1. A three-dimensional modeling apparatus comprising: an input curved surface generating unit generating a plurality of input curved surfaces each of those is formed of a plurality of input points based on coordinates and a moving direction of an input device that moves in three-dimensional data input space; an input point arrangement unit generating three-dimensional coordinate space that corresponds to the data input space and is formed of a plurality of unit grids, and arranging the input points in each of the unit grids; a representative point determining unit determining a representative point of each of the unit grids based on coordinates of the input points included in each of the unit grids and generating a group of representative points with respect to each of the input curved surfaces; a polygon generating unit selecting a representative point sequentially from representative points as a central representative point and generating polygon sequentially with respect to the selected central representative point by connecting the selected central representative point to auxiliary representative points that are representative points adjacent to the selected central representative point; a curved surface model generating unit generating a curved surface model with respect to each of the groups of representative points by connecting polygons that are generated with respect to the respective representative points; and a curved surface model combining unit combining the curved surface models and adjacent curved surface models that are additionally generated to be adjacent to the curved surface models in the coordinate space to generate a final three-dimensional image.