octave: Three-Dimensional Plots
15.2.2 Three-Dimensional Plots
------------------------------
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);
xlabel ("tx");
ylabel ("ty");
zlabel ("tz");
title ("3-D Sombrero plot");
produces the familiar “sombrero” plot shown in 
figmesh. 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.
[image src="mesh.png" text="
+---------------------------------+
| Image unavailable in text mode. |
+---------------------------------+" ]
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);
xlabel ("r.*sin (t)");
ylabel ("r.*cos (t)");
zlabel ("z");
title ("plot3 display of 3-D helix");
displays the spiral in three dimensions shown in
figplot3.
[image src="plot3.png" text="
+---------------------------------+
| Image unavailable in text mode. |
+---------------------------------+" ]
Figure 15.6: Three-dimensional spiral.
Finally, the ‘view’ function changes the viewpoint for
three-dimensional plots.
-- : mesh (X, Y, Z)
-- : mesh (Z)
-- : mesh (..., C)
-- : mesh (..., PROP, VAL, ...)
-- : mesh (HAX, ...)
-- : 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 ‘X = 1:columns (Z), Y =
1:rows (Z)’. Thus, columns of 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
axes, rather than the current axes returned by ‘gca’.
The optional return value H is a graphics handle to the created
surface object.
DONTPRINTYET See also: ezmesh XREFezmesh, meshc XREFmeshc, *noteDONTPRINTYET DONTPRINTYET See also: ezmesh XREFezmesh, meshc XREFmeshc,
meshz XREFmeshz, trimesh XREFtrimesh, *notecontour:
DONTPRINTYET DONTPRINTYET See also: ezmesh XREFezmesh, meshc XREFmeshc,
meshz XREFmeshz, trimesh XREFtrimesh, contour
XREFcontour, surf XREFsurf, surface XREFsurface,
DONTPRINTYET meshgrid XREFmeshgrid, hidden XREFhidden, *noteDONTPRINTYET DONTPRINTYET meshgrid XREFmeshgrid, hidden XREFhidden,
shading XREFshading, colormap XREFcolormap, *notecaxis:
DONTPRINTYET DONTPRINTYET meshgrid XREFmeshgrid, hidden XREFhidden,
shading XREFshading, colormap XREFcolormap, caxis
XREFcaxis.
-- : meshc (X, Y, Z)
-- : meshc (Z)
-- : meshc (..., C)
-- : meshc (..., PROP, VAL, ...)
-- : meshc (HAX, ...)
-- : 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 ‘X = 1:columns (Z), Y =
1:rows (Z)’. Thus, columns of 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
axes, 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.
DONTPRINTYET See also: ezmeshc XREFezmeshc, mesh XREFmesh, *noteDONTPRINTYET DONTPRINTYET See also: ezmeshc XREFezmeshc, mesh XREFmesh,
meshz XREFmeshz, contour XREFcontour, *notesurfc:
DONTPRINTYET DONTPRINTYET DONTPRINTYET See also: ezmeshc XREFezmeshc, mesh XREFmesh,
meshz XREFmeshz, contour XREFcontour, surfc
XREFsurfc, surface XREFsurface, *notemeshgrid:
DONTPRINTYET DONTPRINTYET DONTPRINTYET See also: ezmeshc XREFezmeshc, mesh XREFmesh,
meshz XREFmeshz, contour XREFcontour, surfc
XREFsurfc, surface XREFsurface, meshgrid
XREFmeshgrid, hidden XREFhidden, shading XREFshading,
colormap XREFcolormap, caxis XREFcaxis.
-- : meshz (X, Y, Z)
-- : meshz (Z)
-- : meshz (..., C)
-- : meshz (..., PROP, VAL, ...)
-- : meshz (HAX, ...)
-- : 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 ‘X = 0:(columns (Z) -
1), Y = 0:(rows (Z) - 1’). Thus, columns of 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
axes, rather than the current axes returned by ‘gca’.
The optional return value H is a graphics handle to the created
surface object.
DONTPRINTYET See also: mesh XREFmesh, meshc XREFmeshc, *noteDONTPRINTYET DONTPRINTYET See also: mesh XREFmesh, meshc XREFmeshc,
contour XREFcontour, surf XREFsurf, *notesurface:
DONTPRINTYET DONTPRINTYET DONTPRINTYET See also: mesh XREFmesh, meshc XREFmeshc,
contour XREFcontour, surf XREFsurf, surface
XREFsurface, waterfall XREFwaterfall, *notemeshgrid:
DONTPRINTYET DONTPRINTYET DONTPRINTYET See also: mesh XREFmesh, meshc XREFmeshc,
contour XREFcontour, surf XREFsurf, surface
XREFsurface, waterfall XREFwaterfall, meshgrid
XREFmeshgrid, hidden XREFhidden, shading XREFshading,
colormap XREFcolormap, caxis XREFcaxis.
