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Topic: Hermite spline

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	Rendering Jellyfish - CS348B Spring 2004 Final Project
		Hermite splines were chosen to give us the ability to more carefully define the shape of the bell.
		The backbone spline of the generalized cylinder is given by a Catmull-Rom spline whose control points are determined by the locations of particles in a mass-spring simulation discussed in part 2.
		The control points of the small and large tentacle backbone splines are animated via a simple damped mass-spring particle system (we simulate a rope with stretch and bend springs, attached at one end to a point on the surface of the bell).
	graphics.stanford.edu /~kayvonf/cs348b/jellies (1442 words)

	Spline Macro File Tutorial - Objects (Site not responding. Last check: 2007-10-09)
		Splines on their own aren't much at all: just a mathematical description of a curve in space, an idea of the path traced out by a point moving from one location to another.
		Blob splines are similar to pipe splines, but because we use blobs the results are often smoother.
		The coil spline is similar to the torus pipe spline, but the torus segments are specially arranged to form a coil around the spline curve.
	www.geocities.com /ccolefax/spline/tutorial2.html (1471 words)

	Advanced Digital Cinematography by Yootai Kim (Site not responding. Last check: 2007-10-09)
		In the case of Bezier and Hermite spline bases, the number of spline knots must be 4n+3 and 4n+2, respectively.
		In the case of linear spline basis, the first and last knot are unused, but are nonetheless required to maintain consistency with the cubic bases.
		For all spline types, an array of values may be used instead of a list of values to specify the control points of a spline.
	accad.osu.edu /~ykim/ADC/reference.html (403 words)

	ipedia.com: Spline (mathematics) Article (Site not responding. Last check: 2007-10-09)
		In the picture, the curve that passes through A, B, C, and D is an interpolating spline (specifically, a linear spline) and the curve that passes through A and D, but not B and C, is an approximating spline (specifically, a Bézier spline).
		An important characteristic of splines is that they are given by polynomials, but only piecewise: different polynomials may be used in different parts of a curve.
		The simplicity of representation and the ease with which a complex spline's shape may be computed make splines popular representations for curves in computer science, predominantly in computer graphics but also for other kinds of interpolation, such as smoothing of digital audio.
	www.ipedia.com /spline__mathematics_.html (387 words)

	[No title]
		Hermite cubics C can produce a "visually pleasing" and monotone interpolant to C monotone data.
		C C Sets derivatives needed to determine a monotone piecewise cubic C Hermite interpolant to the data given in X and F. C Default boundary conditions are provided which are compatible C with monotonicity.
		May be used by itself C for Hermite interpolation, or as an evaluator for DPCHIM C or DPCHIC.
	iris.gmu.edu /~snash/nash/software/NMS__double/ch04.f (7838 words)

	Spline Macro File Tutorial (Site not responding. Last check: 2007-10-09)
		Notice also that the colour of the previewed spline changes from red at the first point to white at the last: this lets us know which direction the spline is travelling in.
		The next option we can try is the spline bias value: like the spline tension this is normally zero, which means that the spline is curved equally on either side of each point in the spline.
		Bezier splines have the advantage over TCB splines of allowing you to set the curvature of the spline directly for each section, so you can create some sharp corners and some smooth, and generally have more control over the spline's shape.
	www.geocities.com /ccolefax/spline (1676 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The cubic spline is a piecewise cubic polynomial.
		T(N), at which the spline is to be evalulated.
		The constraint on the linear spline is that it is !
	www.csit.fsu.edu /~burkardt/f_src/spline/spline.f90 (6750 words)

	NTCC Software Catalog (Site not responding. Last check: 2007-10-09)
		The 1D spline and Hermite routines are based on standard methods; the 2D and 3D spline or Hermite interpolation functions are constructed from 1D spline or Hermite interpolation functions in a straightforward manner.
		The splines are continuously twice differentiable in all directions across all grid cell boundaries and over the entire grid domain; Hermite functions are continuously once differentiable in all directions over the entire grid domain.
		Spline and Hermite interpolation functions are often much faster to evaluate than other representations using e.g.
	w3.pppl.gov /rib/repositories/NTCC/catalog/Asset/pspline.html (271 words)

	PiXELS:3D studio3.x (Site not responding. Last check: 2007-10-09)
		Splines can be divided into two broad categories: Interpolating and Approximating.
		A very biased spline will be flatter on one side a control point than the other.
		The simplest spline that can be drawn—it is always the shortest distance between two points on screen.
	www.pixels3d.com /Manual37/UM_html/02um010.html (219 words)

	Cubic Hermite spline - Wikipedia, the free encyclopedia
		In the mathematical subfield of numerical analysis a cubic Hermite spline, named in honor of Charles Hermite (Hermite is pronounced air MIT), is a third-degree spline with each polynomial of the spline in Hermite form.
		The Hermite form consists of two control points and two control tangents on each for each polynomial.
		Since each subinterval must share tangents with neighboring subintervals, many techniques exist to determine values for shared tangents.
	en.wikipedia.org /wiki/Cubic_Hermite_spline (131 words)

