Two methods to create surface grids by interpolation are available:
-
- Creation of a surface by rotating a point distributions,
- Creation of a surface by translating a point distributions.
Creating a surface by rotatory interpolation
This method uses three point distributions to interpolate
a surface. These distributions have to be arranged to form
the top, side, and bottom section of the body.
Figure 1: Basic objects used for the interpolation.
The process creates an algebraic surface grid, whose points
in circumferential direction are distributed along lines
of Theta = const..
The values of the angle Theta are determined by dividing
a half circle in segments relative to a fourth point
distribution.
Usage:
- Select top section (point distribution),
- Select side section (point distribution),
- Select bottom section (point distribution) and
- Select relative distribution of angular steps (point distribution).
The first three point distributions must have the same number
of points, of course.
The fourth distribution is mapped on a semi-circle to
derive the true angular positions of the longitudinal grid lines.
Result:
Script process and parameter:
Figure 2: Resulting interpolated body.
By selecting the appropriate direction it is possible to rotate
create both sides of a body by using one side line only.
Remarks:
The axis of rotation is calculated from the intersection
of the planes, which are defined using the top and side sections.
If top and bottom sections have no curvature, the vertical
plane is constructed by a triangle connecting the top
section with one point on the bottom section.
Similar steps are neccessary if top and bottom sections
are colinear. There are cases which cannot be handled
by the current implementation. They will be added
on request.
By selecting the appropriate direction it is possible to rotate
create both sides of a body by using one side line only.
The algorithm is taken from:
Ronzheimer, Arno: `Erweiterung
eines Euler-Verfahrens zur Strömungsberechnung um
dreidimensionale Gondeln mit hohen Bypass-Verhältnissen',
IB 129-89/42, DLR Institut für Entwurfsaerodynamik, 1998.
Usage:
- Select entity (top point distr.)
- Select entity (bottom point distr.)
- Select entity (side point distr.)
- Select entity (point distr.)
Result:
Script process and parameter:
This function creates an interpolatory surface by translating
a point distribution along a path.
This section varies between the given start shape
and an end shape while sweeping along the path.
The path itself is defined by two guides,
point distributions which connect to the endpoints of the sections.
Thus the endpoints
of all point distributions must connect to their neighbours and form
a quadrilateral.
Figure 3: Basic objects used for the interpolation.
Hint:
To simplify the creation of straight guides, it is not
necessary to specify them.
The selection of the start shape and the end shape, plus two
arbitrary point distributions, which define the number of cells
and their relative distribution is sufficient.
The same technique is necessary, if the guides would have a length
of zero, e.g. when building a wing tip from two semi airfoil sections,
one vertical part at the end of the wing surface and a segment in
the wing plane, connecting to the vertical section.
Figure 4: Interpolation without guides.
Usage:
- Select entity with point distr. (start section)
- Select entity with point distr. (end section)
- Select entity with point distr (guide line or step distr.)
- Select entity with point distr (guide line or step distr.)
Result:
Script process and parameter: interpol_translate1
- Index of entity (start section)
- Index of entity (end section)
- Index of entity (guide line or step distr.)
- Index of entity (guide line or step distr.)
{Build by Martin Hepperle}
{Rebuild 845: Saturday, 31, 1997 at 11:46:32, March, by Olaf Brodersen}