-- : hidden
-- : hidden on
-- : hidden off
-- : 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.
DONTPRINTYET See also: mesh XREFmesh, meshc XREFmeshc, *noteDONTPRINTYET DONTPRINTYET See also: mesh XREFmesh, meshc XREFmeshc,
meshz XREFmeshz, ezmesh XREFezmesh, *noteezmeshc:
DONTPRINTYET DONTPRINTYET DONTPRINTYET See also: mesh XREFmesh, meshc XREFmeshc,
meshz XREFmeshz, ezmesh XREFezmesh, ezmeshc
XREFezmeshc, trimesh XREFtrimesh, *notewaterfall:
DONTPRINTYET DONTPRINTYET DONTPRINTYET See also: mesh XREFmesh, meshc XREFmeshc,
meshz XREFmeshz, ezmesh XREFezmesh, ezmeshc
XREFezmeshc, trimesh XREFtrimesh, waterfall
XREFwaterfall.
-- : surf (X, Y, Z)
-- : surf (Z)
-- : surf (..., C)
-- : surf (..., PROP, VAL, ...)
-- : surf (HAX, ...)
-- : 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 ‘X = 1:columns (Z),
Y = 1:rows (Z)’. Thus, columns of 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.
If the first argument HAX is an axes handle, then plot into this
axes, 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.
DONTPRINTYET See also: ezsurf XREFezsurf, surfc XREFsurfc, *noteDONTPRINTYET DONTPRINTYET See also: ezsurf XREFezsurf, surfc XREFsurfc,
surfl XREFsurfl, surfnorm XREFsurfnorm, *notetrisurf:
DONTPRINTYET DONTPRINTYET See also: ezsurf XREFezsurf, surfc XREFsurfc,
surfl XREFsurfl, surfnorm XREFsurfnorm, trisurf
XREFtrisurf, contour XREFcontour, mesh XREFmesh,
DONTPRINTYET surface XREFsurface, meshgrid XREFmeshgrid, *noteDONTPRINTYET DONTPRINTYET surface XREFsurface, meshgrid XREFmeshgrid,
hidden XREFhidden, shading XREFshading, *notecolormap:
DONTPRINTYET DONTPRINTYET surface XREFsurface, meshgrid XREFmeshgrid,
hidden XREFhidden, shading XREFshading, colormap
XREFcolormap, caxis XREFcaxis.
-- : surfc (X, Y, Z)
-- : surfc (Z)
-- : surfc (..., C)
-- : surfc (..., PROP, VAL, ...)
-- : surfc (HAX, ...)
-- : 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 ‘X = 1:columns (Z),
Y = 1:rows (Z)’. Thus, columns of 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.
If the first argument HAX is an axes handle, then plot into this
axes, 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.
DONTPRINTYET See also: ezsurfc XREFezsurfc, surf XREFsurf, *noteDONTPRINTYET DONTPRINTYET See also: ezsurfc XREFezsurfc, surf XREFsurf,
surfl XREFsurfl, surfnorm XREFsurfnorm, *notetrisurf:
DONTPRINTYET DONTPRINTYET See also: ezsurfc XREFezsurfc, surf XREFsurf,
surfl XREFsurfl, surfnorm XREFsurfnorm, trisurf
XREFtrisurf, contour XREFcontour, mesh XREFmesh,
DONTPRINTYET surface XREFsurface, meshgrid XREFmeshgrid, *noteDONTPRINTYET DONTPRINTYET surface XREFsurface, meshgrid XREFmeshgrid,
hidden XREFhidden, shading XREFshading, *notecolormap:
DONTPRINTYET DONTPRINTYET surface XREFsurface, meshgrid XREFmeshgrid,
hidden XREFhidden, shading XREFshading, colormap
XREFcolormap, caxis XREFcaxis.
-- : surfl (Z)
-- : surfl (X, Y, Z)
-- : surfl (..., LSRC)
-- : surfl (X, Y, Z, LSRC, P)
-- : surfl (..., "cdata")
-- : surfl (..., "light")
-- : surfl (HAX, ...)
-- : 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 ‘X = 1:columns (Z),
Y = 1:rows (Z)’. Thus, columns of 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
If the first argument HAX is an axes handle, then plot into this
axes, 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 XREFdiffuse, specular XREFspecular,
DONTPRINTYET surf XREFsurf, shading XREFshading, *notecolormap:
DONTPRINTYET surf XREFsurf, shading XREFshading, colormap
XREFcolormap, caxis XREFcaxis.
-- : surfnorm (X, Y, Z)
-- : surfnorm (Z)
-- : surfnorm (..., PROP, VAL, ...)
-- : surfnorm (HAX, ...)
-- : [NX, NY, NZ] = surfnorm (...)
Find the vectors normal to a meshgridded surface.
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. If only a single input
Z is given then X is taken to be ‘1:columns (Z)’ and Y is ‘1:rows
(Z)’.
