### Table 2: Run times in milliseconds of the computation of in- terpolating spherical spline curves to approximately 16 digits of accuracy. The first column reports the time needed to compute the control points. The second and third columns report this time plus the time needed to compute 64 and 256 points on the interpolating curve for equally spaced values of t. Algorithm S2 was used to compute the control points, and Algorithm A2 used to compute the points equally spaced on the curve. Algorithm A2 was seeded with good estimates for the successive points (see text).

2001

"... In PAGE 33: ... computes the control points which define a spline curve based on piecewise cubic blending functions which interpolates the control points at the specified values of t. Column 1 of Table2 reports the time required to compute the control points from the interpolated points, using Algorithm S2. The run times of Algorithm S2 are quite satisfactory; however, generally one wishes to not only compute the control points, but also to compute points along the curve.... In PAGE 33: ... The runtimes of Algorithms A1 and A2 are only one order of magnitude less the run time of Algorithm S2, so the time to calculate a large number of points along the curve dominates the time needed to calculate the control points. Therefore, we report in Table2 , the total time needed to compute control points and to compute a reasonably large number of points along the curve. The points along the curve were computed using the faster Algorithm A2: we used the previous two points on the curve to make a linear prediction of the next point on the curve, which was used as the initial value q0 in A2.... ..."

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### Table 2: Run times in milliseconds of the computation of in- terpolating spherical spline curves to approximately 16 digits of accuracy. The flrst column reports the time needed to compute the control points. The second and third columns report this time plus the time needed to compute 64 and 256 points on the interpolating curve for equally spaced values of t. Algorithm S2 was used to compute the control points, and Algorithm A2 used to compute the points equally spaced on the curve. Algorithm A2 was seeded with good estimates for the successive points (see text).

2001

"... In PAGE 33: ... computes the control points which deflne a spline curve based on piecewise cubic blending functions which interpolates the control points at the specifled values of t. Column 1 of Table2 reports the time required to compute the control points from the interpolated points, using Algorithm S2. The run times of Algorithm S2 are quite satisfactory; however, generally one wishes to not only compute the control points, but also to compute points along the curve.... In PAGE 33: ... The runtimes of Algorithms A1 and A2 are only one order of magnitude less the run time of Algorithm S2, so the time to calculate a large number of points along the curve dominates the time needed to calculate the control points. Therefore, we report in Table2 , the total time needed to compute control points and to compute a reasonably large number of points along the curve. The points along the curve were computed using the faster Algorithm A2: we used the previous two points on the curve to make a linear prediction of the next point on the curve, which was used as the initial value q0 in A2.... ..."

Cited by 32

### Table 2: Computation time and number of nodes of 10 di erent runs using the cubic spline repre- sentation (4 control points) in the example of Figure 7. the energy function. Indeed, for both distance and energy computations the position of several points and derivatives have to be computed along the curve. In the case of B ezier curves, these values depend on all the control points whereas in the case of splines, they depend on fewer control elements (2 control points and 2 control vectors- note that splines are a local representation). As the energy function and the distance function are called very often, the more expensive computations in the B ezier case a ect the total computation time. To verify this claim, we performed 200 random generations of deformations for each representation. Each deformation was then minimized and tested for the elasticity constraints. Most calls of the energy function occur during the energy minimization. For the splines, the total running time of the above experiment was 131 sec versus

### Table 3 Results obtained in the optimisation of the can- tilever beam constructed by spline curves.

"... In PAGE 9: ... the search point for the ES x = {d0, d1, d2, d3} contains the dimensions for the control points locations. Table3 presents the results obtained for the objective function (8) parameters. In this case the value used for the objective function weights remained equal as in the shape optimisation case (6.... ..."

### Table 1. Control points of the spine curve of the original pipe surface in the example shown in Figure 9.

"... In PAGE 6: ... 4. Experimental Results The original pipe surface BB4D7BN D8B5 of the example shown in Figure 9 is generated with a radius of 1, and a cubic B- spline spine curve with a knot vector (0, 0, 0, 0, 1, 2, 3, 3, 3, 3) and the six control points shown in Table1 . We take 2000 random sample points from BB4D7BN D8B5B7AFB4D7BN D8B5, where AFB4D7BN D8B5 is a perturbation surface that has any random value between A0BCBMBD and BCBMBD for each sample point.... ..."

Cited by 1

### Table 1. Timing comparison of wavelet and reverse-subdivision multiresolution methods for curves of different sizes using cubic B-spline schemes. Both the global and local implementations of Samavati and Bartels11,10 achieve significantly faster times than Finkelstein and Salesin.19

2004

"... In PAGE 18: ... While both approaches have linear-time algo- rithms for decomposition and reconstruction, in practice the reverse subdivision approach is much faster. Table1 shows the average result of several timing runs for a full decomposition and reconstruction of curves with 35, 8195, and 32771 points. We find the global method to be almost six times faster and the local method almost nine times faster.... ..."

Cited by 2

### Table 3-1. Sensor Curves

"... In PAGE 24: ...03% vs. Chromel Type E Type K Type T User Curves or Precision Calibration Option (See Table3 -1) ... In PAGE 30: ... To determine the currently selected curve, press Curve. The default curve for the Model 330-11 is Curve 10 (see Table3 -1). The display tot the right shows both the Channel A and B Sensor using Curve 02 - the default setting for a Model 330-11 with two Silicon Diode Sensors.... In PAGE 30: ... Curves 11-31 are user-defined curves or Precision Option Calibrations. See Table3 -1. To change the curve, while pressing the Curve key, press the s key to increment the Channel A Curve number, or the t key to increment the Channel B Curve number.... In PAGE 34: ... The setpoint is limited in temperature to the range of the curve used for control. Table3 -1 gives these limitations in kelvin for curves 00 through 04 and 06 thru 10. The Control key quickly returns the bottom from displaying the setpoint to the Control sensor reading.... In PAGE 61: ... Input: ACUR XX Returned: Nothing Remarks: Enter integer from 0 through 31 for Channel A. Table3 -1 lists sensor curve numbers. ACUR? Curve Number for Channel A Query.... In PAGE 61: ... Input: ACUR? Returned: XX (an integer from 00 to 31) Remarks: Returns the currently selected sensor curve number for Channel A. Table3 -1 lists sensor curve numbers. ATYPE? Channel A Input Type Query.... In PAGE 61: ... Input: BCUR XX Returned: Nothing Remarks: Enter an integer from 0 through 31 for Channel B. Table3 -1 lists sensor curve numbers. ... In PAGE 62: ... Input: BCUR? Returned: XX (an integer from 00 to 31) Remarks: Returns the currently selected sensor curve number for Channel B. Table3 -1 lists sensor curve numbers. BTYPE? Channel B Input Type Query.... ..."

### Table 4: Errors of the spline approximations in Figure 4.

1994

"... In PAGE 15: ... By comparing the results visually, we note an improvement compared with the control point transformation method presented in [10]. Table4 lists the number of sample points of each curve, the number of control points used in each spline, the approximation errors, and the number of iterations for the optimization process to converge.... ..."

Cited by 7

### Table 4: Errors of the spline approximations in Figure 4.

"... In PAGE 15: ... By comparing the results visually,we note an improvement compared with the control point transformation method presented in [10]. Table4 lists the number of sample points of each curve, the number of control points used in each spline, the approximation errors, and the number of iterations for the optimization process to converge.... ..."