Figure 2-14: A polygon in the form of a square constructed through arrays in .NET

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Figure 2-14: A polygon in the form of a square constructed through arrays
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In this example, we used the arrays to fill in the points and then we passed them to the vertex() method. The advantage of this method is that the arrays not only store information that can be reused later but can be changed and modified through the course of the session. However, it would be perhaps better if we could create a general algorithm that would fill the arrays with the necessary coordinates instead of pre-calculating and hard-coding the data. This problem is addressed in the next section.
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2.5 Equilateral Polygons
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In an equilateral polygon, vertex points are distributed along a circle in equal intervals. Earlier in this chapter you learned how to create circles using parametric equations (i.e., involving an angle and a radius). The next step is to create circular polygons, that is, polygons created through arrays that are obtained by distributing points equally on the perimeter of a circle. The following code demonstrates this method with a simple algorithm making use of our knowledge of the sine and cosine:
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 int n = 5; float[] xArray = new float[n]; //allocate memory for 5 points float[] yArray = new float[n]; void setup(){ float angle = 2 * PI / n; //divide the circle in n sections for(int i =0; i< n; i++){ //create points along a circle xArray[i] = 50. + 30. * sin(angle*i); yArray[i] = 50. + 30. * cos(angle*i); } } void draw (){ beginShape(POLYGON); for(int i = 0; i < n; i++) vertex(xArray[i],yArray[i]); endShape(CLOSE); }
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After creating the arrays of size n, you need to fill them with points. To do that, loop for n times and each time the x and y values are assigned. These values are calculated through the following algorithm:
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First, divide a full circle (2*PI) by n sections, which correspond to the number of the equilateral polygon s sides (or the size of the array), and name this ratio angle . Then, store the coordinates of each polygon s vertex in the arrays by using the parametric equation of the circle. Use the stored values in the arrays to draw the polygon vertices.
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The resulting shape is shown in Figure 2-15.
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Figure 2-15: A central polygon implemented for five sides
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2.6 Responsive Polygons
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So far, the polygons that we have been constructing reside on the screen at a specific location, but they are not interactive. In other words, after a point is laid down, there is no way for the system to interact with it in order to rearrange it in another pattern or make it responsive to the user s actions. The following code develops a method of locating the coordinate positions for each point and then using that information to track and reposition them.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 int n = 5; float[] px = new float[n]; float[] py = new float[n]; void setup(){ float angle = 2 * PI / n; //divide the circle in n sect for(int i =0; i< n; i++){ px[i] = 50. + 30. * sin(angle*i); py[i] = 50. + 30. * cos(angle*i); } } void draw (){ background(200); beginShape(POLYGON); for(I nt i = 0; i < n; i++) vertex(px[i],py[i]); endShape(CLOSE); for(int i=0; i<n; i++){ if(dist(mouseX,mouseY,px[i],py[i])<20) stroke(255,0,0); else stroke(0,0,0); rect(px[i],py[i],5,5); } }
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26 27 28 29 30 31 32 33 34
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void mouseDragged(){ for(int i=0; i<n; i++)z if(dist(mouseX,mouseY,px[i],py[i])<20){ px[i] += (mouseX-pmouseX); //push only py[i] += (mouseY-pmouseY); px[i] = constrain(px[i],5,width-5); py[i] = constrain(py[i],5,height-5); } }
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In lines 2 and 3, we create two arrays, px[] and py[], that will store the x and y coordinates of the objects that we will place in the scene. Therefore, we allocate memory for five points here, that is, for as many as the variable n has. In lines 7 to 9, we populate the array with the coordinates of an equilateral polygon (created through the methods we discussed in the previous section). Those numbers are also used to place a rectangle at the end points of the polygon. Notice that we use rectangles instead of points only because they can be bigger and therefore more visible. In the draw() section, we draw these rectangles, but we also check to see whether the mouse is close enough so that we can highlight them as red. This is done in lines 18 through 21. First, we loop through all points and then compute the distance of each point from the mouse s location. If it falls less than a certain predefined tolerance (e.g., 20 pixels here), then we change the stroke color to red; otherwise, it defaults to black. In the mouseDragged() section, we allow the user to interact with the selected (i.e., red) points. This is done in lines 26 to 34. We loop through all points and determine their distance from the mouse. If it falls within the range of 20 pixels, then we add an offset to it. This offset is the difference between the current position of the mouse (mouseX) and its previous position (pmouseX). This difference makes the rectangle move by an offset so that it appears that the mouse is pushing the rectangles. Lines 31 and 32 make sure that the modified points do not exceed the limits of the screen (within a frame of 5 pixels all around the window). Figure 2-16 shows the result.