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Spline Interpolation [复制链接]

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Based on http://terpconnect.umd.edu/~petersd/interp.html

CubicSpline.py

2 KB, 下载次数: 822

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Important Materials

The problems with a single Bezier spline range from the need of a high degree curve to accurately fit a complex shape, which is inefficient to process. To overcome the problems, a piecewise curve is used. Therefore the order of the curve is not dependent on the number of control points.


http://escience.anu.edu.au/lecture/cg/Spline/index.en.html

http://escience.anu.edu.au/lecture/cg/Spline/whyBSpline.en.html

B-Spline versus Bezier Spline (i.e. composite Bezier Curves)

http://escience.anu.edu.au/lectu ... ineVsBezier.en.html

Bezier and B-Spline Technology.pdf (1.08 MB, 下载次数: 1140)

http://math.fullerton.edu/mathews/n2003/B-SplinesMod.html

An Introduction to B-Spline Curves.pdf (147.78 KB, 下载次数: 1230)

http://www.codeproject.com/Articles/16689/Bspline-in-C

http://www.cs.mtu.edu/~shene/COU ... ine-curve-coef.html

http://chi3x10.wordpress.com/2009/10/18/de-boor-algorithm-in-c/


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The Advantage of Using B-spline Curves

B-spline curves require more information (i.e., the degree of the curve and a knot vector) and a more complex theory than Bézier curves. But, it has more advantages to offset this shortcoming. First, a B-spline curve can be a Bézier curve. Second, B-spline curves satisfy all important properties that Bézier curves have. Third, B-spline curves provide more control flexibility than Bézier curves can do. For example, the degree of a B-spline curve is separated from the number of control points. More precisely, we can use lower degree curves and still maintain a large number of control points. We can change the position of a control point without globally changing the shape of the whole curve (local modification property). Since B-spline curves satisfy the strong convex hull property, they have a finer shape control. Moreover, there are other techniques for designing and editing the shape of a curve such as changing knots.

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