If your machine has a dedicated NVIDIA or ATI graphics card (as opposed to an integrated graphics chip), provided that the card is relatively new/powerful RIFT should work fine. Older NVIDIA cards on the Mac such as the GeForce 7300/7600 series do not support enough of the OpenGL extensions necessary to play RIFT.
ATI users, particularly on the Mac, will experience worse performance than NVIDIA users (even if your Mac and ATI card are the "latest and greatest"), and it is recommended that ATI users run RIFT with the "Legacy Renderer" enabled. You can apply this setting in the in-game Video>Advanced settings, or by editing the "rift.conf" file as described in the above "Quick fixes" article.
If your machine uses an Intel on-board graphics chip such as a GMA 950 or HD 3000, RIFT will almost certainly *not* work on your machine via Crossover. These chips' drivers don't handle the complex openGL function calls very well, and also utilize software rendering, whereby the graphical rendering happens inside the CPU. (With a dedicated NVidia or ATI card the graphics are rendered by the graphics hardware, which is more capable of the task.)
If you're unsure about what kind of graphics card you've got, go to About this Mac>More Info>Graphics/Displays. Remember that all Macs capable of running Crossover have an Intel processor - what you need to determine is the graphics chipset.
On Linux, there are a variety of commands you can use to determine you graphics card. Two easy ones are
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