isofinish (p) set (gca, "PlotBoxAspectRatioMode", "manual", ... "PlotBoxAspectRatio", [1 1 1]); set (p, "FaceColor", "interp"); ## set (p, "FaceLighting", "flat"); ## light ("Position", [1 1 5]); ## Available with JHandles endfunction N = 15; # Increase number of vertices in each direction iso = .4; # Change isovalue to .1 to display a sphere lin = linspace (0, 2, N); [x, y, z] = meshgrid (lin, lin, lin); c = abs ((x-.5).^2 + (y-.5).^2 + (z-.5).^2); figure (); # Open another figure window subplot (2,2,1); view (-38, 20); [f, v] = isosurface (x, y, z, c, iso); p = patch ("Faces", f, "Vertices", v, "EdgeColor", "none"); cdat = rand (size (c)); # Compute random patch color data isocolors (x, y, z, cdat, p); # Directly set colors of patch isofinish (p); # Call user function isofinish subplot (2,2,2); view (-38, 20); p = patch ("Faces", f, "Vertices", v, "EdgeColor", "none"); [r, g, b] = meshgrid (lin, 2-lin, 2-lin); cdat = isocolors (x, y, z, c, v); # Compute color data vertices set (p, "FaceVertexCData", cdat); # Set color data manually isofinish (p); subplot (2,2,3); view (-38, 20); p = patch ("Faces", f, "Vertices", v, "EdgeColor", "none"); cdat = isocolors (r, g, b, c, p); # Compute color data patch set (p, "FaceVertexCData", cdat); # Set color data manually isofinish (p); subplot (2,2,4); view (-38, 20); p = patch ("Faces", f, "Vertices", v, "EdgeColor", "none"); r = g = b = repmat ([1:N] / N, [N, 1, N]); # Black to white cdat = isocolors (x, y, z, r, g, b, v); set (p, "FaceVertexCData", cdat); isofinish (p);

**See also:**isosurface, isonormals.

- Function File:
**shrinkfaces***(*`p`,`sf`) - Function File:
`nfv`=**shrinkfaces***(*`p`,`sf`) - Function File:
`nfv`=**shrinkfaces***(*`fv`,`sf`) - Function File:
`nfv`=**shrinkfaces***(*`f`,`v`,`sf`) - Function File:
*[*`nf`,`nv`] =**shrinkfaces***(…)* -
Reduce the faces area for a given patch, structure or explicit faces and points matrices by a scale factor

`sf`. The structure`fv`must contain the fields`"faces"`

and`"vertices"`

. If the factor`sf`is omitted then a default of 0.3 is used.Given a patch handle as the first input argument and no output parameters, perform the shrinking of the patch faces in place and redraw the patch.

If called with one output argument, return a structure with fields

`"faces"`

,`"vertices"`

, and`"facevertexcdata"`

containing the data after shrinking which can then directly be used as an input argument for the`patch`

function.Performing the shrinking on faces which are not convex can lead to undesired results.

For example,

[phi r] = meshgrid (linspace (0, 1.5*pi, 16), linspace (1, 2, 4)); tri = delaunay (phi(:), r(:)); v = [r(:).*sin(phi(:)) r(:).*cos(phi(:))]; clf () p = patch ("Faces", tri, "Vertices", v, "FaceColor", "none"); fv = shrinkfaces (p); patch (fv) axis equal grid on

draws a triangulated 3/4 circle and the corresponding shrunken version.

**See also:**patch.

- Function File:
**diffuse***(*`sx`,`sy`,`sz`,`lv`) Calculate diffuse reflection strength of a surface defined by the normal vector elements

`sx`,`sy`,`sz`.The light source location vector

`lv`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`,`lv`,`vv`) - Function File:
**specular***(*`sx`,`sy`,`sz`,`lv`,`vv`,`se`) Calculate specular reflection strength of a surface defined by the normal vector elements

`sx`,`sy`,`sz`using Phong’s approximation.The light source location and viewer location vectors can be specified using parameter

`lv`and`vv`respectively. The location vectors can given as 2-element vectors [azimuth, elevation] in degrees or as 3-element vectors [x, y, z].An optional sixth argument describes the specular exponent (spread)

`se`.

