The problem of finding the intersection of curves and surfaces arises
in numerous computer aided design applications. The methods generally
used rely on iterative numerical techniques based on the solution of a
set of non-linear equations. These systems of equations are generally
local and need adequate starting points in order to yield convergent
solutions. This article presents two general algorithms based on geome
tric considerations to find the intersections of C-0 curves and surfac
es. The first method can be applied when one object is defined by a pa
rametric equation and the other by an implicit equation. The second me
thod is based on a succession of orthogonal projections from one objec
t to the other. The same algorithm can be applied to curves and surfac
es. These methods are implemented in the general framework provided by
dual kriging for parametric curve and surface modelling. Finally, the
conjugate tangent approach can speed up considerably the algorithm by
considering alternatively tangent lines or planes in the iterative pr
ocess together with orthogonal projections.