Ammad, Muhammad
(2020)
Exponential Parameterized Cubic
B-Spline Curves And Surfaces.
Masters thesis, Universiti Sains Malaysia.
Abstract
The use of B-spline interpolation function for curves and surfaces has been developed
for many reasons. One reason is the higher degree of continuity and smoothness.
A general B-Spline is a polynomial curve and its shape is determined by the
control points. To interpolate data points, various works have been done by previous
researchers who studies B-Spline parameterization. In this thesis, we develop a new
way for interpolating cubic B-Spline curve by taking the first and the second derivative
at endpoints and only the first derivative at inner points. The proposed method is the
extension in the B-spline interpolation technique of using arbitrary derivatives at end
points. In developing B-spline curve interpolation method, an algorithm is presented
for interpolating data points. The algorithm computes knot values for parameterization
methods. These knot values are used in constructing a matrix of B-Spline basis
function and derivative of the basis function. Then, we solve it for control points by
using the LU decomposition method, such that the curve will pass through the given
data points. Selection of proper parametrization technique is critical for curve and
surface reconstruction process. The parametrization method used in this study is an
exponential parameterization method with a = 0:8. The main advantage of developing
B-spline curve interpolation method is that we can generate different shapes of
curves by setting different direction at all data points. As an application, we applied
the proposed method in curve reconstruction on a road map from given data points
and driving directions, and also for path planning in autonomous vehicle with given
starting and goal position.
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