If no return arguments are requested, a surface plot with the
normal vectors to the surface is plotted.
Any property/value input pairs are assigned to the surface object.
If the first argument HAX is an axes handle, then plot into this
axes, rather than the current axes returned by ‘gca’.
If output arguments are requested then the components of the normal
vectors are returned in NX, NY, and NZ and no plot is made. The
normal vectors are unnormalized (magnitude != 1). To normalize,
use
len = sqrt (nx.^2 + ny.^2 + nz.^2);
nx ./= len; ny ./= len; nz ./= len;
An example of the use of ‘surfnorm’ is
surfnorm (peaks (25));
Algorithm: The normal vectors are calculated by taking the cross
product of the diagonals of each of the quadrilateral faces in the
meshgrid to find the normal vectors at the center of each face.
Next, for each meshgrid point the four nearest normal vectors are
averaged to obtain the final normal to the surface at the meshgrid
point.
For surface objects, the "VertexNormals" property contains
equivalent information, except possibly near the boundary of the
surface where different interpolation schemes may yield slightly
different values.
DONTPRINTYET See also: isonormals XREFisonormals, *notequiver3:
DONTPRINTYET See also: isonormals XREFisonormals, quiver3
XREFquiver3, surf XREFsurf, meshgrid XREFmeshgrid.
-- : FV = isosurface (V, ISOVAL)
-- : FV = isosurface (V)
-- : FV = isosurface (X, Y, Z, V, ISOVAL)
-- : FV = isosurface (X, Y, Z, V)
-- : FVC = isosurface (..., COL)
-- : FV = isosurface (..., "noshare")
-- : FV = isosurface (..., "verbose")
-- : [F, V] = isosurface (...)
-- : [F, V, C] = isosurface (...)
-- : isosurface (...)
Calculate isosurface of 3-D volume data.
An isosurface connects points with the same value and is analogous
to a contour plot, but in three dimensions.
The input argument V is a three-dimensional array that contains
data sampled over a volume.
The input ISOVAL is a scalar that specifies the value for the
isosurface. If ISOVAL is omitted or empty, a "good" value for an
isosurface is determined from V.
When called with a single output argument ‘isosurface’ returns a
structure array FV that contains the fields FACES and VERTICES
computed at the points ‘[X, Y, Z] = meshgrid (1:l, 1:m, 1:n)’ where
‘[l, m, n] = size (V)’. The output FV can be used directly as
input to the ‘patch’ function.
If called with additional input arguments X, Y, and Z that are
three-dimensional arrays with the same size as V or vectors with
lengths corresponding to the dimensions of V, then the volume data
is taken at the specified points. If X, Y, or Z are empty, the
grid corresponds to the indices (‘1:n’) in the respective direction
(meshgrid XREFmeshgrid.).
The optional input argument COL, which is a three-dimensional array
of the same size as V, specifies coloring of the isosurface. The
color data is interpolated, as necessary, to match ISOVAL. The
output structure array, in this case, has the additional field
FACEVERTEXCDATA.
If given the string input argument "noshare", vertices may be
returned multiple times for different faces. The default behavior
is to eliminate vertices shared by adjacent faces with ‘unique’
which may be time consuming.
The string input argument "verbose" is supported for MATLAB
compatibility, but has no effect.
Any string arguments must be passed after the other arguments.
If called with two or three output arguments, 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, the isosurface geometry is
directly plotted with the ‘patch’ command and a light object is
added to the axes if not yet present.
For example,
[x, y, z] = meshgrid (1:5, 1:5, 1:5);
v = rand (5, 5, 5);
isosurface (x, y, z, v, .5);
will directly draw a random isosurface geometry in a graphics
window.
An example of 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);
v = abs ((x-.5).^2 + (y-.5).^2 + (z-.5).^2);
figure ();
subplot (2,2,1); view (-38, 20);
[f, vert] = isosurface (x, y, z, v, iso);
p = patch ("Faces", f, "Vertices", vert, "EdgeColor", "none");
pbaspect ([1 1 1]);
isonormals (x, y, z, v, p)
set (p, "FaceColor", "green", "FaceLighting", "gouraud");
light ("Position", [1 1 5]);
subplot (2,2,2); view (-38, 20);
p = patch ("Faces", f, "Vertices", vert, "EdgeColor", "blue");
pbaspect ([1 1 1]);
isonormals (x, y, z, v, p)
set (p, "FaceColor", "none", "EdgeLighting", "gouraud");
light ("Position", [1 1 5]);
subplot (2,2,3); view (-38, 20);
[f, vert, c] = isosurface (x, y, z, v, iso, y);
p = patch ("Faces", f, "Vertices", vert, "FaceVertexCData", c, ...
"FaceColor", "interp", "EdgeColor", "none");
pbaspect ([1 1 1]);
isonormals (x, y, z, v, p)
set (p, "FaceLighting", "gouraud");
light ("Position", [1 1 5]);
subplot (2,2,4); view (-38, 20);
p = patch ("Faces", f, "Vertices", vert, "FaceVertexCData", c, ...
