An Explicit Example

 

Additional to the Time-Object data for task, frame and parameter the Explicit description files with extension *.ex contain information about the domain of the surface and the explicit formulas for the surface.

By default a rectangular domain [umin, umax] [vmin, vmax] with a basic grid of ulines points in the u-direction and vlines points in the v-direction is used for Explicit surfaces:

# domain triangulation: u- and v-lines, sub-points
ulines; vlines; usub; vsub;

# domain size: umin / vmin / umax / vmax
umin; vmin; umax; vmax;

The domain is time-dependent, i.e. the variable t can be used for umin, vmin, umax and vmax.

The sub-points allow to refine the grid of the ulines vlines points. usub/vsub additional points are inserted between each two neighbours of the ulines/vlines points, therefore the total number of points in the u-direction is .

Of course you can also create a finer grid without using usub/vsub by just increasing ulines/vlines. Using sub-points only makes sense in connection with parameter lines which are computed by "assign-cons-send" (see 7.4.5.6). The parameter lines are only computed for the basic ulines vlines grid therefore distinguishing between points and sub-points makes it possible to compute the surface on a finer grid than the one used for the parameter lines.

After reading in a description file you will find in the option menu additional to the parameter and domain min/max rulers two rulers controlling the distribution of the points in u- and v-direction. These point distributions can't be defined in the description file but of course they can be edited interactively and then saved, the next time the description file is read the saved splines are found and read automatically.

With the following example description file you can compute the logo of the SFB 256, the Henneberg surface, which can be found on all publications of the SFB, for example on the title page of the printed GRAPE manual and on the GRAPE home page http://www-sfb256.iam.uni-bonn.de/grape/main.html:

#
# GRAPE Logo: The Henneberg Surface
#

# task
GEOMETRY;

# frame / number of frames
0; 1;

# no parameter
0; 0;

# part / number of parts
1; 1;

# flag (unused)
0;

# domain triangulation: u- and v-lines, sub-points
11; 80; 0; 0;

# domain size: umin / vmin / umax / vmax
pi/5.0; 0.0; 2.0*pi/5.0; 2.0*pi;

# coordinate functions
-1.0 + cosh(2.0 * x) * cos(2.0 * y);
-sinh(x) * sin(y) - sinh(3.0 * x) * sin(3.0 * y) / 3.0;
-sinh(x) * cos(y) + sinh(3.0 * x) * cos(3.0 * y) / 3.0;

Since currently only one part (surface patch) is supported the part numbers always have to be set to one, the flag is not yet used and should be set to zero.

For the three coordinate functions the (time-dependent) double variables and the time t can be used (refer to section 8.2.2.1 for naming conventions), the points in the domain are referenced with (x, y).