It has been suggested in the literature that ordinary finite-precision floating-point arithmetic is inadequate for geometric computation, and that researchers in numerical analysis may believe that the difficulties of error in geometric computation can be overcome by simple approaches. It is the purpose of this paper to show that these suggestions, based on an example showing failure of a certain algorithm for computing planar convex hulls, are misleading, and why this is so.It is first shown how the now-classical backward error analysis can be applied in the area of computational geometry. This analysis is relevant in the context of uncertain data, which may well be the practical context for computational-geometry algorithms such as, say, those for computing convex hulls. The exposition will illustrate the fact that the backward error analysis does not pretend to overcome the problem of finite precision: it merely provides a way to distinguish those algorithms that overcome the problem to whatever extent it is possible to do so.It is then shown that often the situation in computational geometry is exactly parallel to other areas, such as the numerical solution of linear equations, or the algebraic eigenvalue problem. Indeed, the example mentioned can be viewed simply as an example of the use of an unstable algorithm, for a problem for which computational geometry has already discovered provably stable algorithms.Finally, the paper discusses the implications of these analyses for applications in three-dimensional solid modeling. This is done by considering a problem defined in terms of a simple extension of the planar convex-hull algorithm, namely, the verification of the well-formedness of extruded objects. A brief discussion concerning more difficult problems in solid modeling is also included.