- Function File:
*[*`xx`,`yy`] =**meshgrid***(*`x`,`y`) - Function File:
*[*`xx`,`yy`,`zz`] =**meshgrid***(*`x`,`y`,`z`) - Function File:
*[*`xx`,`yy`] =**meshgrid***(*`x`) - Function File:
*[*`xx`,`yy`,`zz`] =**meshgrid***(*`x`) Given vectors of

`x`and`y`coordinates, return matrices`xx`and`yy`corresponding to a full 2-D grid.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`.If the optional

`z`input is given, or`zz`is requested, then the output will be a full 3-D grid.`meshgrid`

is most frequently used to produce input for a 2-D or 3-D function that will be plotted. The following example creates a surface plot of the “sombrero” function.f = @(x,y) sin (sqrt (x.^2 + y.^2)) ./ sqrt (x.^2 + y.^2); range = linspace (-8, 8, 41); [

`X`,`Y`] = meshgrid (range, range); Z = f (X, Y); surf (X, Y, Z);Programming Note:

`meshgrid`

is restricted to 2-D or 3-D grid generation. The`ndgrid`

function will generate 1-D through N-D grids. However, the functions are not completely equivalent. If`x`is a vector of length M and`y`is a vector of length N, then`meshgrid`

will produce an output grid which is NxM.`ndgrid`

will produce an output which is MxN (transpose) for the same input. Some core functions expect`meshgrid`

input and others expect`ndgrid`

input. Check the documentation for the function in question to determine the proper input format.

- Function File:
*[*`y1`,`y2`, …,`y`n] =**ndgrid***(*`x1`,`x2`, …,`x`n) - Function File:
*[*`y1`,`y2`, …,`y`n] =**ndgrid***(*`x`) Given n vectors

`x1`, …,`x`n,`ndgrid`

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

`y1`,`y2`, …,`y`n] = ndgrid (`x`, …,`x`)Programming Note:

`ndgrid`

is very similar to the function`meshgrid`

except that the first two dimensions are transposed in comparison to`meshgrid`

. Some core functions expect`meshgrid`

input and others expect`ndgrid`

input. Check the documentation for the function in question to determine the proper input format.**See also:**meshgrid.

- Function File:
**plot3***(*`x`,`y`,`z`) - Function File:
**plot3***(*`x`,`y`,`z`,`prop`,`value`, …) - Function File:
**plot3***(*`x`,`y`,`z`,`fmt`) - Function File:
**plot3***(*`x`,`cplx`) - Function File:
**plot3***(*`cplx`) - Function File:
**plot3***(*`hax`, …) - Function File:
`h`=**plot3***(…)* Produce 3-D 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 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`,`cplx`)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 (

`cplx`)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`, "", …)Multiple property-value pairs may be specified which will affect the line objects drawn by

`plot3`

. If the`fmt`argument is supplied it will format the line objects in the same manner as`plot`

.`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a graphics handle to the created plot.Example:

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***([*`azimuth``elevation`]) - Function File:
**view***([*`x``y``z`]) - Function File:
**view***(2)* - Function File:
**view***(3)* - Function File:
**view***(*`hax`, …) - Function File:
*[*`azimuth`,`elevation`] =**view***()* Query or set the viewpoint for the current axes.

The parameters

`azimuth`and`elevation`can be given as two arguments or as 2-element vector. The viewpoint can also be specified with Cartesian coordinates`x`,`y`, and`z`.The call

`view (2)`

sets the viewpoint to`azimuth`= 0 and`elevation`= 90, which is the default for 2-D graphs.The call

`view (3)`

sets the viewpoint to`azimuth`= -37.5 and`elevation`= 30, which is the default for 3-D graphs.If the first argument

`hax`is an axes handle, then operate on this axis rather than the current axes returned by`gca`

.If no inputs are given, return the current

`azimuth`and`elevation`.

