1. A graphics-rendering apparatus comprising: a vector data group management unit that manages a vector data group including sets of vector data forming a polygon based on first management information; a vector data extraction unit that extracts vector data as a target vector to be processed from the vector data group in accordance with the first management information; a starting-point-and-end-point computing unit that computes starting-point-and-end-point information that indicates starting and end points of the processing, based on the vector data extracted by the vector data extraction unit; a target point management unit that generates a second management information for managing a target point by determining the target point to be processed in accordance with the starting-point-and-end-point information, and notifies the vector data group management unit of completion of processing of the target vector; a target point computing unit that computes coordinates of a pixel of the target point to be processed, based on the second management information; a target point determination unit that determines whether or not to fill in each of pixels positioned at both sides of the coordinates of the pixel of the target point to be processed by examining a vector of the vector data set forming the polygon and considering (i) positional relations of the pixel of the target point relative to the examined vector, and (ii) whether the examined vector changes from right to left or from left to right; a fill-in information computing unit that computes fill-in information regarding the target point based on the determination result of the target point determination unit and predefined rules for filling in a closed area of the polygon; a fill-in information storage unit that stores the fill-in information; a fill-in information registration unit that registers into the fill-in information storage unit the fill-in information computed by the fill-in information computing unit; a rendering area computing unit that computes and updates a rendering area where the polygon is to be rendered, based on the vector data extracted by the vector data extraction unit; a rendering area correction unit that generates rendering area information by performing a correction to the rendering area computed by the rendering area computing unit; a rendering data correction unit that generates data optimal for rendering by performing a correction to the fill-in information stored in the fill-in information storage unit; and a rendering unit that renders the polygon by use of the rendering area information and the data generated by the rendering data correction unit.