Mathematical Problems in Engineering / 2012 / Article / Tab 1

Research Article

Parameterization Method on B-Spline Curve

Table 1

Comparison among parameterization methods.

Parameterization MethodAdvantagesDisadvantages

Uniform [6]The parameter value is easy to calculateIn many cases, interpolation between edit points is not as good and can lead to unpredictable stretching of textures during rendering.
Chord length [10]Minimizes stretching and squeezing of texturesA large bulge and twists away from the data point polygon may be generated.
Centripetal [11]In some cases, may make smoother objects. On surface of very evenly spaced control points, it may give slightly better texture mapping resultsA small loop may be produced.
Exponential [7]Can freely select the resulting curve, in other word, generalization of uniform, chord length, and centripetal methodDifficult to find the suitable value of for better curve result
Universal [8]Affine invariantSimilar to uniform parameterization method
Hybrid [9]Give better accuracyUnstable and more computation effort due to the calculation of centripetal and chord length method.

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