PRODUCT SPECIFICATION
TMC2302A
19
P
FOV is the 16-bit field-of-view parameter, normally set so
that the spiral walk proceeds in single-pixel steps. FOV can
be increased to expand the step size and thus the spiral walk,
subsampling the image. See Table 1 and Table 6. Also,
CAX(ca) is the current value of the coefficient address. See
the Interpolation Coefficient Lookup Table Addressing. If
the spiral walk isn’t used, CAX = 0 and FOV is ignored.
We can reform the two-dimensional polynomial as:
x(u,v) = (a + ev + iv
2
+ mv
3
) + (b + fv + jv
2
+ nv
3
)u
+ (c + gv + kv
2
+ ov
3
)u
2
+ (d + hv + Iv
2
+ pv
3
)u
3
,
and retain the simpler three-dimensional form:
x(u, v, w) = a + bu + ev + kw + fuv + ivw + luw + juvw
and define each of the polynomial coefficients in arithmetic
terms as shown in Table 5.
Table 5. Transformation Polynomial Coefficients
Parameter
Two-Dimensional
Three-Dimensional
Term
X
0
DXU
—
—
DXV
DXUV
X
0
DXU
DXVW
DXUVW
DXW
DXUW
—
—
—
—
Name
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Term
Coefficient
Coefficient
a
b
0
0
e
f
a
b
i
j
k
I
0
0
0
0
X
0
DXU
DXUU
DXUUU
DXV
DXUV
DXUUV
DXUUUV
DXVV
DXUVV
DXUUVV
DXUUUVV
DXVVV
DXUVVV
DXUUVVV
DXUUUVVV
a
b + c + d
2c + 6d
6d
e + i + m
f + g + h + j + k + I + n + o + p
2(g + k + o) + 6(h + I +p)
6(h + I + p)
2i + 6m
2(j + k + I) + 6(n + o + p)
4k + 12I + 12o + 36p
12I + 36p
6m
6(n + o + p)
12o + 36p
36p
Understanding the Polynomial
Coefficients
An Overview
As the formulae indicate, the source address is a polynomial
function of the two (or three) dimensions of the target
address. Each of the 16 terms of the equation is of the form:
and may be treated approximately as a mixed partial
difference of order m, n, and p.
m
du
dv
dw
p
n
p
+
+
x
-------------------------------
The simplest term, X
0
, is a zeroeth (non-) function of the
target addresses; it specifies the source address point corre-
sponding to the upper left point in the target space. X
0
generates image translation or “pan.”
The next-simplest terms, dX/dU and dY/dV, govern the rela-
tive scales of the source and target images, i.e., how large a
step in source space corresponds to a unit step in the corre-
sponding direction in the target space. As long as the cross-
terms, dX/dV and dY/dU, are zero, this is a straight scale
(“zoom”) operation, without rotation or shear.