The Reduce tool allows you to re-mesh a set of selected faces such that they approximate the shape with a smaller number of triangles. This is particularly useful if you need to import a large mesh into some other tool that cannot handle large files. You might also find yourself Reducing inside meshmixer, to make the different tool run more quickly.
The shift+r shortcut starts the Reduce tool, when you have an active selection.
The property pane for Reduce is shown on the right. The Reduce Target specifies what you are trying to achieve with the Reduce operation, and the Reduce Type controls how we remesh the surface (more on that below).
There are three Reduce Target modes, shown below. In Percentage mode, the goal is to reduce the triangle count to a fraction of the input triangle count, specified by the Percentage slider. In Triangle Budget mode, the goal is to reduce to a specific triangle count, specified by the Tri Count slider. And finally in Max Deviation mode, the goal is to reduce as much as possible while ensuring that the surface does not shift too far from the input surface, with "too far" defined by the Max Deviation slider. Note that in this mode, we are only checking deviation at the vertices, so points inside faces may deviate a larger amount.
The Preserve Boundaries checkbox controls whether we allow any boundary loops to be modified. Note that currently if you are applying Reduce to a sub-selection of a larger surface, and you un-check this option, holes will be created when you Accept the operation.
The Preserve Group Boundaries checkbox controls whether we constrain the border loops of facegroups. We always try to approximately preserve facegroup borders, but when this box is un-checked, the border loops will still be resampled. When checked, they are precisely preserved, although this can introduce sliver triangles and/or local normal flips near the borders.
There are two different Types of Reduce operation that we can perform, shown to the right. In the Uniform mode, we try to achieve regularly-shaped triangles, using a shortest-edges-first criteria. In the Shape Preserving mode (the default), we incrementally collapse edges which will have the smallest effect on the shape. The image below shows an original mesh and reduced results with the two types (Shape Preserving is in the middle).