"FaceColor", "interp", "EdgeColor", "blue");
pbaspect ([1 1 1]);
isonormals (x, y, z, v, p)
set (p, "FaceLighting", "gouraud");
light ("Position", [1 1 5]);
DONTPRINTYET See also: isonormals XREFisonormals, *noteisocolors:
DONTPRINTYET DONTPRINTYET See also: isonormals XREFisonormals, isocolors
XREFisocolors, isocaps XREFisocaps, *notesmooth3:
DONTPRINTYET DONTPRINTYET DONTPRINTYET See also: isonormals XREFisonormals, isocolors
XREFisocolors, isocaps XREFisocaps, smooth3
XREFsmooth3, reducevolume XREFreducevolume, *noteDONTPRINTYET DONTPRINTYET DONTPRINTYET See also: isonormals XREFisonormals, isocolors
XREFisocolors, isocaps XREFisocaps, smooth3
XREFsmooth3, reducevolume XREFreducevolume,
reducepatch XREFreducepatch, patch XREFpatch.
-- : [VN] = isonormals (VAL, VERT)
-- : [VN] = isonormals (VAL, HP)
-- : [VN] = isonormals (X, Y, Z, VAL, VERT)
-- : [VN] = isonormals (X, Y, Z, VAL, HP)
-- : [VN] = isonormals (..., "negate")
-- : isonormals (VAL, HP)
-- : isonormals (X, Y, Z, VAL, HP)
-- : isonormals (..., "negate")
Calculate normals to an isosurface.
The vertex normals VN are calculated from the gradient of the
3-dimensional array VAL (size: lxmxn) with the data for an
isosurface geometry. The normals point towards lower values in
VAL.
If called with one output argument VN and the second input argument
VERT holds the vertices of an isosurface, the normals VN are
calculated at the vertices VERT on a grid given by ‘[x, y, z] =
meshgrid (1:l, 1:m, 1:n)’. The output argument VN has the same
size as VERT and can be used to set the "VertexNormals" property of
the corresponding patch.
If called with further input arguments X, Y, and Z which are
3-dimensional arrays with the same size as VAL, the volume data is
taken at these points. Instead of the vertex data VERT, a patch
handle HP can be passed to this function.
If the last input argument is the string "negate", compute the
reverse vector normals of an isosurface geometry (i.e., pointed
towards higher values in VAL).
If no output argument is given, the property "VertexNormals" of the
patch associated with the patch handle HP is changed directly.
DONTPRINTYET See also: isosurface XREFisosurface, *noteisocolors:
DONTPRINTYET See also: isosurface XREFisosurface, isocolors
XREFisocolors, smooth3 XREFsmooth3.
-- : FVC = isocaps (V, ISOVAL)
-- : FVC = isocaps (V)
-- : FVC = isocaps (X, Y, Z, V, ISOVAL)
-- : FVC = isocaps (X, Y, Z, V)
-- : FVC = isocaps (..., WHICH_CAPS)
-- : FVC = isocaps (..., WHICH_PLANE)
-- : FVC = isocaps (..., "verbose")
-- : [FACES, VERTICES, FVCDATA] = isocaps (...)
-- : isocaps (...)
Create end-caps for isosurfaces of 3-D data.
This function places caps at the open ends of isosurfaces.
The input argument V is a three-dimensional array that contains
data sampled over a volume.
The input ISOVAL is a scalar that specifies the value for the
isosurface. If ISOVAL is omitted or empty, a "good" value for an
isosurface is determined from V.
When called with a single output argument, ‘isocaps’ returns a
structure array FVC with the fields: ‘faces’, ‘vertices’, and
‘facevertexcdata’. The results are computed at the points ‘[X, Y,
Z] = meshgrid (1:l, 1:m, 1:n)’ where ‘[l, m, n] = size (V)’. The
output FVC can be used directly as input to the ‘patch’ function.
If called with additional input arguments X, Y, and Z that are
three-dimensional arrays with the same size as V or vectors with
lengths corresponding to the dimensions of V, then the volume data
is taken at the specified points. If X, Y, or Z are empty, the
grid corresponds to the indices (‘1:n’) in the respective direction
(meshgrid XREFmeshgrid.).
The optional parameter WHICH_CAPS can have one of the following
string values which defines how the data will be enclosed:
"above", "a" (default)
for end-caps that enclose the data above ISOVAL.
"below", "b"
for end-caps that enclose the data below ISOVAL.
The optional parameter WHICH_PLANE can have one of the following
string values to define which end-cap should be drawn:
"all" (default)
for all of the end-caps.
"xmin"
for end-caps at the lower x-plane of the data.
"xmax"
for end-caps at the upper x-plane of the data.
"ymin"
for end-caps at the lower y-plane of the data.
"ymax"
for end-caps at the upper y-plane of the data.
