1. A drawing device for receiving an original image of a texture and drawing a mipmap image generated by reducing the original image on a polygon image, the drawing device comprising: a wavelet transform unit for transforming the original image into wavelet coefficients using a Han wavelet transform formula; a level obtaining unit for obtaining a mipmap level of the mipmap image; an inverse wavelet transform unit for receiving and subjecting at least a portion of the wavelet coefficients obtained by the transformation by the wavelet transform unit, to an inverse transform using an inverse Han wavelet transform formula until an order having a value equal to the mipmap level is obtained, and outputting an image represented by at least a portion of a low-frequency component of wavelet coefficients having the order having the value equal to the mipmap level; and a polygon drawing unit for drawing the image output by the inverse wavelet transform unit, as a mipmap image, on the polygon image.