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Drawing geodesic lines

First, as we mentioned in the section of the process, we set points on the perimeter that will serve as the ends of the geodesic lines.
For this example, we will use the same decagonal membrane that we have generated in the section on geodesic lines.

Trazad6First, we will draw the first geodesic line between two high points of the membrane. During form finding, we have chosen perimeter of a regular decagon. We created a triangular regular mesh inside, but as the mesh was not centered with the perimeter, the cut in the mesh is not symmetrical. This does not have much importance in general, but if we manage this membrane we realize that it is not symmetrical.

For example, we can observe that there are four bars between high point 115 and its adjacent fixed point 109 while on the other side, there are only three between point 115 and 110. As we want to generate two patterns on each side, in strips delimited by nodes 1,7,110,115 and 1,6,109,115, the first thing we will do is to divide the bars 111-113, 3-5 into two. We will thus have ends to generate a geodesic line that is in the midst of the 7-110 and 6-109.

We can divide a bar into two in two ways:

  1. using auxiliary by the menu Auxiliary | New and then select line option and use 2 segments, using knots 111 and 133 on one side and 3 and 5 on the other.
  2. by directly dividing bars into two parts using the menu Bars| Divide bars. With this method, we alter the structure, but as we are in the stage of pattern design, it does not have much importance. It is better to save this in a different file.

geodesics-createThen, using the menu Geodesics | Create geodesic will get the selection tool (finger). Mark an end node first and then the other (an extensible red line helps us in this work).

The program will then ask us the number of segments in the geodesic line or length of the segments. For short geodesic, it is better to set the number of segments if we do not have a geodesic with very few points. In the most cases it is better to set the length of the segment, as this way we will have a long geodesic with the many points and short geodetic with less, but all segments will be similar.

Trazad7The number should depend on the geodesic curvature (the more curved, the more segments) and the same length (the longer, the more segments). In addition, the experience will see that it is desirable that the number of segments of a geodesic is based on the number of segments of the adjacent geodesic with that is to make the pattern. It is not completely necessary, but it facilitates the work.

The image on the left shows 5 geodesic lines we have drawn. At first glance we already see the patterns on sides are wider than the central. This means that the selection of the end points of lines 2 and 4 has not been the most appropriate. We should delete this lines, choose new end nodes and draw them again.

To choose new end nodes, we must not forget the ease of the menu Auxiliary | New. It allows us to pick Point option to create auxiliary points on any anywhere of the perimeter. Then we try the two geodesic lines missing for the pattern and the rest that fits on each side.

Once all the geodesic lines are plotted and satisfied with the distribution of the pattern, we pass to the phase of Triangularization.

If we want to eliminate any geodesic line which we created, we go to the menu Geodesics | Delete by numbers to delete them. The program will ask us which lines we want to delete, or we can use comma script code.