When plotting the surface illustrated below, the "x" and "z" values of the region were treated as a grid of points, and then the height, or the "y" component, was calculated. This shows how the "y" component changes with respect to both "x" and "z". A similar surface parallel to the "x-y" plane could be used to study how "z" depends upon the other variables.
In many scientific experiments, there are often four or variables involved in relationships, but it is difficult for those of us live in 3D to visualize something in 4-Dimensions. However, we can combine the 3-dimensional surface with color to represent that fourth component, thus giving us a way to visualize a four dimensional data set.
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This program generates 3-D surface and includes the use
of lighting effects.
In order to draw the surface the region is cut into a number of triangle
strips that go from one side to the other. The height of the surface is
calculated by finding the product of two sine waves, thus giging the
undulating quality. For each triangle, the three vertex points are sent
to a special routine that calculates the normal vector,
a directional value that is perpendicular to the triangle surface.
From this information and the color of the surface at that point,
the OpenGL lighting commands determine how much light will strike the surface
and what color the triangel will be. Look closely at the computer code that
calculates the normals as well as the description in your text to learn
more about normal vectors and lighting as well as the following page on
Normal Vectors and other 3-D Graphics Details.
It is important to note that the normals must be
calculated in the proper sequence because they are directional. Ones that
point in the direction of the light source will receive light whereas
those that point away will be in shadow. If all of the vectors of a
surface are not calculated in the same way, some triangles will be colored
yet others will be appear dark because they are in the shade. This
can cause strangely colored surfaces!
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Using the basic format of the surface program above, the following example replaces two routines in order to generate a more interesting surface. It essentially tries to overlay the graphic of the azalea image on top of an embossed or raised surface that also relates to the same picture. Look at how the two algorithms are used to create an interesting effect:
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Determing the Altitude To generate the altitude, I used a combination of the black and white silhouette algorithm used preveiosly along with the sine wave function described in the surface program given on this page. Essentially, wherever the picture was white, a wavy surface ranging from -2 to + 2 was used. Where the picture was colored in the region of the azalea plant and flower, the altitude was set at a uniform 20 units high. |
 Black and White |
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Determining the Color To determine the color of the surface, the RGB values in the original picture were used. One thing to note is that the pixel values in a PPM image are given in RGB format as integers whereas the OpenGL command expects color values to be expressed as floats. Good programmers should be able to make the conversion easily. |
 Original Picture |
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