Figure 8-9: A 2D rectangle in .NET

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Figure 8-9: A 2D rectangle
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Moving from two dimensions to three dimensions requires two points of reference: a viewer and an object. The following code shows a cube in a threedimensional environment clipped within a viewing window. In this case, the size() command creates a clipped window view into a 3D world (grey area in Figure 8-10) which is accomplished by using a library called P3D (i.e., the third parameter of size()). The camera() command defines the viewer s position by taking nine parameters: the xyz location of the viewer s eye, the xyz location of the point towards viewing, and a vector representing the direction of the axis perpendicular to the ground. The box() command constructs a cube positioned at the center of the camera s view.
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size(200,200,P3D); camera(100,100,-100,0,0,0,0,0,1); box(50);
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Figure 8-10: A 3D cube
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The camera offers a fixed point of view. In this case, it is stationed at location 100,100,-100. In order to rotate the camera and offer an interactive view of the scene, we can replace the x an y parameters of the camera s position with the mouse s x and y position. In addition, we need to redraw the screen, using the draw() loop, while continuously repainting the background:
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void setup(){ size(100,100,P3D); } void draw(){ background(200); camera(mouseX,mouseY,-100,0,0,0,0,0,1); box(50); }
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The result is shown in Figure 8-11.
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Figure 8-11: A 3D cube that can be rotated in space
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To transform the location, rotation, and size of an object we can use the
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translate(), rotateX(), rotate(), rotateZ(), and scale() commands. Note that these should be enclosed between the pushMatrix() and popMatrix()
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commands. A matrix is a mathematical table by which each xyz coordinate of each point in a 3D scene is operated upon. In essence, the original matrix, the one we start with before a transformation is applied, is modified after each transformation. In order to avoid a propagating effect, whereby each transformation is affecting the next one, we need to reset the matrix to the original form, using the pushMatrix() / popMatrix() sequence. For example, a series of transformations on two box() objects may look as follows:
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size(100,100, P3D); camera(-100,100,-100,0,0,0,0,0,1); for(int x=0; x<3; x++){ pushMatrix(); translate(x*60, 0, 0); box(40); popMatrix(); }
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The result will be three cubes of a length of 40 units positioned every 60 units apart, as shown in Figure 8-12.
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Figure 8-12: Three cubes aligned
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The problem with the Processing/P3D representation mentioned above is that, while objects do appear in the scene, they are not identifiable. For instance, suppose that one object is to be selected after it is created. This is not possible with the current code. There is no reference or memory of any drawn object in the scene. They are simply displayed on the screen. In order to establish an identity for each object in the scene, we need to create classes of 3D objects that will contain the information about their unique name, position, attributes, and transformations. Thus, we will construct a class called MyObject that will illustrate a partial solution to this problem.
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1 2 3 4 5 class MyObject{ float dim = 40; float x,y,z; boolean picked = false; color c_face = color(255); //size of the object //position coordinates //picked status //color of object
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//determine whether an object is picked void pick(float xp, float yp){ //is the distance enough to pick if(dist(xp,yp,screenX(x,y,z),screenY(x,y,z))<dim) picked = true; else picked = false; } void draw3(){ if(picked==true) fill(255,0,0); else fill(c_face); box(dim); } } MyObject b = new MyObject(); //create an object void setup(){ size(500,500, P3D); //setup the screen camera(-100,100,-100,0,0,0,0,0,1); //get a viewpoint } void draw(){ b.draw3(); //draw the object } void mousePressed(){ b.pick(mouseX,mouseY); //see if the mouse can pick }