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qr code vb.net open source Distorted Spheres in VS .NET
Distorted Spheres Code39 Decoder In Visual Studio .NET Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in Visual Studio .NET applications. USS Code 39 Generator In .NET Using Barcode encoder for Visual Studio .NET Control to generate, create Code 39 image in .NET applications. Spheres can be made out of the round by increasing or decreasing the axial radii in the x, y, and z directions individually Code 39 Full ASCII Decoder In .NET Framework Using Barcode recognizer for VS .NET Control to read, scan read, scan image in .NET framework applications. Bar Code Creator In VS .NET Using Barcode generation for .NET framework Control to generate, create bar code image in VS .NET applications. Alternative equation for a sphere centered at the origin Once again, consider the general equation of a perfect sphere centered at the origin That equation, in standard form, is Bar Code Decoder In .NET Using Barcode reader for .NET Control to read, scan read, scan image in .NET framework applications. Encoding ANSI/AIM Code 39 In C# Using Barcode encoder for .NET Control to generate, create Code39 image in Visual Studio .NET applications. x2 + y2 + z2 = r2 where r is the radius If we divide through by r2, we get x2/r2 + y2/r2 + z2/r2 = 1 This equation tells us that the radius is always the same, whether we measure it in the direction of the x axis, y axis, or z axis To emphasize the fact that we can, if desired, change any of all of these axial radii, let s rewrite the above equation as x2/a2 + y2/b2 + z2/c2 = 1 where a, b, and c are positive real numbers representing the radii along the x, y, and z axes, respectively In the case of a perfect sphere, we have a=b=c If these three positive realnumber constants a, b, and c are not all the same, then we have a distorted sphere Code 3 Of 9 Encoder In .NET Using Barcode creation for ASP.NET Control to generate, create Code 3 of 9 image in ASP.NET applications. Create Code 39 In VB.NET Using Barcode creator for .NET framework Control to generate, create Code 3/9 image in .NET framework applications. Distorted Spheres
Encode GS1 DataBar Truncated In .NET Using Barcode creator for Visual Studio .NET Control to generate, create DataBar image in .NET framework applications. Print Data Matrix 2d Barcode In .NET Using Barcode generation for VS .NET Control to generate, create DataMatrix image in .NET applications. Oblate sphere centered at the origin Suppose that we take a perfect sphere and then shorten one of the three axial radii This process gives us an object called an oblate sphere It s flattened, like a soft rubber ball when pressed between our hands Figure 175 shows an example This is what we get if we take the sphere from Fig 173 and reduce the axial radius b (the one that goes along the y axis), while leaving the axial radii a and c unchanged The center of the object is still at the origin, but we can no longer say that all the points on its surface are equidistant from the origin The general equation for an oblate sphere centered at the origin is Barcode Encoder In Visual Studio .NET Using Barcode creator for .NET Control to generate, create bar code image in VS .NET applications. Painting Postnet In .NET Using Barcode creator for .NET Control to generate, create Delivery Point Barcode (DPBC) image in Visual Studio .NET applications. x2/a2 + y2/b2 + z2/c2 = 1 where a is the xaxial radius, b is the yaxial radius, c is the zaxial radius, and exactly one of the following relationships holds true among them: a<b=c b<a=c c<a=b Making Barcode In None Using Barcode creator for Software Control to generate, create bar code image in Software applications. Recognize ECC200 In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. Alternative equation for a sphere centered away from the origin Earlier in this chapter, we learned that the general equation of a sphere centered at some point other than the origin in Cartesian xyz space is Scan UPCA In VB.NET Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications. UCC  12 Printer In Java Using Barcode creation for Android Control to generate, create UCC.EAN  128 image in Android applications. (x x0)2 + (y y0)2 + (z z0)2 = r2
Code 39 Drawer In ObjectiveC Using Barcode encoder for iPad Control to generate, create Code 39 image in iPad applications. Read Barcode In .NET Framework Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. Center is at (0, 0, 0) Data Matrix Printer In None Using Barcode creator for Software Control to generate, create Data Matrix ECC200 image in Software applications. Creating 2D Barcode In C#.NET Using Barcode creator for .NET framework Control to generate, create Matrix Barcode image in VS .NET applications. Radius in y direction =b
Radius in z direction =c y
Radius in x direction =a
Figure 175 An oblate sphere in Cartesian xyz space, centered at the origin
Surfaces in ThreeSpace
where r is the radius, and (x0,y0,z0) are the coordinates of the center Dividing through by r2, we obtain (x x0)2/r2 + (y y0)2/r2 + (z z0)2/r2 = 1 As we did with the sphere centered at the origin, we can rewrite this equation, getting (x x0)2/a2 + (y y0)2/b2 + (z z0)2/c2 = 1 where a, b, and c are the radii parallel to the x, y, and z axes, respectively As before, with a perfect sphere, we have a=b=c If a, b, and c are not all the same, then the sphere is distorted Oblate sphere centered away from the origin If we take a sphere that s centered at (x0,y0,z0) and shorten one of the axial radii, we get an oblate sphere defined by the general equation (x x0)2/a2 + (y y0)2/b2 + (z z0)2/c2 = 1 where exactly one of the following is true: a<b=c b<a=c c<a=b Figure 176 should give you a general idea of what happens in a case like this Imagine a sphere centered at (x0,y0,z0) that has been squashed in the direction defined by a line parallel to the y axis Ellipsoid centered at the origin Again, imagine that we have a perfect sphere centered at the origin in Cartesian xyz space Let s lengthen one of the axial radii while leaving the other two unchanged This stretching process produces an ellipsoid It s elongated, like a football with blunted ends Figure 177 shows an example Imagine that we take the sphere from Fig 173 and then stretch it in the z direction The general equation for an ellipsoid centered at the origin is x2/a2 + y2/b2 + z2/c2 = 1 where a is the xaxial radius, b is the yaxial radius, c is the zaxial radius, and exactly one of the following relationships is true: a>b=c b>a=c c>a=b

