## 3D Models

### from Minimal Embedding Dimensions of Rectangle k-Visiblitiy Graphs

#### How to Navigate:

• Choose one of the figures from the list above; it will appear below.
• Drag the image to rotate it in 3 dimensions.
• Drag with the `[Control]` key (Windows, Linux) or `[Option]` key (Mac) to pan image
• Zoom in and out using your scrolling wheel or by dragging with the `[Shift]` key
These keyboard shortcuts are available when you click on the image to focus on it:
• `[h]`: Home (reset the image to its original size/orientation)
• `[x]`: Spin about the X-axis
• `[y]`: Spin about the Y-axis
• `[z]`: Spin about the Z-axis
• `[m]`: Toggle mesh (outline) mode on/off
• `[+]`,`[=]`,`[>]`: Zoom in
• `[-]`,`[_]`,`[<]`: Zoom out
Figure 5: The Cartesian product of two graphs, represented as the Cartesian product of their representations
Figure 11: A representation of the rooted product G(H)
Figure 13: A representation of the corona product G ⊙ H
Figure 14: Projections of Sm into Sm
Figure 16: All possible projections of an additional vertex vi, overlapping a central point O and all rectangles in S
Figure 18: All possible projections of an additional vertex vi, overlapping a central point O and adjacent to all rectangles in Sm.
Figure 21: Projections of 22 rectangles stacked on top of each other
Figure 22: 22(⌊k/2⌋+1) rectangles stacked, representing K22(⌊k/2⌋+1) with k=4.
Figure 23: Representation of K2(d-1)(k+1)+22(⌊k/2⌋+1) with k=4, d=3.
Figure 24: A representation of the 3-dimensional RVG K6,8
Figure 25: An overhead orthographic projection of a representation of the 4-dimensional RVG K6,8,5
Figure 29: A 3-dimensional URVG representation of Q3
Figure 33: A 3-dimensional URVG representation of Q9
Figure 36: A 3-dimensional RVG representation of Q12