Parametric height field ray tracing
Proceedings of the conference on Graphics interface '92
A unified distance transform algorithm and architecture
Machine Vision and Applications
Height distributional distance transform methods for height field ray tracing
ACM Transactions on Graphics (TOG)
Directional distance transforms and height field preprocessing for efficient ray tracing
Graphical Models and Image Processing
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Hidden Line Elimination in Projected Grid Surfaces
ACM Transactions on Graphics (TOG)
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The linear Parameter Plane Transform (PPT) of a height field attributes an inverted cone of empty space to each height field cell. In is known that height field ray-tracing efficiency can be improved by traversing rays in steps across inverted cones of empty space. However, steps across inverted cones of empty space along rays close to the base of a steep ridge will be short, even if there are no obstructions along the line of sight, because the cones will be narrow. This weakness can be virtually eliminated by allowing the opening angles of the inverted cones of empty space to vary between sectors, i.e., by directionalizing the linear PPT. An efficient algorithm for computing the linear directional PPT of a height field is given and its properties are investigated.