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In this paper we proposed a new methodology for designing freeform reflectors tailored to redistribute the radiant flux emitted by a point light source onto a target plane with the prescribed irradiance pattern. Based on the laws of reflection and energy conservation, a skew freeform model with a set of second-order ordinary differential equations formulating the ray tracing between the source and target domain was presented. A 3D freeform reflector was constructed by using such skew freeform model with quadric surface fitting accordingly. Proposed scheme is applicable for arbitrary geometric-based mapping without the restrictions subject to the target, source, collective solid angle, or target topography, respectively. Keywords: Geometric optical design, Non-imaging optics, Illumination design, Computation methods