1. A color processing apparatus comprising: a point group generator that generates a point group existing in a color gamut of an output apparatus; a design point group extracting unit that extracts, from the point group, a design point group, which is a point group that satisfies predetermined design conditions; a corresponding point group setting unit that sets, on the basis of the design point group, a corresponding point group, which is a point group indicating a boundary of a color gamut represented by the design point group, such that points of the corresponding point group are associated with individual points of a boundary point group existing on a boundary of the color gamut of the output apparatus; and a design color gamut boundary generator that generates a boundary of a design color gamut, which is a color gamut that satisfies the predetermined design conditions, by using a set of the boundary point group and the corresponding point group.