Results:

• Correctly trace an intersection curve segment.
• Validated (strict) error bounds on the intersection curve segment.
• An algorithm which avoids the phenomenon of straying or looping.
• Scheme is able to accommodate the errors while obtaining the starting point for the intersection curve.
• Method handles perturbation in the surface itself (extremely useful in the events of various tolerance used in data exchange or during reverse engineering).
• Rounding during digital computation (Due to floating point arithmetic).
• Presentation on the above results (Surface intersection with validated error bounds).

• Developing interval governing ODEs for tangential intersections.
• Application to self-intersection (Useful in NC machining where we require offset surfaces).
• Presentation on the governing equations for SSI in general.

• Techniques for reducing error bounds
• Error bound reduction in parametric space.
• Error bound reduction in model space.
• Presentation on reducing the bound.

• Obtaining the zero of a polynomial robustly for accurate starting point evaluation.
• Even in the case of polynomials involving roots with high multiplicity. (Needed for the case of tangential and higher order intersections).
• Presentation on multiple zeros of a polynomial.

• Definition of multiplicity for the case of Univariate and Bivariate systems of polynomial equations

• Development of the Bisection Algorithm
  
• Presentation on the Bisection Algorithm, application of Degree of Gauss Map and Cauchy index to Multiple zeros of Polynomials.