1. A graphics-rendering apparatus comprising: a vector data group management unit that manages a vector data group including sets of vector data 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 processing sequence computing unit that computes a processing sequence of the target vector 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 processing sequences and notifies the vector data group management unit of completion of processing of the target vector; a fill-in information computing unit that determines whether or not the target point is to be filled in based on the second management information, and computes fill-in information that indicates the determination result of filling the target point in; and a rendering unit that renders a polygon by use of the fill-in information.