- 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:
**slice***(…,*`method`) - Function File:
**slice***(*`hax`, …) - Function File:
`h`=**slice***(…)* Plot slices of 3-D 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 (`

and`v`, 1)`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"`

.`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a graphics handle to the created surface object.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***(*`y`) - Function File:
**ribbon***(*`x`,`y`) - Function File:
**ribbon***(*`x`,`y`,`width`) - Function File:
**ribbon***(*`hax`, …) - 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)`

).`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a vector of graphics handles to the surface objects representing each ribbon.

- Function File:
**shading***(*`type`) - Function File:
**shading***(*`hax`,`type`) Set the shading of patch or surface 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.

`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.

- Function File:
**scatter3***(*`x`,`y`,`z`) - Function File:
**scatter3***(*`x`,`y`,`z`,`s`) - Function File:
**scatter3***(*`x`,`y`,`z`,`s`,`c`) - Function File:
**scatter3***(…,*`style`) - Function File:
**scatter3***(…, "filled")* - Function File:
**scatter3***(…,*`prop`,`val`) - Function File:
**scatter3***(*`hax`, …) - Function File:
`h`=**scatter3***(…)* Draw a 3-D scatter plot.

A marker is plotted at each point defined by the coordinates in the vectors

`x`,`y`, and`z`.The size of the markers is determined by

`s`, which can be a scalar or a vector of the same length as`x`,`y`, and`z`. If`s`is not given, or is an empty matrix, then a default value of 8 points is used.The color of the markers is determined by

`c`, which can be a string defining a fixed color; a 3-element vector giving the red, green, and blue components of the color; a vector of the same length as`x`that gives a scaled index into the current colormap; or an Nx3 matrix defining the RGB color of each marker individually.The marker to use can be changed with the

`style`argument, that is a string defining a marker in the same manner as the`plot`

command. If no marker is specified it defaults to`"o"`

or circles. If the argument`"filled"`

is given then the markers are filled.Additional property/value pairs are passed directly to the underlying patch object.

`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a graphics handle to the hggroup object representing the points.[x, y, z] = peaks (20); scatter3 (x(:), y(:), z(:), [], z(:));

- Function File:
**waterfall***(*`x`,`y`,`z`) - Function File:
**waterfall***(*`z`) - Function File:
**waterfall***(…,*`c`) - Function File:
**waterfall***(…,*`prop`,`val`, …) - Function File:
**waterfall***(*`hax`, …) - Function File:
`h`=**waterfall***(…)* Plot a 3-D waterfall plot.

A waterfall plot is similar to a

`meshz`

plot except only mesh lines for the rows of`z`(x-values) are shown.`x`,`y`] are typically the output of`meshgrid`

. over a 2-D rectangular region in the x-y plane.`z`determines the height above the plane of each vertex. If only a single`z`matrix is given, then it is plotted over the meshgrid

. Thus, columns of`x`= 1:columns (`z`),`y`= 1:rows (`z`)`z`correspond to different`x`values and rows of`z`correspond to different`y`values.`z`values to fit the range of the current colormap. Use`caxis`

and/or change the colormap to control the appearance.Optionally the color of the mesh can be specified independently of

`z`by supplying a color matrix,`c`.Any property/value pairs are passed directly to the underlying surface object.

`hax`is an axes handle, then plot into this axis, rather than the current axes returned by`gca`

.The optional return value

`h`is a graphics handle to the created surface object.**See also:**meshz, mesh, meshc, contour, surf, surface, ribbon, meshgrid, hidden, shading, colormap, caxis.

• Aspect Ratio: | ||

• Three-dimensional Function Plotting: | ||

• Three-dimensional Geometric Shapes: |

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