A surface gravity wave generator (302,402,500,700,800,900,1000) and wave pool (100,300,400) is disclosed. A wave pool is formed of opposing side walls (102,104) and a center channel (106) of water. The channel (106) includes a bottom contour (112) with a depth that runs from a deep end (202) to a shoal (206) or beach. One or more three-dimensional foils (500,600) are vertically arranged along at least one side wall (102,104), and moved against the water in the channel. Each foil has a curvilinear cross-sectional geometry that defines a leading surface (502) that is adapted to generate a wave in water moving past the leading surface, and a trailing surface (504) configured for flow recovery to avoid separation of the flow of water in the wave and to mitigate drag from the foil from the water moving past the leading surface.