 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
asp.net barcode reader free Solution in .NET framework
Solution ANSI/AIM Code 39 Scanner In VS .NET Using Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in .NET applications. Making Code39 In .NET Using Barcode drawer for VS .NET Control to generate, create Code 39 Extended image in .NET framework applications. This situation doesn t resemble anything we ve seen so far in Cartesian, polar, or cylindrical coordinates If we hold the vertical angle constant in a spherical coordinate system, we get the set of points formed by a line passing through the origin and rotated with respect to the vertical axis If k is a realnumber constant, then the graph of f=k is a double cone whose axis corresponds to the vertical axis and whose apex is at the origin, as shown in Fig 98 Recognize Code 3/9 In Visual Studio .NET Using Barcode decoder for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications. Creating Bar Code In VS .NET Using Barcode generation for .NET framework Control to generate, create barcode image in Visual Studio .NET applications. Alternative ThreeSpace
Scan Bar Code In Visual Studio .NET Using Barcode decoder for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications. Draw Code 39 In C#.NET Using Barcode generation for .NET framework Control to generate, create Code 39 Full ASCII image in Visual Studio .NET applications. Constant vertical angle
Code 39 Maker In .NET Using Barcode printer for ASP.NET Control to generate, create Code 39 Extended image in ASP.NET applications. Generate Code 3 Of 9 In VB.NET Using Barcode maker for .NET Control to generate, create USS Code 39 image in VS .NET applications. Cone extends upward forever
Creating Code 39 Extended In VS .NET Using Barcode generator for Visual Studio .NET Control to generate, create Code39 image in .NET framework applications. Draw Linear Barcode In .NET Using Barcode generator for .NET framework Control to generate, create Linear 1D Barcode image in .NET framework applications. Reference plane
Bar Code Maker In .NET Framework Using Barcode maker for VS .NET Control to generate, create bar code image in VS .NET applications. Creating Industrial 2 Of 5 In .NET Using Barcode creator for .NET Control to generate, create 2 of 5 Standard image in .NET applications. f = p /4 Create Code 128 Code Set C In Visual Studio .NET Using Barcode drawer for Reporting Service Control to generate, create Code 128C image in Reporting Service applications. Scan Barcode In .NET Using Barcode reader for VS .NET Control to read, scan read, scan image in VS .NET applications. z Cone extends downward forever
UPCA Supplement 5 Recognizer In .NET Framework Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET applications. Data Matrix Encoder In ObjectiveC Using Barcode generation for iPad Control to generate, create Data Matrix 2d barcode image in iPad applications. Figure 98 Create USS Code 128 In Visual Basic .NET Using Barcode maker for VS .NET Control to generate, create Code 128 Code Set A image in VS .NET applications. Bar Code Encoder In None Using Barcode generator for Online Control to generate, create bar code image in Online applications. When we set the vertical angle equal to a constant in spherical coordinates, we get a double cone whose axis corresponds to the vertical axis Paint ECC200 In Java Using Barcode creation for Java Control to generate, create DataMatrix image in Java applications. Matrix 2D Barcode Generation In Java Using Barcode generation for Java Control to generate, create Matrix 2D Barcode image in Java applications. Spherical Conversions
Converting coordinates between xyz space and spherical threespace is a little tricky, but not too difficult Let s think about a point P whose spherical coordinates are (q,f,r) and whose Cartesian coordinates are (x,y,z) Spherical to Cartesian: finding x In spherical coordinates, the radius is usually outside of the reference plane, so we can t use it directly in the same formulas as the cylindrical radius But we can construct a projection radius identical to the cylindrical radius: the distance from the origin to the projection point P in the reference plane In Fig 99, the projection radius is called r From this geometry, we can see that r is equal to the true spherical radius times the sine of the vertical angle As an equation, we have r = r sin f
Spherical Conversions
The x value conversion formula from cylindrical coordinates, which we learned earlier in this chapter, tells us that x = r cos q where q is the horizontal direction angle, which is the same in spherical and cylindrical coordinates Substituting the quantity (r sin f) for r gives us x = r sin f cos q Spherical to Cartesian: finding y When we found the cylindrical equivalent of the Cartesian y value, we took the radius in the reference plane and multiplied by the sine of the direction angle in that plane In the sphericalcoordinate situation of Fig 99, that translates to y = r sin q where q is the horizontal direction angle We can substitute (r sin f) for r to get y = r sin f sin q Spherical to Cartesian: finding z Let s look again at Fig 99, and locate the projection point P on the z axis, such that the z values of P and P are equal We can see that P , P, P , and the origin form the vertices of a +z Reference axis
x P
Reference plane
Figure 99 Conversion between spherical and Cartesian threespace coordinates involves several geometric variables Alternative ThreeSpace
rectangle perpendicular to the reference plane It follows that P , P, and the origin are at the vertices of a right triangle By trigonometry, the z value of P is equal to the spherical radius r times the cosine of the vertical angle f Because the z values of P and P are the same, we can deduce that the z value of P is given by z = r cos f Cartesian to spherical: finding r Now let s figure out how to get from Cartesian xyz space to spherical threespace The radius is the easiest coordinate to find, so let s do it first Recall that the spherical radius of a point is its distance from the origin Therefore, when we want to find the spherical radius r for point P in terms of its xyz space coordinates, we can apply the Cartesian threespace distance formula to get r = (x2 + y2 + z2)1/2 Cartesian to spherical: finding q The horizontal angle in spherical coordinates is identical to its counterpart in cylindrical coordinates, so we can use the conversion table from earlier in this chapter q=0 by default q=0 q = Arctan ( y /x) q = p/2 q = p + Arctan ( y /x) q=p q = p + Arctan ( y /x) q = 3p/2 q = 2p + Arctan ( y /x) When x = 0 and y = 0 that is, at the origin When x > 0 and y = 0 When x > 0 and y > 0 When x = 0 and y > 0 When x < 0 and y > 0 When x < 0 and y = 0 When x < 0 and y < 0 When x = 0 and y < 0 When x > 0 and y < 0 The Arccosine Before we can find the vertical spherical angle for a point that s given to us in Cartesian coordinates, we must be familiar with the arccosine relation It s abbreviated arccos (cos 1 in some texts), and it undoes the work of the cosine function For example, we know that