"zmin"
for end-caps at the lower z-plane of the data.
"zmax"
for end-caps at the upper z-plane of the data.
The string input argument "verbose" is supported for MATLAB
compatibility, but has no effect.
If called with two or three output arguments, the data for faces
FACES, vertices VERTICES, and the color data FACEVERTEXCDATA are
returned in separate arrays instead of a single structure.
If called with no output argument, the end-caps are drawn directly
in the current figure with the ‘patch’ command.
DONTPRINTYET See also: isosurface XREFisosurface, *noteisonormals:
DONTPRINTYET See also: isosurface XREFisosurface, isonormals
XREFisonormals, patch XREFpatch.
-- : [CD] = isocolors (C, V)
-- : [CD] = isocolors (X, Y, Z, C, V)
-- : [CD] = isocolors (X, Y, Z, R, G, B, V)
-- : [CD] = isocolors (R, G, B, V)
-- : [CD] = isocolors (..., P)
-- : isocolors (...)
Compute isosurface colors.
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);
DONTPRINTYET See also: isosurface XREFisosurface, *noteisonormals:
DONTPRINTYET See also: isosurface XREFisosurface, isonormals
XREFisonormals.
-- : SMOOTHED_DATA = smooth3 (DATA)
-- : SMOOTHED_DATA = smooth3 (DATA, METHOD)
-- : SMOOTHED_DATA = smooth3 (DATA, METHOD, SZ)
-- : SMOOTHED_DATA = smooth3 (DATA, METHOD, SZ, STD_DEV)
Smooth values of 3-dimensional matrix DATA.
This function can be used, for example, to reduce the impact of
noise in DATA before calculating isosurfaces.
DATA must be a non-singleton 3-dimensional matrix. The smoothed
data from this matrix is returned in SMOOTHED_DATA which is of the
same size as DATA.
The option input METHOD determines which convolution kernel is used
for the smoothing process. Possible choices:
"box", "b" (default)
to use a convolution kernel with sharp edges.
"gaussian", "g"
to use a convolution kernel that is represented by a
non-correlated trivariate normal distribution function.
SZ is either a vector of 3 elements representing the size of the
convolution kernel in x-, y- and z-direction or a scalar, in which
case the same size is used in all three dimensions. The default
value is 3.
When METHOD is "gaussian", STD_DEV defines the standard deviation
of the trivariate normal distribution function. STD_DEV is either
a vector of 3 elements representing the standard deviation of the
Gaussian convolution kernel in x-, y- and z-directions or a scalar,
in which case the same value is used in all three dimensions. The
default value is 0.65.
DONTPRINTYET See also: isosurface XREFisosurface, *noteisonormals:
DONTPRINTYET See also: isosurface XREFisosurface, isonormals
XREFisonormals, patch XREFpatch.
-- : [NX, NY, NZ, NV] = reducevolume (V, R)
-- : [NX, NY, NZ, NV] = reducevolume (X, Y, Z, V, R)
-- : NV = reducevolume (...)
Reduce the volume of the dataset in V according to the values in R.
V is a matrix that is non-singleton in the first 3 dimensions.
R can either be a vector of 3 elements representing the reduction
factors in the x-, y-, and z-directions or a scalar, in which case
the same reduction factor is used in all three dimensions.
‘reducevolume’ reduces the number of elements of V by taking only
every R-th element in the respective dimension.
Optionally, X, Y, and Z can be supplied to represent the set of
coordinates of V. They can either be matrices of the same size as
V or vectors with sizes according to the dimensions of V, in which
case they are expanded to matrices (meshgrid XREFmeshgrid.).
If ‘reducevolume’ is called with two arguments then X, Y, and Z are
assumed to match the respective indices of V.
The reduced matrix is returned in NV.
Optionally, the reduced set of coordinates are returned in NX, NY,
and NZ, respectively.
Examples:
V = reshape (1:6*8*4, [6 8 4]);
NV = reducevolume (V, [4 3 2]);
V = reshape (1:6*8*4, [6 8 4]);
X = 1:3:24; Y = -14:5:11; Z = linspace (16, 18, 4);
[NX, NY, NZ, NV] = reducevolume (X, Y, Z, V, [4 3 2]);
DONTPRINTYET See also: isosurface XREFisosurface, *noteisonormals:
DONTPRINTYET See also: isosurface XREFisosurface, isonormals
XREFisonormals.
-- : REDUCED_FV = reducepatch (FV)
-- : REDUCED_FV = reducepatch (FACES, VERTICES)
-- : REDUCED_FV = reducepatch (PATCH_HANDLE)
-- : reducepatch (PATCH_HANDLE)
-- : REDUCED_FV = reducepatch (..., REDUCTION_FACTOR)
-- : REDUCED_FV = reducepatch (..., "fast")
-- : REDUCED_FV = reducepatch (..., "verbose")
-- : [REDUCED_FACES, REDUCES_VERTICES] = reducepatch (...)
