The Single Helix Problem

Background:

The problem consists of assisting a small biotechnological company in designing, proving, programming, and testing a mathematical algorithm to locate "in real time" all the intersections of a helix and a plane in general positions in space.

Similar programs for Computer Aided Geometric Design(CAGD) enable engineers to view a plane section of the object that they design, for example, an aircraft jet engine, an automobile suspension, or a medical device. Moreover, engineers may also display on the plane section such quantities as air flow, stress, or temperature, coded by colors or level curves. Furthermore, engineers may rapidly sweep such plane sections through the entire object to gain a three-dimensional visualization of the object and its reactions to motion, forces, or heat. To achieve such results, the computer programs must locate all the intersections of the viewed plane and every part of the designed object with sufficient speed and accuracy. General "equation solvers" may in principle compute such intersections; but for specific problems, special methods may prove faster and more accurate than general methods. In particular, general software for Computer Aided Geometrical Design may prove too slow to complete computation in real time, or too large to fit in the finished medical devices being developed by the company to the following problem.