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Example 313 14 0 obj << /FunctionType 0 /Domain [ 10 10 10 10] /Size [21 31] /Encode [0 20 0 30] /BitsPerSample 4 /Range [ 10 10] /Decode [ 10 10] /Length /Filter >> stream 651 sample values endstream endobj
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The Decode entry can be used creatively to increase the accuracy of encoded samples corresponding to certain values in the range For example, if the desired range of the function is [ 10 10] and BitsPerSample is 4, the usual value of Decode would be [ 10 10] and the sample values would be integers in the interval [0 15] (as shown in Figure 36) But if these values were used, the midpoint of the range, 00, would not be represented exactly by any sample value, since it would fall halfway between 7 and 8 On the other hand, if the Decode array were [ 10 +11429] (11429 being approximately equal to 16 14) and the sample values supplied were in the interval [0 14], then the desired effective range of [ 10 10] would be achieved, and the range value 00 would be represented by the sample value 7
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/Decode [ 1 1]
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/Decode [ 1 11429]
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FIGURE 36 Mapping with the Decode array
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The Size value for an input dimension can be 1, in which case all input values in that dimension will be mapped to the single allowed value If Size is less than 4, cubic spline interpolation is not possible and Order 3 will be ignored if speci ed
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392 Type 2 (Exponential Interpolation) Functions
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Type 2 functions (PDF 13) include a set of parameters that de ne an exponential interpolation of one input value and n output values: f ( x ) = y0 , , yn 1 In addition to the entries in Table 326 on page 108, a type 2 function dictionary includes those; listed in Table 328 (See implementation note 27 in Appendix H)
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TABLE 328 Additional entries speci c to a type 2 function dictionary
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KEY TYPE VALUE
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C0 C1 N
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(Optional) An array of n numbers de ning the function result when x = 00 (hence the 0 in the name) Default value: [00] (Optional) An array of n numbers de ning the function result when x = 10 (hence the 1 in the name) Default value: [10] (Required) The interpolation exponent Each input value x will return n values, given by yj = C0j + xN (C1j C0j ), for 0 j < n
Values of Domain must constrain x in such a way that if N is not an integer, all values of x must be nonnegative, and if N is negative, no value of x may be zero Typically, Domain will be declared as [00 10], and N will be a positive number The Range attribute is optional and can be used to clip the output to a desired range Note that when N is 1, the function performs a linear interpolation between C0 and C1; this can also be expressed as a sampled function (type 0)
393 Type 3 (Stitching) Functions
Type 3 functions (PDF 13) de ne a stitching of the subdomains of several 1-input functions to produce a single new 1-input function Since the resulting stitching function is a 1-input function, the domain is given by a two-element array, [Domain0 Domain1 ]
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In addition to the entries in Table 326 on page 108, a type 3 function dictionary includes those listed in Table 329 (See implementation note 28 in Appendix H)
TABLE 329 Additional entries speci c to a type 3 function dictionary
KEY TYPE VALUE
Functions
array
(Required) An array of k 1-input functions making up the stitching function The output dimensionality of all functions must be the same, and compatible with the value of Range if Range is present (Required) An array of k 1 numbers that, in combination with Domain, de ne the intervals to which each function from the Functions array applies Bounds elements must be in order of increasing value, and each value must be within the domain de ned by Domain (Required) An array of 2 k numbers that, taken in pairs, map each subset of the domain de ned by Domain and the Bounds array to the domain of the corresponding function