Directional Distance Transforms and Height Field Preprocessing for Efficient Ray Tracing

It is known that height field ray tracing efficiency can be improved if the empty space above the height field surface is first parameterized in terms of apex heights and opening angles of inverted cones of empty space whose vertical axes are regularly spaced. Once such a parameterization has been performed, rays can be traversed in steps across inverted cones of empty space rather than across successive height field grid cells. As the cone opening angles increase, ray tracing efficiency tends to improve because steps along rays across the inverted cones get longer. Circular horizontal cross-sections of an inverted cone can be divided into contiguous nonoverlapping sectors. Given that the inverted cones can contain nothing but empty space, the maximum possible opening angle within any such sector may significantly exceed the opening angle of the inverted cone. It is shown that ray tracing efficiency can be significantly improved by replacing the inverted cones of empty space with cones that have narrow sectors. It is also known that the parameters of the inverted cones can be derived from distance transforms (DTs) of successive horizontal cross-sections of the height field. Each cross-section can be represented as a 2D binary array, whose DT gives the distance from each element to the nearest element of value 1. DTs can be directionalized by requiring the element of value 1 closest to a given element to lie within a sector emanating from that given element. The parameters of inverted cones within specific sectors can be derived from such directional DTs. An efficient new algorithm for generating directional DTs is introduced.