Point-to-curve raytracing by algebraic rasterization

Abstract

Boundary-value raytracing problems can be concatenated to a smooth one-parameter family of problems, that can be solved by continuation. This has been the purpose of point-to-curve raytracing. A global approach, based on algorithms taken from computer graphics (algebraic rasterization of implicit curves), has several advantages. Subject to relatively mild assumptions -Lipschitz continuity of the emergence point as function of initial parameters -all solution branches are found, there are no problems with initialization, bifurcation, or closed loop solutions. The algebraic rasterization benefits to boundary value raytracing problems in a wide range of applications: shot-to-profile shooting, VSP raytracing, normal raytracing, and more. The algorithm is sufficiently robust to continue even beyond points where the Lipschitz continuity does not apply, such as faults.