Height distributional distance transform (HDDT) methods are introduced as a new class of methods for height field ray tracing. HDDT methods utilize results of height field preprocessing. The preprocessing involves computing a height field transform representing an array of cone-like volumes of empty space above the height field surface that are as wide as possible. There is one cone-like volume balanced on its apex centered above each height field cell. Various height field transforms of this type are developed. Each is based on distance transforms of height field horizontal cross-sections. HDDT methods trace rays through empty cone-like volumes instead of through successive height field cells. The performance of HDDT methods is evaluated experimentally against existing height field ray tracing methods.