You can enhance the information content of surface plots by controlling the way MATLAB® graphics apply color to these plots. MATLAB can map particular data values to colors specified explicitly or can map the entire range of data to a predefined range of colors called a colormap.
You can apply three different coloring techniques:
Indexed Color Surfaces — Direct and Scaled Color Mapping — MATLAB colors the surface plot by assigning each data point an index into the figure's colormap. The way MATLAB applies these colors depends on the type of shading used (faceted, flat, or interpolated).
Truecolor Surfaces — MATLAB colors the surface
plot using the explicitly specified colors (i.e., the RGB triplets).
The way MATLAB applies these colors depends on the type of shading
used (faceted, flat, or interpolated). To be rendered accurately,
truecolor requires computers with 24-bit displays; however, MATLAB simulates
truecolor on indexed systems. See the
for information on the types of shading.
Texture Mapping — Texture mapping displays a 2-D image mapped onto a 3-D surface.
Provide no explicit color data, in which case MATLAB generates colormap indices from the z-data.
Specify an array of color data that is equal in size to the z-data and is used for indexed colors.
Specify an m-by-n-by-3 array of color data that defines an RGB triplet for each element in the m-by-n z-data array and is used for truecolor.
Each MATLAB figure window has a colormap associated with it. A colormap is simply a three-column matrix whose length is equal to the number of colors it defines. Each row of the matrix defines a particular color by specifying three values in the range zero to one. These values define the RGB components (i.e., the intensities of the red, green, and blue video components).
with no arguments, returns the current figure's colormap. For example,
the MATLAB hsv colormap contains 64 colors by default and the
33rd color is cyan.
colormap hsv cm = colormap; cm(33,:) ans = 0 1 1
You can create colormaps with MATLAB array operations or
you can use any of several functions
that generate useful maps, including
gray. Each function has an optional parameter
that specifies the number of rows in the resulting map.
creates an m-by-3 matrix whose rows specify the RGB intensities of a map that varies from black, through shades of red, orange, and yellow, to white.
If you do not specify the colormap length, MATLAB creates
a colormap the same length as the current colormap. The default colormap
If you use long colormaps (> 64 colors) in each of several figure windows, it might become necessary for the operating system to swap in different color lookup tables as the active focus is moved among the windows.
displays the current colormap, either vertically or horizontally,
in the figure window along with your graph. For example, the statements
produce a surface plot and a vertical strip of color corresponding to the colormap. The colorbar indicates the mapping of data value to color with the axis labels.
MATLAB can use two different methods to map indexed color data to the colormap — direct and scaled.
Direct mapping uses the color data directly as indices into
the colormap. For example, a value of 1 points to the first color
in the colormap, a value of 2 points to the second color, and so on.
If the color data is noninteger, MATLAB rounds it toward zero.
Values greater than the number of colors in the colormap are set equal
to the last color in the colormap (i.e., the number
Values less than one are set to one.
Scaled mapping uses a two-element vector
[cmin cmax] (specified
caxis command) to
control the mapping of color data to the figure colormap.
the data value to map to the first color in the colormap and
the data value to map to the last color in the colormap. Data values
in between are linearly transformed from the second to the next-to-last color, using the expression
colormap_index = fix((color_data-cmin)/(cmax-cmin)*cm_length)+1
cm_length is the length of the colormap.
By default, MATLAB sets
span the range of the color data of all graphics objects within the
axes. However, you can set these limits to any range of values. This
enables you to display multiple axes within a single figure window
and use different portions of the figure's colormap for each one.
By default, MATLAB uses scaled mapping. To use direct mapping, you must turn off scaling when you create the plot. For example:
surface for more
information on specifying color data.
When creating a surface plot with a single matrix argument,
example, the argument
Z specifies both the height
and the color of the surface. MATLAB transforms
obtain indices into the current colormap.
With two matrix arguments, the statement
independently specifies the color using the second argument.
The Laplacian of a surface plot is related to its curvature;
it is positive for functions shaped like
i^2 + j^2 and
negative for functions shaped like
-(i^2 + j^2).
the discrete Laplacian of any matrix. For example, use
determine the color for the data returned by
P = peaks(40); C = del2(P); surf(P,C) title('surf(P,del2(P))')
Creating a color array by applying the Laplacian to the data is useful because it causes regions with similar curvature to be drawn in the same color.
Compare this surface coloring with that produced by the statements
which use the same colormap, but map regions with similar z value (height above the x-y plane) to the same color.
Because colormaps are matrices,
you can manipulate them like other arrays. The
brighten function takes advantage of this fact to increase or
decrease the intensity of the colors. Plotting the values of the R,
G, and B components of a colormap using
the effects of
b = .30*red + .59*green + .11*blue = sum(diag([.30 .59 .11])*map')';
Using the nonlinear grayscale map,
colormap([b b b])
effectively converts a color image to its NTSC black-and-white equivalent.
Computer systems with 24-bit displays are capable of displaying over 16 million (224) colors, as opposed to the 256 colors available on 8-bit displays. You can take advantage of this capability by defining color data directly as RGB values and eliminating the step of mapping numerical values to locations in a colormap.
Specify truecolor using an m-by-n-by-3
array, where the size of
Z is m-by-n.
For example, the statements
Z = peaks(25); C(:,:,1) = rand(25); C(:,:,2) = rand(25); C(:,:,3) = rand(25); surf(Z,C)
create a plot of the
with random coloring.
You can set surface properties as with indexed color.
surf(Z,C,'FaceColor','interp','FaceLighting','gouraud') camlight right
Texture mapping is a technique for mapping a 2-D image onto a 3-D surface by transforming color data so that it conforms to the surface plot. It allows you to apply a "texture," such as bumps or wood grain, to a surface without performing the geometric modeling necessary to create a surface with these features. The color data can also be any image, such as a scanned photograph.
Texture mapping allows the dimensions of the color data array to be different from the data defining the surface plot. You can apply an image of arbitrary size to any surface. MATLAB interpolates texture color data so that it is mapped to the entire surface.
This example creates a spherical surface using the
sphere function and texture maps it with an image of the earth
taken from space. Because the earth image is a view of earth from
one side, this example maps the image to only one side of the sphere,
padding the image data with 1s. In this case, the image data is a
257-by-250 matrix, so it is padded equally on each side with two 257-by-125
matrices of 1s by concatenating the three matrices.
To use texture mapping, set the
assign the image to the surface's
load earth % Load image data, X, and colormap, map sphere; h = findobj('Type','surface'); hemisphere = [ones(257,125),X,ones(257,125)]; set(h,'CData',flipud(hemisphere),'FaceColor','texturemap') colormap(map) axis equal view([90 0])