Solid Geometry in .NET

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will need; that is, the number of points of the base plus 2 (an extruded object has a bottom face, a top face and, as side faces, as many as the number of points).
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faces = new MyFace[inPoints.length + 2];
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Next, you create the bottom face, which is formed by whatever points are in the input base:
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faces[0] = new MyFace(inPoints);
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Then you do the same thing for the top, except you move it by height units in the z direction:
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faces[1] = new MyFace(inPoints); faces[1].setMove(0., 0., height);
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You also increment the numFaces as you add more faces:
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numFaces++;
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Finally, you need to construct the side faces. Thus, you loop for the number of incoming point minus one, and for each loop you collect: 1. The current point of the bottom face 2. The next point of the bottom face 3. The next point of the top face 4. The current point of the top face Put these four points in a MyPoint[] array called side[], which you use to construct the side face.
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MyPoint[] side; side = new MyPoint[4]; for(int i=0; i<inPoints.length-1; i++){ side[0] = new MyPoint(faces[0].points[i].x,faces[0].points[i].y, faces[0].points[i].z ); side[1] = new MyPoint(faces[0].points[i+1].x, faces[0].points[i+1].y, faces[0].points[i+1].z ); side[2] = new MyPoint(faces[1].points[i+1].x, faces[1].points[i+1].y, faces[1].points[i+1].z ); side[3] = new MyPoint(faces[1].points[i].x, faces[1].points[i].y, faces[1].points[i].z ); faces[numFaces] = new MyFace(side); numFaces++; }
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Figure 9-4 illustrates the position of the points and faces for a hexagon:
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If i = 1 3 i+1 2 3 i+1 2 1 1 1 1 4 0 0 4 5 5 faces[0] faces[1] 1 1 2 If i = 2 i+1 3 i+1 3 1 1 4 4 0 0 5 5 faces[0] faces[1]
Figure 9-4: Sequence of point in an extruded solid
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These loops take care of the inPoints.length-1 sides, that is, n 1, where n is the number of points. You cannot construct the last face because i + 1 will take you out of the boundaries of the array when i = inPoints.length. So, you construct the first n 1 side-face and, then, construct the last side face, which is:
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int last = inPoints.length-1; side[0] = new MyPoint(faces[0].points[last].x,faces[0]. points[last].y, faces[0].points[last].z ); side[1] = new MyPoint(faces[0].points[0].x, faces[0].points[0].y, faces[0].points[0].z ); side[2] = new MyPoint(faces[1].points[0].x, faces[1].points[0].y, faces[1].points[0].z ); side[3] = new MyPoint(faces[1].points[last].x,faces[1]. points[last].y, faces[1].points[last].z ); faces[numFaces] = new MyFace(side); numFaces++;
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void draw(Graphics g){ for(int i=0; i<numFaces; i++) faces[i].draw(g); }
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The standard transformations can be invoked using their inheriting methods
move(), scale(), and rotate():
void setRotatex ( float angle) { for(int i=0; i<numFaces; i++) faces[i].setRotatex(angle); }
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void setRotatey ( float angle) { for(int i=0; i<numFaces; i++) faces[i].setRotatey(angle); } void setRotatez ( float angle) { for(int i=0; i<numFaces; i++) faces[i].setRotatez(angle); }
Solid Geometry
void setScale( float xs, float ys, float zs){ for(int i=0; i<numFaces; i++) faces[i].setScale(xs, ys, zs); } void setMove( float xoff, float yoff, float zoff){ for(int i=0; i<numFaces; i++) faces[i].setMove(xoff, yoff, zoff); }
In the main code, you create an array of points that functions as the profile polyline to be extruded. This array (i.e., points[]) is passed to the constructor new MySolid(points, 20.) together with a float that indicates the height to be extruded (i.e., 20.). The solid object can be drawn using the draw() method that is also passing down to the face s method draw().
MyPoint [] points; MySolid solid; void setup(){ size(200, 200, P3D); noFill(); camera(70.0, 35.0, 120.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0); points = new MyPoint[4]; points[0] = new MyPoint( 50, 50, 0); points[1] = new MyPoint(-50, 50, 0); points[2] = new MyPoint(-50, -50, 0); points[3] = new MyPoint( 50, -50, 0); solid = new MySolid(points, 20.); } int xf, yf; void draw(){ background(255); solid.rotatex((mouseX - xf) * PI/180.,origin); solid.rotatey((mouseY - yf) * PI/180.,origin); solid.draw(); xf = mouseX; yf = mouseY; }
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Solid Geometry
The output is shown in Figure 9-5.
Figure 9-5: Six planar polygon in the formation of a cube (wireframe)
You may notice that the faces do not appear in the right order. In fact, when paint() draws the faces, it fills a polygon in the index order 0, 1, 2, 3, 4, 5, and so forth. But faces[0] is the bottom, faces[1] is the top and the rest are side faces. This order from the furthest away to the closest is not the order they should be painted. The solution to this problem is to either paint them in the right order or find a way to omit the faces that are hidden, that is, the faces in the back. This is discussed in the following section.