SECTION 3.9
171
Functions
That value is encoded:
e
i
=
Interpolate
(
x
i
′,
Domain
2i
,
Domain
2i
+
1
,
Encode
2i
,
Encode
2i
+
1
)
That value is clipped to the size of the sample table in that dimension:
e
i
′
=
min
(
max
(
e
i
,
0
) ,
Size
i
–
1
)
The encoded input values are real numbers, not restricted to integers.
Interpolation is used to determine output values from the nearest surrounding
values in the sample table. Each output value
r
j
, for 0
≤
j
<
n,
is then decoded:
r
j
′
=
Interpolate
(
r
j
,
0
,
2
BitsPerSample
–
1
,
Decode
2j
,
Decode
2j
+
1
)
Finally, each decoded value is clipped to the range:
y
j
=
min
(
max
(
r
j
′,
Range
2j
) ,
Range
2j
+
1
)
Sample data is represented as a stream of unsigned 8-bit bytes (integers in the
range 0 to 255). The bytes constitute a continuous bit stream, with the high-order
bit of each byte first. Each sample value is represented as a sequence of
BitsPerSample
bits. Successive values are adjacent in the bit stream; there is no
padding at byte boundaries.
For a function with multidimensional input (more than one input variable), the
sample values in the first dimension vary fastest, and the values in the last
dimension vary slowest. For example, for a function
f
(a,
b, c),
where
a, b,
and
c
vary from 0 to 9 in steps of 1, the sample values would appear in this order:
f
(0, 0, 0),
f
(1, 0, 0), … ,
f
(9, 0, 0),
f
(0, 1, 0),
f
(1, 1, 0), … ,
f
(9, 1, 0),
f
(0, 2, 0),
f
(1, 2, 0), … ,
f
(9, 9, 0),
f
(0, 0, 1),
f
(1, 0, 1), and so on.
For a function with multidimensional output (more than one output value), the
values are stored in the same order as
Range
.
The stream data must be long enough to contain the entire sample array, as
indicated by
Size
,
Range
, and
BitsPerSample
; see “Stream Extent” on page 61.
containing 21 columns and 31 rows (651 values). The function takes two
arguments,
x
and
y,
in the domain
[−1.0 1.0 ]
, and returns one value,
z,
in that
same range. The
x
argument is linearly transformed by the encoding to the