This page is a presentation of several rooms tested with the HGVG tracing software. Every trace was performed in a completly enclosed room although some images may show the ceiling or sides of particular rooms removed(Unless otherwise noted). Each room is a set of four images which build greater complexity over the room previous to it. Eventually all the major types of HGVG edges and nodes are displayed and discussed.

The following four images display each of four most basic HGVG edges in a relatively simple environment. Note that accessing is performed in the upper left corner of this room. The first image, 1a, shows just the gvg. Cij edges are included in 2a. Blue dots along the yellow cij edges represent detetected gvg2 nodes, however the gvg2 edges aren't traced untill image 3a. Finally, linking is performed in 4a.
1a	2a	3a	4a

This image displays the adaptive behavior of cij, gvg, and gvg2 edges to slanted surfaces during tracing. Image 4 is a side overlay of all edges to show how they curve in response to the angular floor. This highlights the need for a step and correct behavior to tracing to ensure that the edges each retain equidistance.
1b	2b	3b	4b

The concept of a cycle is introduced in this room, namely a GVG cycle. Note that in images 2 and 3 it is easy to see that linking is performed at every GVG2 meetnode and at every GVG link node. This is a very important design issue. In observing image 2 and 4 one can see that tracing begains directly under a GVG cycle. If branching is not performed at the point where accessing meets the GVG cycle, there is no way to reach the rest of the outside graph. The other GVG link nodes aparent on the cycle are all created from linking performed from the outer graph towards the GVG cycle as the carefull observer will acknowledge.
1c	2c	3c	4c

This room introduces the occluding edge. As seen here, the linking edges run into an occluding edge when they reach the top of bottom of the box. At this point, one of the three objects defining the gvg cycle around the box disappears. The disappearing object is either the ceiling or the floor depending on the link in question.
1d	2d	3d	4d

Notice that as seen in image 3 tracing begins at the orange dot underneath the box. Such a position for starting demonstrates the importance of linking. Close examination reveals that there is no other connection other than linking edges between the occluding edges near the box and the outside gvg cycle, nor between the gvg cycle and outside gvg2 edges. It's important to keep in mind that linking can either ascend or descend a gradient, thus explaining why some links seem to spring out of the middle of a gvg/gvg2 edge for no apparent reason.
1e	2e	3e	4e

The graph for this room is reasonably intuitive. Rather than one gvg cycle there are now two for each box. The carefull observer will also note that the occluding cycles above and below each box are incomplete.
1f	2f	3f	4f

This room highlights both a drawback and an advantage to using an HGVG for navigation. The drawback is the extreamly complicated structure required to pass through the hole in the room's center and explore the other side. Extensive structure that is really not even required can be seen on either side of the hole. However, the advantage is that not only is the hole discovered and passed through correctly, but the edges of the hole are highlighted with cij edges to detect the hole's boundries. Note that some cij edges are missing as seen clearly in image 4. This is most likely due to the constant tolerance used in branching occluding edges for this particular trace. A lower constant will result in more accurate examinatinon of the branching space, but also more time spent tracing.
1g	2g	3g	4g

This trace introduces another type of node, namely the diverge node. A diverge node typically occurs when a compound GVG/GVG2 edge splits into several singular edges while the total number of minima stays the same. For instance, in image 2 there is a tunnel between the two larger rooms. In the middle of this tunnel is a GVG edge defined by four equidistant sides. This is a compound GVG since a singular GVG requires only three equidistant objects. However, at the two white dots(the divergent meetnodes) two GVG edges sprout out along with a GVG2 edge in the middle of the two.
1h	2h	3h	4h

While this is the same room as the previous, this trace was only partially performed and done so on the room as is in image 1. The previous room trace was performed on image 1 enclosed with walls on all sides. The result exhibits the escape node which is created after tracing a constant preset distance away from any objects. In other words the tracer assumes such an edge would continue on infinitely. Another interesting property of this trace is that it exhibits the ability of a GVG2 edges to trace both into and out of a GVG diverge node, which was a major error in previous versions of the software.
1i	2i	3i	4i

This room represents some of the more complicated edge interactions an HGVG could encounter. Examining image four shows four light blue nodes, each of which is a spliting GVG or splitting GVG2 node. The reason for the name is because in each case a minima is splitting into two which creates floating splitting nodes in the case of the two GVG edges on the side (the vertical post and one of the two horizontal posts are combining) while the two above are caused by the two horizontal arms splitting out from the vertical one, and signal a transition from a singular GVG/GVG2 edge to a compound edge.
1j	2j	3j	4j