Reduce the number of faces and vertices in a patch object while
retaining the overall shape of the patch.
The input patch can be represented by a structure FV with the
fields ‘faces’ and ‘vertices’, by two matrices FACES and VERTICES
(see, e.g., the result of ‘isosurface’), or by a handle to a patch
object PATCH_HANDLE (patch XREFpatch.).
The number of faces and vertices in the patch is reduced by
iteratively collapsing the shortest edge of the patch to its
midpoint (as discussed, e.g., here:
<http://libigl.github.io/libigl/tutorial/tutorial.html#meshdecimation>).
Currently, only patches consisting of triangles are supported. The
resulting patch also consists only of triangles.
If ‘reducepatch’ is called with a handle to a valid patch
PATCH_HANDLE, and without any output arguments, then the given
patch is updated immediately.
If the REDUCTION_FACTOR is omitted, the resulting structure
REDUCED_FV includes approximately 50% of the faces of the original
patch. If REDUCTION_FACTOR is a fraction between 0 (excluded) and
1 (excluded), a patch with approximately the corresponding fraction
of faces is determined. If REDUCTION_FACTOR is an integer greater
than or equal to 1, the resulting patch has approximately
REDUCTION_FACTOR faces. Depending on the geometry of the patch,
the resulting number of faces can differ from the given value of
REDUCTION_FACTOR. This is especially true when many shared
vertices are detected.
For the reduction, it is necessary that vertices of touching faces
are shared. Shared vertices are detected automatically. This
detection can be skipped by passing the optional string argument
"fast".
With the optional string arguments "verbose", additional status
messages are printed to the command window.
Any string input arguments must be passed after all other
arguments.
If called with one output argument, the reduced faces and vertices
are returned in a structure REDUCED_FV with the fields ‘faces’ and
‘vertices’ (see the one output option of ‘isosurface’).
If called with two output arguments, the reduced faces and vertices
are returned in two separate matrices REDUCED_FACES and
REDUCED_VERTICES.
DONTPRINTYET See also: isosurface XREFisosurface, *noteisonormals:
DONTPRINTYET DONTPRINTYET See also: isosurface XREFisosurface, isonormals
XREFisonormals, reducevolume XREFreducevolume, *notepatch:
DONTPRINTYET DONTPRINTYET See also: isosurface XREFisosurface, isonormals
XREFisonormals, reducevolume XREFreducevolume, patch
XREFpatch.
-- : shrinkfaces (P, SF)
-- : NFV = shrinkfaces (P, SF)
-- : NFV = shrinkfaces (FV, SF)
-- : NFV = shrinkfaces (F, V, SF)
-- : [NF, NV] = shrinkfaces (...)
Reduce the size of faces in a patch by the shrink factor SF.
The patch object can be specified by a graphics handle (P), a patch
structure (FV) with the fields "faces" and "vertices", or as two
separate matrices (F, V) of faces and vertices.
The shrink factor SF is a positive number specifying the percentage
of the original area the new face will occupy. If no factor is
given the default is 0.3 (a reduction to 30% of the original size).
A factor greater than 1.0 will result in the expansion of faces.
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. This structure can be used directly as an input
argument to the ‘patch’ function.
*Caution:*: Performing the shrink operation on faces which are not
convex can lead to undesirable results.
Example: a triangulated 3/4 circle and the corresponding shrunken
version.
[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
See also: patch XREFpatch.
-- : diffuse (SX, SY, SZ, LV)
Calculate the 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 a 2-element
vector [azimuth, elevation] in degrees or as a 3-element vector [x,
y, z].
See also: specular XREFspecular, surfl XREFsurfl.
-- : specular (SX, SY, SZ, LV, VV)
-- : specular (SX, SY, SZ, LV, VV, SE)
Calculate the 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 are specified
using parameters 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 specifies the specular exponent (spread)
SE. If not given, SE defaults to 10.
See also: diffuse XREFdiffuse, surfl XREFsurfl.
-- : lighting (TYPE)
-- : lighting (HAX, TYPE)
Set the lighting of patch or surface graphic objects.
Valid arguments for TYPE are
"flat"
Draw objects with faceted lighting effects.
"gouraud"
Draw objects with linear interpolation of the lighting effects
between the vertices.
"none"
Draw objects without light and shadow effects.
If the first argument HAX is an axes handle, then change the
lighting effects of objects in this axes, rather than the current
axes returned by ‘gca’.
The lighting effects are only visible if at least one light object
is present and visible in the same axes.
