Fermat's principles. In the Huygens' wave propagation construction, each point on the wavefront emanates light rays in the form of a one parameter family of radial curves. This can be applied to discrete domain rather easily, but it is inefficient due to excessive overlap. In Fermat's principle, the light rays propagate orthogonal to the wavefront and the new wavefront may be constructed by moving along the light rays. However, tracing the light rays on the discrete domain would leave gaps on the wavefront. Instead of using a full circle in the first case and a thin beam in the second, we proposeusing a sector of discrete beams with minimal overlap as in the CEDT algorithm [Ragnemal:neighborhoods:cviu92],Specifically, the CEDT algorithm which typically uses discrete wave directions from discrete boundary locations is now generalized to free-form curve segments,yet maintaining propagation using discrete grid locations and directions. In our approach, instead of propagating only distance information (time), we also propagate geometric models of the sub-pixel boundary.
Analytic distance values from the source boundary segments are then computed at each step of propagation process.
- Wavefront is represented by a set of discrete points
- Each discrete point on a wavefront contains
- direction
- distance
- source
- Propagation takes place from the smallest value
- Analytic distance values from the source boundary segments are then computed at each step of propagation process
