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Section 4.5 View Settings menu

View settings menu

Subsection 4.5.1 Adding Top Titles

This submenu allows you to add up to three distinct titles at the top of the 3D plot on the top-left, top-center, and top-right.

Each title can use LaTeX, as each is processed through MathJax.

Top titles submenu

Subsection 4.5.2 Hidden Surface Mode

This submenu allows you to select which hidden surface mode to use for 3D rendering. There are pros and cons for each of them. There is a trade-off between speed and accuracy.

See the options and their descriptions below.

Hidden Surface Mode submenu
Array Depthsort:

This is the default hidden surface mode as it is the least time and memory intensive mode. It uses a depth sort on arrays of polygons and other objects, minimizing the memory used and the time taken to process the view.

It is great for morphing surfaces that use parameters, e.g., level surfaces, but it does not handle intersections of surfaces well.

Array Depthsort Tri.:

This mode is the same as the previous mode, except that it triangularizes each polygon. That is, if it was not a triangle already, it is broken into four triangles using its midpoint. This will produce an improved surface rendering, but will be slower than the non-triangularized mode, as it uses a lot more polygon arrays.

This mode also morphs well, but does not handle surface intersections well.

BSP Tree:

This mode will automatically be selected if two intersecting surfaces are plotted together, as it handles surface intersections fairly well, and is still not overly slow.

It is generated using objects rather than arrays and uses a Binary Space Partitioning Tree to order the collection of polygon faces in the view. A first face is selected using some criteria and then the rest of the faces are divided into a collection of faces that are in front of the chosen face and those that are behind it. Any faces that are partly in front and partly behind this dividing face are split into two polygons (one of which is in front of the chosen face and one that is behind it). This process is then repeated on the front collection of faces and the back collection of faces. Once all faces (and other objects) are organized in this way, we draw the back collection first, then the splitting face and then the front collection, using what is often called the “Painter's Algorithm”.

BSP Tree Triangulated:

This mode uses a BSP Tree after first triangularizing each polygonal face. That is, if any polygon is not already a triangle, it will be split into 4 triangles using its midpoint (and calculating the correct \(z\)-coordinate for the midpoint).

This is the most accurate 3D rendering mode, but it also will take the most time to process initially and will generate the most extra polygons, so it will rotate more slowly.

It provides the nicest rendering of self-intersecting surfaces or of plots containing two or more intersecting surfaces.

Object Depth Sort:

This mode uses a depth sort using an object model. It is therefore very similar to the Array Depthsort, but may use a little more memory and be somewhat slower than the Array Depthsort mode.

Object Depth Sort Tri.:

This uses the same depthsort and object model as the previous mode, but it first triangularizes any non-triangular faces.

Subsection 4.5.3 Show two views

Select this option if you want to have two linked or unlinked 3D views containing related plots.

When this option is selected, a new option will appear on the Surface Settings for each surface (and eventually also on the settings for other objects too), allowing you to specify in which view(s) you want it to appear. For more information on this see Subsection 2.11.4 on the Surface Settings help page.

two views dropdown

Although this mode looks a lot like the Stereo View 3D mode, it is not rendering the two views from a different perspective this time, but exactly the same. It allows related plots to be displayed next to each other with the same viewpoint.

Subsection 4.5.4 Unlink two views

This option is not yet implemented, but it is intended to allow the two parallel views without requiring them to rotate with the same viewpoint.

Subsection 4.5.5 Set Viewpoint

This option allows you to enter a specified viewpoint for the 3D plot using either Cartesian or Spherical coordinates.

When this option is selected, a dialog will appear asking you which coordinate system you wish to use to specify the viewpoint.

viewpoint coordinate system dialog

Depending on which selection you make you will see a different series of dialogs asking you to specify the viewpoint.

\(\Large\textbf{Cartesian Coordinates:}\) If you select Cartesian, you will be asked for viewpoint coordinates (the coordinates of the point where you wish the user's eye to be, viewing the focus point of the plot) and the components of the up direction (as a vector).

These dialogs are shown in the figure below.

viewpoint point dialog
viewpoint up vector dialog
Figure 4.5.1 Dialogs shown for entering a viewpoint in Cartesian coordinates.

If you wish to change the focus point, see the Format Axes help page in Section 1.4.

\(\Large\textbf{Spherical Coordinates:}\) If you select Spherical, you will be asked for the eye distance from the focus point, the angle theta, and the angle phi, as well as the components of the up direction (as a vector).

These dialogs are shown in the figure below.

spherical viewpoint eye distance dialog
spherical viewpoint theta dialog
spherical viewpoint phi dialog
viewpoint up vector dialog
Figure 4.5.2 Dialogs shown for entering a viewpoint in Spherical coordinates.

Subsection 4.5.6 Reset 3D View

Resets the 3D plot's viewpoint to the default 3D view from the 1st octant.

Subsection 4.5.7 View above \(xy\)-plane

Sets the 3D plot's viewpoint to be from a point on the \(z\)-axis above the \(xy\)-plane with the \(y\)-axis being in the up-direction. This option does not alter whether the view is projected in parallel or perspective mode.

Subsection 4.5.8 View above \(xz\)-plane

Sets the 3D plot's viewpoint to be from a point on the \(y\)-axis above the \(xz\)-plane with the \(z\)-axis being in the up-direction. This option does not alter whether the view is projected in parallel or perspective mode.

Subsection 4.5.9 View above \(yz\)-plane

Sets the 3D plot's viewpoint to be from a point on the \(x\)-axis above the \(yz\)-plane with the \(z\)-axis being in the up-direction. This option does not alter whether the view is projected in parallel or perspective mode.