RegionIntersection

RegionIntersection[reg1, reg2, ...] gives the intersection of the regions.

Examples

Intersection of disks:

RegionIntersection[Disk[{0, 0}, 1], Disk[{0.5, 0}, 1]]

Intersection of ball and box:

RegionIntersection[Ball[], Cuboid[{0, 0, 0}, {1, 1, 1}]]

Please visit the official Wolfram Language Reference for more details.