DONTPRINTYET See also: light XREFlight, fill XREFfill, *notemesh:
DONTPRINTYET DONTPRINTYET See also: light XREFlight, fill XREFfill, mesh
XREFmesh, patch XREFpatch, pcolor XREFpcolor, *noteDONTPRINTYET DONTPRINTYET DONTPRINTYET See also: light XREFlight, fill XREFfill, mesh
XREFmesh, patch XREFpatch, pcolor XREFpcolor,
surf XREFsurf, surface XREFsurface, *noteshading:
DONTPRINTYET DONTPRINTYET DONTPRINTYET See also: light XREFlight, fill XREFfill, mesh
XREFmesh, patch XREFpatch, pcolor XREFpcolor,
surf XREFsurf, surface XREFsurface, shading
XREFshading.
-- : material shiny
-- : material dull
-- : material metal
-- : material default
-- : material ([AS, DS, SS])
-- : material ([AS, DS, SS, SE])
-- : material ([AS, DS, SS, SE, SCR])
-- : material (HLIST, ...)
-- : MTYPES = material ()
-- : REFL_PROPS = material (MTYPE_STRING)
Set reflectance properties for the lighting of surfaces and
patches.
This function changes the ambient, diffuse, and specular strengths,
as well as the specular exponent and specular color reflectance, of
all ‘patch’ and ‘surface’ objects in the current axes. This can be
used to simulate, to some extent, the reflectance properties of
certain materials when used with ‘light’.
When called with a string, the aforementioned properties are set
according to the values in the following table:
MTYPE ambient- diffuse- specular- specular- specular-
strength strength strength exponent color-
reflectance
-----------------------------------------------------------------------------
"shiny" 0.3 0.6 0.9 20 1.0
"dull" 0.3 0.8 0.0 10 1.0
"metal" 0.3 0.3 1.0 25 0.5
"default" "default" "default" "default" "default" "default"
When called with a vector of three elements, the ambient, diffuse,
and specular strengths of all ‘patch’ and ‘surface’ objects in the
current axes are updated. An optional fourth vector element
updates the specular exponent, and an optional fifth vector element
updates the specular color reflectance.
A list of graphic handles can also be passed as the first argument.
In this case, the properties of these handles and all child ‘patch’
and ‘surface’ objects will be updated.
Additionally, ‘material’ can be called with a single output
argument. If called without input arguments, a column cell vector
MTYPES with the strings for all available materials is returned.
If the one input argument MTYPE_STRING is the name of a material, a
1x5 cell vector REFL_PROPS with the reflectance properties of that
material is returned. In both cases, no graphic properties are
changed.
DONTPRINTYET See also: light XREFlight, fill XREFfill, *notemesh:
DONTPRINTYET DONTPRINTYET See also: light XREFlight, fill XREFfill, mesh
XREFmesh, patch XREFpatch, pcolor XREFpcolor, *noteDONTPRINTYET DONTPRINTYET See also: light XREFlight, fill XREFfill, mesh
XREFmesh, patch XREFpatch, pcolor XREFpcolor,
surf XREFsurf, surface XREFsurface.
-- : camlight
-- : camlight right
-- : camlight left
-- : camlight headlight
-- : camlight (AZ, EL)
-- : camlight (..., STYLE)
-- : camlight (HL, ...)
-- : H = camlight (...)
Add a light object to a figure using a simple interface.
When called with no arguments, a light object is added to the
current plot and is placed slightly above and to the right of the
camera’s current position: this is equivalent to ‘camlight right’.
The commands ‘camlight left’ and ‘camlight headlight’ behave
similarly with the placement being either left of the camera
position or centered on the camera position.
For more control, the light position can be specified by an
azimuthal rotation AZ and an elevation angle EL, both in degrees,
relative to the current properties of the camera.
The optional string STYLE specifies whether the light is a local
point source ("local", the default) or placed at infinite distance
("infinite").
If the first argument HL is a handle to a light object, then act on
this light object rather than creating a new object.
The optional return value H is a graphics handle to the light
object. This can be used to move or further change properties of
the light object.
Examples:
Add a light object to a plot
sphere (36);
camlight
Position the light source exactly
camlight (45, 30);
Here the light is first pitched upwards from the camera position by
30 degrees. It is then yawed by 45 degrees to the right. Both
rotations are centered around the camera target.
Return a handle to further manipulate the light object
clf
sphere (36);
hl = camlight ("left");
set (hl, "color", "r");
See also: light XREFlight.
-- : [XX, YY] = meshgrid (X, Y)
-- : [XX, YY, ZZ] = meshgrid (X, Y, Z)
-- : [XX, YY] = meshgrid (X)
-- : [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.
DONTPRINTYET See also: ndgrid XREFndgrid, mesh XREFmesh, *noteDONTPRINTYET See also: ndgrid XREFndgrid, mesh XREFmesh,
contour XREFcontour, surf XREFsurf.
-- : [Y1, Y2, ..., Yn] = ndgrid (X1, X2, ..., Xn)
-- : [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 to calling ndgrid with all n input arguments equal to X:
[Y1, Y2, ..., Yn] = 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 XREFmeshgrid.
-- : plot3 (X, Y, Z)
-- : plot3 (X, Y, Z, PROP, VALUE, ...)
