  A composite quadric model (CQM) is an object modeled by piecewise linear or
quadric patches. We study the continuous detection problem of a special type of
CQM objects which are commonly used in CAD/CAM, that is, the boundary surfaces
of such a CQM intersect only in straight line segments or conic curve segments.
We present a framework for continuous collision detection (CCD) of this special
type of CQM (which we also call CQM for brevity) in motion. We derive algebraic
formulations and compute numerically the first contact time instants and the
contact points of two moving CQMs in $\mathbb R^3$. Since it is difficult to
process CCD of two CQMs in a direct manner because they are composed of
semi-algebraic varieties, we break down the problem into subproblems of solving
CCD of pairs of boundary elements of the CQMs. We present procedures to solve
CCD of different types of boundary element pairs in different dimensions. Some
CCD problems are reduced to their equivalents in a lower dimensional setting,
where they can be solved more efficiently.
