We address the problem of computing a guaranteed drawing of high resolution of a plane curve defined by a bivariate polynomial equation P (x, y) = 0. The drawing is a subset of pixels defined on a grid of a given resolution with the guarantee that the pixels enclose all the parts of the curve that intersect the grid. Our main contribution is to use a non-uniform grid based on the Chebyshev nodes to take advantage of multipoint evaluation techniques via the Discrete Cosine Transform. We propose two new algorithms that compute guaranteed drawings and compare them experimentally on several classes of high degree polynomials. Notably, one of those approaches is faster than state-of-the-art drawing software, even when they are not guaranteed.