-- : plot3 (X, Y, Z, FMT)
-- : plot3 (X, CPLX)
-- : plot3 (CPLX)
-- : plot3 (HAX, ...)
-- : 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’.
If the first argument HAX is an axes handle, then plot into this
axes, 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;");
See also: ezplot3 XREFezplot3, plot XREFplot.
-- : view (AZIMUTH, ELEVATION)
-- : view ([AZIMUTH ELEVATION])
-- : view ([X Y Z])
-- : view (2)
-- : view (3)
-- : view (HAX, ...)
-- : [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
axes rather than the current axes returned by ‘gca’.
If no inputs are given, return the current AZIMUTH and ELEVATION.
-- : slice (X, Y, Z, V, SX, SY, SZ)
-- : slice (X, Y, Z, V, XI, YI, ZI)
-- : slice (V, SX, SY, SZ)
-- : slice (V, XI, YI, ZI)
-- : slice (..., METHOD)
-- : slice (HAX, ...)
-- : 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 (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".
If the first argument HAX is an axes handle, then plot into this
axes, 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);
See also: interp3 XREFinterp3, surface XREFsurface,
pcolor XREFpcolor.
-- : ribbon (Y)
-- : ribbon (X, Y)
-- : ribbon (X, Y, WIDTH)
-- : ribbon (HAX, ...)
-- : H = ribbon (...)
Draw a ribbon plot for the columns of Y vs. X.
If X is omitted, a vector containing the row numbers is assumed
(‘1:rows (Y)’). Alternatively, X can also be a vector with same
number of elements as rows of Y in which case the same X is used
for each column of Y.
The optional parameter WIDTH specifies the width of a single ribbon
(default is 0.75).
If the first argument HAX is an axes handle, then plot into this
axes, 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.
DONTPRINTYET See also: surface XREFsurface, *notewaterfall:
DONTPRINTYET See also: surface XREFsurface, waterfall
XREFwaterfall.
-- : shading (TYPE)
-- : 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 black edges.
"interp"
Colors between patch vertices are interpolated and the patch
edges are invisible.
If the first argument HAX is an axes handle, then plot into this
axes, rather than the current axes returned by ‘gca’.
DONTPRINTYET See also: fill XREFfill, mesh XREFmesh, *notepatch:
DONTPRINTYET DONTPRINTYET See also: fill XREFfill, mesh XREFmesh, patch
XREFpatch, pcolor XREFpcolor, surf XREFsurf, *noteDONTPRINTYET DONTPRINTYET DONTPRINTYET See also: fill XREFfill, mesh XREFmesh, patch
XREFpatch, pcolor XREFpcolor, surf XREFsurf,
surface XREFsurface, hidden XREFhidden, *notelighting:
DONTPRINTYET DONTPRINTYET DONTPRINTYET See also: fill XREFfill, mesh XREFmesh, patch
XREFpatch, pcolor XREFpcolor, surf XREFsurf,
surface XREFsurface, hidden XREFhidden, lighting
XREFlighting.
-- : scatter3 (X, Y, Z)
-- : scatter3 (X, Y, Z, S)
-- : scatter3 (X, Y, Z, S, C)
-- : scatter3 (..., STYLE)
-- : scatter3 (..., "filled")
-- : scatter3 (..., PROP, VAL)
-- : scatter3 (HAX, ...)
-- : 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.
If the first argument HAX is an axes handle, then plot into this
axes, 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(:));
DONTPRINTYET See also: scatter XREFscatter, patch XREFpatch, *noteDONTPRINTYET See also: scatter XREFscatter, patch XREFpatch,
plot XREFplot.
-- : waterfall (X, Y, Z)
-- : waterfall (Z)
-- : waterfall (..., C)
-- : waterfall (..., PROP, VAL, ...)
-- : waterfall (HAX, ...)
-- : 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.
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 ‘X = 1:columns (Z), Y =
1:rows (Z)’. Thus, columns of 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
axes, rather than the current axes returned by ‘gca’.
The optional return value H is a graphics handle to the created
surface object.
DONTPRINTYET See also: meshz XREFmeshz, mesh XREFmesh, *noteDONTPRINTYET See also: meshz XREFmeshz, mesh XREFmesh,
meshc XREFmeshc, contour XREFcontour, surf XREFsurf,
DONTPRINTYET surface XREFsurface, ribbon XREFribbon, *noteDONTPRINTYET DONTPRINTYET surface XREFsurface, ribbon XREFribbon,
meshgrid XREFmeshgrid, hidden XREFhidden, *noteshading:
DONTPRINTYET DONTPRINTYET surface XREFsurface, ribbon XREFribbon,
meshgrid XREFmeshgrid, hidden XREFhidden, shading
XREFshading, colormap XREFcolormap, caxis XREFcaxis.
Menu
Info Catalog
octave: Two-Dimensional Plots
octave: High-Level Plotting
octave: Plot Annotations