There are two groups of settings: Visual (how things are drawn) and computational (level of detail) settings. All of these can be adjusted from the settings box on the right side of every plot window.
Display modes:
Points
Wireframe
Hiddenline
Flatshaded
Smoothshaded
Textures can be applied to any display mode that draws surfaces (everything but Points and Wireframe). To set the texture images, either drag and drop an image onto the texture box or use its context menu to load one of the builtin textures. The builtins are some simple computed textures.
Texture
Another way of texturing are reflection textures, which can be applied to any display mode that has surface normals (Flatshaded and Smoothshaded).
Reflection
The texturing modes can also be combined and both have a strength setting. For texturing this blends with the fill color and for reflection it sets the reflectiveness of the surface.
Texture + reflection + red fill color
Similar to reflection is shininess, which adds hilights to a surface:
Shininess On and Off
Colors that can be changed are: Fill, Grid, Axis and Background. Transparency of the background affects the copied image (as in ⌘C on the graph view) and icon of the saved file. Grid transparency blends the grid and fill colors. Fill transparency sets the transparency of the surface itself, which can make the inside structure of parametrics more visible. The way the surface transparency works can be set with the transparency mode (in version 1.0 transparent surfaces still have a few issues).
Fill, grid and background colors
Transparency, Multiply mode
Another way of looking inside of a surface are meshes. A mesh is similar to a texture but it cuts away parts of the surface. And unlike textures, meshes are scaled with the grid, so grid density also affects mesh density. Meshes also have another density setting (the slider below), that adjusts how much they cut away or affects their scale in some way (this depends on the selected mesh type). For most mesh types the left and right sides are inverse to each other (the right side setting cuts away what the left side setting does not).
Mesh
Surfaces can be overlaid with a grid, which is the image of a rectangular grid on the preimage range (Grid mode "On") or the borders of every drawn triangle (Mode "Full Mesh"), which is useful for checking the quality settings (see below under "Computational Settings"). The grid can be scaled with the grid density slider (below the mode selector) and its line width can be adjusted. The Wireframe mode draws only the grid and the Points mode draws the grid points, so they are both controlled by the grid settings.
Grid
Fog can be added to give non-shaded plots (i.e. Points, Wireframe, Hiddenline) more depth.
With Fog
Without Fog
Finally there are some settings for the axis / coordinate system: In 2D whether to draw polar or rectangular grid or none at all. Whether or not to draw the axis, and if the graph should be clipped to the axis box in 3D.
Butterfly curve with polar axis grid
There are two settings that affect the level of detail in a plot: Quality and grid density.
Quality sets the maximum total number of faces in a surface plot or the number of line segments in a line plot. The more well-behaved a function is, the lower the quality setting can be. The highest setting is best for functions with poles or wildly oscillating ones, as well as for parametric plots that stretch their input range over a lot of space (for instance something like the butterfly curve above).
The grid density defines an initial subdivision of the input space that is further subdivided for higher quality settings. So the grid density restricts both the minimum quality and the possible quality increments.
Lastly, detection of discontinuities can be switched on, which tries to detect and remove jump discontinuities from the graph. For line graphs this uses two heuristics:
Surface plots and implicits use similar ideas, but since their computation is not recursive, the results are not as good as for line graphs.
Not detecting discontinuities
Detecting discontinuities