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标题: Spline Interpolation [打印本页]
作者: milkyjing    时间: 2012-7-24 14:48:55     标题: Spline Interpolation

http://en.wikipedia.org/wiki/Spline_interpolation

http://en.wikipedia.org/wiki/Spline_(mathematics)

http://en.wikipedia.org/wiki/B%C3%A9zier_spline

http://jsxgraph.uni-bayreuth.de/ ... pline_interpolation

http://www.pcs.cnu.edu/~bbradie/cinterpolation.html

http://www.mech.uq.edu.au/staff/jacobs/nm_lib/cmathsrc/spline.c

http://www.codeproject.com/Artic ... et-of-2D-Points-wit

http://www.codeproject.com/Artic ... Image-Curve-Adjustm

http://www.codeproject.com/Artic ... s-and-Cubic-Splines

http://www.codeproject.com/Artic ... nomials-and-Splines

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

http://pages.cs.wisc.edu/~deboor/pgs/






作者: milkyjing    时间: 2012-7-25 13:40:42

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


附件: CubicSpline.py (2012-7-25 13:40:26, 2 KB) / 下载次数 4162
http://www.tcax.org/forum.php?mod=attachment&aid=NzcyfDQ5MDhjMzNkfDE3NjIwNzgzMjV8MHww
作者: milkyjing    时间: 2012-7-25 14:13:03

http://en.wikipedia.org/wiki/B-spline

http://en.wikipedia.org/wiki/De_Boor_algorithm

http://www.cs.mtu.edu/~shene/COU ... spline/de-Boor.html

http://math.fullerton.edu/mathews/n2003/CubicSplinesMod.html

作者: milkyjing    时间: 2012-7-25 20:44:45     标题: 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: 4968)

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

An Introduction to B-Spline Curves.pdf (147.78 KB, 下载次数: 4762)

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/




附件: Bezier and B-Spline Technology.pdf (2012-7-25 21:44:24, 1.08 MB) / 下载次数 4968
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附件: An Introduction to B-Spline Curves.pdf (2012-7-25 22:43:30, 147.78 KB) / 下载次数 4762
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作者: milkyjing    时间: 2012-7-25 21:49:32

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

http://www.cs.uwaterloo.ca/~r3fraser/splines/bspline.html

http://www.ibiblio.org/e-notes/Splines/Basis.htm

http://libnurbs.sourceforge.net/index.shtml

http://developer.berlios.de/projects/libspline/


作者: milkyjing    时间: 2012-7-26 20:08:02     标题: 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.
作者: milkyjing    时间: 2012-7-26 20:26:06     标题: Conclusion

http://en.wikipedia.org/wiki/De_Boor_algorithm

http://www.cs.mtu.edu/~shene/COU ... spline/de-Boor.html

http://www.cs.mtu.edu/~shene/COU ... /bspline-basis.html

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

Uniform cubic B-Spline.png

Python Implementation

http://www.pygame.org/project-pycurve-1390-.html

(https://code.google.com/p/pycurve/)

pycurve-1.0.2.zip (3.9 KB, 下载次数: 4505)

http://www.koders.com/python/fid ... 026C.aspx?s=tkinter




附件: pycurve-1.0.2.zip (2012-7-26 20:43:49, 3.9 KB) / 下载次数 4505
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图片附件: Uniform cubic B-Spline.png (2012-7-26 22:25:17, 10.42 KB) / 下载次数 3197
http://www.tcax.org/forum.php?mod=attachment&aid=Nzc3fDI5NDY1MmI0fDE3NjIwNzgzMjV8MHww

作者: milkyjing    时间: 2012-7-26 22:23:55     标题: Constant Speed Movement

http://www.gamedev.net/topic/514 ... -at-constant-speed/

http://www.geometrictools.com/Do ... eSpecifiedSpeed.pdf

http://community.spinxengine.com ... -interpolation.html

作者: milkyjing    时间: 2012-7-31 22:45:49     标题: Calculate The arc-length

Simpson's Rule

http://en.wikipedia.org/wiki/Simpson%27s_rule

http://math.fullerton.edu/mathews/n2003/SimpsonsRuleMod.html

Gaussian Quadrature

http://www-personal.umich.edu/~mejn/computational-physics/

作者: milkyjing    时间: 2012-8-1 00:54:02     标题: Constant Speed Movement Continued...

http://en.wikipedia.org/wiki/Simpson%27s_rule

http://en.wikipedia.org/wiki/Newton's_method

作者: milkyjing    时间: 2012-8-1 16:09:34     标题: Achievement

http://www.tcax.org/forum.php?mod=viewthread&tid=459

http://www.tcax.org/forum.php?mod=viewthread&tid=465





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