DEGREE REDUCTION OF BEZIER CURVES WITH CHEBYSHEV WEIGHTED G3-CONTINUITY
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This paper considers Chebyshev weighted G3-multi-degree reduction of B´ezier curves. Exact degree reduction is not possible, based on this fact, approximative process to reduce a given B´ezier curve of higher degree n to a B´ezier curve of lower degree m, m<n is required. The weight function w[t]=2t(1 − t), t ∈ [0, 1] is used with the L2 -norm in multi degree reduction with G3- continuity at the end points of the curve. Explicit results and comparisons are verified by examples. The numerical result obtained from the new method yields minimum approximation error, improves the approximation in the middle of the curve, and shows up helpful applications to many scientists and engineers on how to design and reconstruct complex systems.
Abstract
This paper considers Chebyshev weighted G3-multi-degree reduction of B´ezier curves. Exact degree reduction is not possible, based on this fact, approximative process to reduce a given B´ezier curve of higher degree n to a B´ezier curve of lower degree m, m<n is required. The weight function w[t]=2t(1 − t), t ∈ [0, 1] is used with the L2 -norm in multi degree reduction with G3- continuity at the end points of the curve. Explicit results and comparisons are verified by examples. The numerical result obtained from the new method yields minimum approximation error, improves the approximation in the middle of the curve, and shows up helpful applications to many scientists and engineers on how to design and reconstruct complex systems.
참고문헌 (15)
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