A machine for breaking out an inner shape in a glass sheet, includes a cutting tool and a displacement system to produce a cutting line on a first side of the glass sheet that delimits an outer contour of the inner shape and an inner contour of a peripheral shape; a bearing system to bear against a second side of the sheet along the outer contour of the inner shape; a deformation system to deform one of the inner and peripheral shapes by convex bending toward the second side, the convex bending creating a differential deformation between the inner and peripheral shapes to break out the inner shape along the cutting line and separate the inner shape from the peripheral shape so that a distance needed for a contactless extraction is created, and an extraction system to extract the inner or peripheral shape while the convex bending is maintained.