A method of determining a level of detail for texturing a cube map which is a cubic texture comprising six square faces having a normalized size, each of the six square faces including a 2D coordinate system including an s face -axis and a t face -axis based on an origin corresponding to a viewpoint (V P) in an environment of a scene with various objects, the method comprising: determining coordinates of pixels (P0, P1) representing boundary points of a 3D object mapped to the cube map by projection; transforming a coordinate of at least one pixel from among the pixels representing boundary points of the object mapped to the cube map if at least first and second pixels among the pixels respectively are projected to different faces of the cube map, wherein the transforming comprises transforming a coordinate of another pixel from among the pixels based on an origin and a coordinate axis of a face corresponding to a reference pixel from among the pixels; calculating distances between the pixels representing the boundary points of the 3D object mapped to the cube map by using the transformed coordinate; and determining, based on the calculated distances, an LOD for texturing the cube map with the 3D object, wherein the LOD refers to a precision of a 3D graphic image, characterized by calculating derivatives of pixels on a coordinate axis based on the distances, wherein the LOD is based on the derivatives, wherein the derivatives of pixels on a coordinate axis comprise ratios of distances between pixels (P0, P1, P2) on a coordinate axis of the cube map to distances between pixels on a coordinate axis of a 2D screen space within which the 3D object is disposed, wherein the LOD is calculated as λ = log 2 MAX ∂ s / ∂ x p 01 2 + ∂ t / ∂ x p 01 2 ∂ s / ∂ x p 02 2 + ∂ t / ∂ x p 02 2 wherein λ is a value of an LOD, x denotes a coordinate axis of the screen space, p01 denotes a relationship between the pixel P0 and the pixel P1, p02 denotes a relationship between the pixel P0 and the pixel P2, ( ∂s / ∂x) p 01 is a derivative of pixels P0 and P1 on the s face coordinate axis, ( ∂t / ∂x) p 01 is a derivative of the pixels P0 and P1 on the t face coordinate axis, ( ∂s / ∂ x) p 02 is a derivative of the pixels P0 and P2 on the s face coordinate axis, and ( ∂t / ∂x) p 02 is a derivative of the pixels P0 and P2 on the t face coordinate axis. determining coordinates of pixels (P0, P1) representing boundary points of a 3D object mapped to the cube map by projection; transforming a coordinate of at least one pixel from among the pixels representing boundary points of the object mapped to the cube map if at least first and second pixels among the pixels respectively are projected to different faces of the cube map, wherein the transforming comprises transforming a coordinate of another pixel from among the pixels based on an origin and a coordinate axis of a face corresponding to a reference pixel from among the pixels; calculating distances between the pixels representing the boundary points of the 3D object mapped to the cube map by using the transformed coordinate; and determining, based on the calculated distances, an LOD for texturing the cube map with the 3D object, wherein the LOD refers to a precision of a 3D graphic image, characterized by calculating derivatives of pixels on a coordinate axis based on the distances, wherein the LOD is based on the derivatives, wherein the derivatives of pixels on a coordinate axis comprise ratios of distances between pixels (P0, P1, P2) on a coordinate axis of the cube map to distances between pixels on a coordinate axis of a 2D screen space within which the 3D object is disposed, wherein the LOD is calculated as λ = log 2 MAX ∂ s / ∂ x p 01 2 + ∂ t / ∂ x p 01 2 ∂ s / ∂ x p 02 2 + ∂ t / ∂ x p 02 2 wherein λ is a value of an LOD, x denotes a coordinate axis of the screen space, p01 denotes a relationship between the pixel P0 and the pixel P1, p02 denotes a relationship between the pixel P0 and the pixel P2, ( ∂s / ∂x) p 01 is a derivative of pixels P0 and P1 on the s face coordinate axis, ( ∂t / ∂x) p 01 is a derivative of the pixels P0 and P1 on the t face coordinate axis, ( ∂s / ∂ x) p 02 is a derivative of the pixels P0 and P2 on the s face coordinate axis, and ( ∂t / ∂x) p 02 is a derivative of the pixels P0 and P2 on the t face coordinate axis.