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As indicated, this RegularPolygon has the responsibility of returning what is needed to draw that regular polygon using OpenGL: vertices. First we need a mechanism to define what this shape is and where it is in the geometry. For a regular polygon, there may be a number of ways of doing this. In our approach, we have defined the regular polygon using the number of sides and the distance from the center of the regular polygon to one of its vertices. We called this distance the radius, because the vertices of a regular polygon fall on the perimeter of a circle whose center is also the center of the regular polygon. So the radius of such a circle and the number of sides will tell us the polygon we want. By specifying the coordinates of the center we also know where to draw the polygon in our geometry. The responsibility of this RegularPolygon class is to give us the coordinates of all the vertices of the polygon given its center and radius. Again, there may be a number of ways of doing this. Whatever mathematical method you choose to employ (based on middle school or high school math), in the end, as long as you return the vertices, you are good to go. Here is the approach we have used. We started with the assumption that the radius is 1 unit. We figured out the angles for each line connecting the center to each vertex of the polygon. We kept these angles in an array. For each angle we calculated the x-axis

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projection and called this the x multiplier array . (We used multiplier array because we started out with a unit of radius.) When we know the real radius we will multiply these values with the real radius to get the real x coordinate. These real x coordinates are then stored in an array called x array . We do the same for the y-axis projections. Now that you have an idea of what needs to happen in the implementation of the RegularPolygon, we ll give you the source code that addresses these responsibilities. Listing 10 24 shows all the code for the RegularPolygon in one place. (Please note that the source code is a few pages long.) To make the process of going through it less cumbersome, we have highlighted the function names and provided inline comments at the beginning of each function. We define the key functions in a list which follows Listing 10 24. The important thing here is to figure out the vertices and return. If this is too cryptic, it shouldn t be hard to write your own code to get the vertices. You will also note that this code also has functions that deal with texturing. We ll explain these texture functions in the Working with Textures section.

Figure 2-2. Installing ADT using the Software Updates feature in Eclipse Eclipse will then download ADT and install it. You ll need to restart Eclipse for the new plug-in to show up in the IDE. The final step to get ADT functional is to point it to the Android SDK. Select the Window menu and choose Preferences. In the Preferences dialog box, select the Android node and set the SDK Location field to the path of the Android SDK (see Figure 2-3). Then click the OK button. Note that you might see a dialog box asking if you want to send usage statistics to Google concerning the Android SDK.

Listing 10 24. Implementing a RegularPolygon Shape public class RegularPolygon { //Space to hold (x,y,z) of the center: cx,cy,cz //and the radius "r" private float cx, cy, cz, r; private int sides; //coordinate array: (x,y) vertex points private float[] xarray = null; private float[] yarray = null; //texture arrray: (x,y) also called (s,t) points //where the figure is going to be mapped to a texture bitmap private float[] sarray = null; private float[] tarray = null; //********************************************** // Constructor //********************************************** public RegularPolygon(float incx, float incy, float incz, // (x,y,z) center float inr, // radius int insides) // number of sides { cx = incx; cy = incy; cz = incz; r = inr; sides = insides; //allocate memory for the arrays xarray = new float[sides]; yarray = new float[sides]; //allocate memory for texture point arrays

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