4.2 Cylindrical
/ Polar Coordinate Generation
Note Variable Default Description
(1) N [0] Node
number 
1 and 
NUMNP
(2) NUMGP [0] Number
of generation points 0
= 0, no generation
> 0, generate data
(3) R(N) [0.0] R-coordinate of node N
(N) [0.0] 
-coordinate of node N (in degrees)
Z(N) [0.0] Z-coordinate of node N
Notes/
(1) The coordinates of each node must be
defined, but need not be read in order.
If the coordinates of node N are input and/or generated more than one
time, the last values take priority. Terminate with a blank record.
(2) If NUMGP is greater than zero, this record initiates an isoparametric data generation sequence. Records 2 to NUMGP of the sequence define the coordinates of the additional generation points (see Section 4.2.2). The final record of the sequence defines the nodal increment information (See Section 4.2.3). After the generation sequence is completed, additional nodal coordinate records, or generation sequences, may follow.
(3) The coordinates of node N are first computed as:
x(1,
N) = r cos 
x(2,
N) = r sin
x(3, N) = z
in the set of axes defined by the reference direction vectors: [n1, n2, n3]. The coordinates are thereafter referred to the global coordinate axes via the following rotation and translation:
x = x0 + R . x
where R = [n1, n2, n3].
A. Generation Along a
Line
The line may be defined by 2, or 3 generation points (see Figure 4.1.1), and the physical space may be 1, 2, or 3 dimensional.
In the case NUMGP = 2, linear interpolation takes place
resulting in equally spaced nodal points along a line in the {r, , z} space.
In the case NUMGP = 3, quadratic interpolation is employed and graded nodal spacing along a line may be achieved by placing the third generation point (J = 3) off center. The spacing in this case may be determined from the following mapping:
where
is the location of
node number A in 
space (the nodes are
placed at equal intervals in -space); X1g,
X2g and X3g are the coordinates of the three
generation points in {r, , z}-space; and XA denotes the coordinates of the Ath node in {r, , z}-space (see Figure 4.1.2).
B. Generation Over a Surface
The surface may be defined by 4, or 8 generation points (see Figure 4.1.3) and the physical space may be 2, or 3 dimensional. In the 3-dimensional case, the surfaces may be curved.
In the case NUMGP = 4, bilinear interpolation is employed, resulting in equally spaced nodal points along generating lines.
In the case NUMGP = 8, biquadratic "serendipity" interpolation is employed and graded nodal spacing may be achieved by placing generation point 5-8 off center. Note that generation points 5-8 do not generally coincide with any nodal points. The spacing of the nodal points may be determined from the serendipity mapping.
C. Generation Over a Volume
The volume is brick shaped and may be defined by 8, or 20 generation points (see Figure 4.1.4). In this case the physical space must be 3-dimensional.
If NUMGP = 8, trilinear interpolation is employed, resulting in equally spaced nodal points along generating lines.
If NUMGP = 20, triquadratic serendipity interpolation is employed and graded nodal spacing may be achieved by placing generation points 9-20 off center. Note that generation points 9-20 do not generally coincide with any nodal points. The spacing of the nodal points may be determined by the serendipity mapping.
4.2.2 Generation Point Coordinate Data (NUMGP-1)
The coordinates of each generation point are defined by a generation point coordinate record. The records must be read in order (J = 2,..., NUMGP) following the nodal coordinate record which initiated the generation sequence (J = 1). A nodal record (see Section 4.2.3), which completes the sequence, must follow the last generation point record.
Note Variable Default Description
M [0] Node number
MGEN [0] Generation parameter
=
0, coordinates of the Jth generation point are input on this
record;
M is ignored
= 1,
coordinates of the Jth
generation point are set equal to
coordinates
of node M which was previously defined;
coordinates
on this record are ignored.
TEMP(R, J) [0.0] R-coordinate of generation point J
TEMP(, J) [0.0] -coordinate of generation point J
TEMP(Z, J) [0.0] Z-coordinate of generation point J
Note Variable Default Description
NINC(1) [0] Number of nodal increments in the R-direction
INC(1) [0] Node number increment in the R-direction
NINC(2) [0] Number of nodal increments in the -direction
INC(2) [0] Node number increment in the -direction
NINC(3) [0] Number of nodal increments in the Z-direction
INC(3) [0] Node number increment in the Z-direction
Notes . .