COMPUTING THE MINIMUM DISTANCE BETWEEN A POINT TO A NURBS CURVE

NURBS, which is known as Non-Uniform Rational B-spline, have become a significant tool
for the complex analytic and geometric design especially a well-known industry standard for
the complex geometry in the Computer-Aided Design (CAD), Computer-Aided Manufacturing
(CAM) and Computer-Aided Engineering (CAE). Because of the incredible mathematical
basis, the numerically stable and fast algorithm and the common geometric transformations,
NURBS curve and surface had been considered as a very popular role in the industry. However,
the topic of NURBS has been known as a complex problem for the researchers. Concerns have
been raised such the minimum distance between a point to a NURBS curve might have been
estimated if the basis function of the B-spline algorithm is optimized, an initial point is good
to be considered in the boundary and the backtracking line search method might be applied.
Several approaches have been conducted to investigate into this computation of the minimum
distance between a point to a B-spline curve and results have shown that the B-spline basis
function algorithm has been done. The points on the B-spline curve are smoothly drawn. In
addition, the line search method and backtracking line search method have been carried out to
assist to find the right direction from the initial point to a point on the B-spline curve in order
to reduce the unnecessary computation on finding the roots. Finally, the minimum distance
between a point to a B-spline curve will be calculated.