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Like polylines, splines have their own editing command. To understand how to edit splines, you need to understand how AutoCAD stores them. When you pick points to create the spline, AutoCAD stores these points as fit points (or data points). If the tolerance is zero, the curve lies on these fit points. When you select a spline at the command line, grips appear at these fit points. However, when you use the SPLINEDIT command, to see the fit points as grips, you must choose the Fit Data option first. Only then can you edit the fit points. AutoCAD calculates control points based on the fit points. The spline is then calculated based on the control points, not the fit points. Most of the control points are not on the spline. When you use SPLINEDIT to edit a spline, and use the Move vertex option described later, AutoCAD displays the control points as grips, and you can move the control points. Figure 16-8 shows a spline created using point objects as the fit points these were the points picked when creating the spline. Note that the spline passes through each fit point.

Theorem 9.2 indicates a particular case of the theorem above where l 1. The number of bytes in the vectors X and Y, where Xi and Yi are i-th bytes of X and Y, respectively, that satisfy dH Xi ; Yi ! e 1, can be expressed as

Figure 16-8: The point objects were used as the pick points. These are the fit points of the spline.

The output of the code when the trace setting is set to 4 is as follows:

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As the value of e becomes equal to b, the value above rapidly becomes small, and therefore the error locating codes rapidly become equal to the error correcting codes. So we have the following theorem on the relation between the error locating codes and the error detecting codes. Theorem 9.24 If byte length is equal to code length, an error locating code is an error detecting code. Proof By Theorems 9.21 and 9.22, the conditions of the le=b EL codes and the me=b ED codes are expressed as ge X; Y 0 and gb X; Y ! 1, respectively. If there exists only 1 e 1 one byte in the codeword, it is apparent that these conditions are equivalent, and therefore an error locating code is an error detecting code. Q.E.D.

Figure 16-9 shows the same spline as in Figure 16-8 as it appears when selected with no command active. Notice that the grips are exactly on the fit points. Because AutoCAD calculates the spline based on the control points, it doesn t need the fit points to generate the spline. In fact, if you use the Move vertex or Refine options to move or edit a control point, AutoCAD now has to use only the control points to generate the spline and discards the fit point information so that you can no longer edit it. The Fit Data option also disappears from the prompt. You can edit the fit points using grips, as shown in Figure 16-10.

This This This This is is is is the the the the Verbose Trace = 4 Info Trace = 3 Warning Trace = 2 Error Trace = 1

EXERCISES 9.1 9.2 Derive the bound expressed in (9.1). Let CD be a binary (5, 1) quadruple-bit error detecting code generated by the polynomial g x x4 x3 x2 x 1, and let Cc be a (7, 5) single-symbol error correcting code over the eld generated by the polynomial g x . Design the H matrix of the (35, 27) S4=5 EL code using the tensor product of the H matrices of the CD and Cc codes. Prove Theorem 9.2. Prove that the SEC-Sb=p b EL code of design method I can locate an erroneous block that includes single b-bit burst error. Design the H matrix of the SEC-S2=3 2 EL code of design method I with R 6 bits. Prove Lemma 9.1. Obtain the eight nonsingular odd-weight 4 4 square matrices.

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