	[No title]
		C Produces a cubic spline interpolator in cubic Hermite C form.
		C Evaluates a single cubic Hermite function and its C first derivative at an array of points.
		C Computes the definite integral of a piecewise cubic C Hermite function when the integration limits are data C points.
	www.netlib.org /slatec/pchip/pchdoc.f (1061 words)

	[No title]
		While designed for C use by PCHFD, it may be useful directly as an evaluator for C a piecewise cubic Hermite function in applications, such as C graphing, where the interval is known in advance.
		May be used by itself for Hermite interpolation, C or as an evaluator for PCHIM or PCHIC.
		C These values will determine a monotone cubic Hermite func- C tion on each subinterval on which the data are monotonic, C except possibly adjacent to switches in monotonicity.
	iris.gmu.edu /~snash/nash/software/NMS__single/ch04.f (15520 words)

	SPLINE - Interpolation and Approximation of Data
		SPLINE is a package of simple routines for setting up and evaluating splines and related functions, whose goal is either to
		There are a variety of types of splines available, including least squares polynomials, divided difference polynomials, piecewise polynomials, and various B, Bernstein, beta, Bezier, Hermite and Overhauser splines.
		Also included are a set of routines that return the local "basis matrix", which allows the evaluation of the spline in terms of local function data.
	orion.math.iastate.edu /burkardt/f_src/spline/spline.html (449 words)

	DirectVolumeRenderer: DVR::Math::PositionalSpline class Reference
		A Catmull-Rom spline is a derivitive of the Hermite spline.
		The difference is that the Hermite spline allows you to specifiy 2 endpoints and 2 tangents, then the spline is generated.
		A Catmull-Rom spline allows you to just supply 1-n number of points and the tangents will be automatically calculated.
	www.cg.tuwien.ac.at /courses/Visualisierung/2004-2005/Beispiel1/BauchingerMaquil/doxygen/classDVR_1_1Math_1_1PositionalSpline.html (228 words)

	Error Estimates and Convergence Rates for Variational Hermite Interpolation - Luo, Levesley (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		The optimal Hermite interpolant, which minimises the semi--norm of the reproducing kernel Hilbert space C h determined by given r-CPDm function h, is just the h-spline Hermite interpolant.
		The results on error estimation and convergence rate of the h-spline interpolant generalise those in [11, 12, 18, 10] to the case of Hermite interpolation.
		1 Hermite interpolation on the lattice grid (context) - Jetter, Riemenschneider et al.
	citeseer.ist.psu.edu /luo97error.html (495 words)

	[No title]
		Boundary conditions are C computed from the derivative of a local quadratic unless this C alters monotonicity.
		C C The resulting piecewise cubic Hermite function may be evaluated C by PCHFE or PCHFD.
		C*DESCRIPTION C C PCHSP: Piecewise Cubic Hermite Spline C C Computes the Hermite representation of the cubic spline** inter- C polant to the data given in X and F satisfying the boundary C conditions specified by IC and VC.
	www.rh.edu /~ernesto/C_S2003/NAE/Programs/s03/pchezwd.f (7718 words)

	U.S. Treasury - Treasury Yield Curve Methodology
		The Treasury’s yield curve is derived using a quasi-cubic hermite spline function.
		Because the on-the-run securities typically trade close to par, those securities are designated as the knot points in the quasi-cubic hermite spline algorithm and the resulting yield curve is considered a par curve.
		However, Treasury reserves the option to input additional bid yields if there is no on-the-run security available for a given maturity range that we deem necessary for deriving a good fit for the quasi-cubic hermite spline curve.
	www.ustreas.gov /offices/domestic-finance/debt-management/interest-rate/yieldmethod.html (561 words)

	Error Estimates for Hermite Interpolation on Spheres: A Variational Approach - Luo, Levesley (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		Using the basis function h, the semi-Hilbert space C h is introduced and its reproducing property established.
		The resulting optimality of the h-spline interpolant leads to error estimates for Hermite interpolation of sufficiently smooth functions.
		Luo, Z. and J. Levesley, Error estimates for Hermite interpolation on spheres: A variational approach, Technical Report 1997/10, Univ. of Leicester, 1997.
	citeseer.ist.psu.edu /93638.html (558 words)

	Bowl -- Step 2 (Site not responding. Last check: 2007-10-09)
		Once the point tool is selected, you will be able to add points to the spline by clicking with the CTRL key down.
		If you wind up deselecting the spline, you can select it again by clicking on its name in the object manager.
		Drag the spline's points and tangents as you like to make the right shape for the cross section of the bowl.
	www.technoscope.com /c4d/bowl/step2.html (317 words)

	Extended IDL Help
		This is an intermediate step in the computation of the natural spline that requires only the X and Y vectors.
		EXPLANATION: Hermite interpolation computes the cubic polynomial that agrees with the tabulated function and its derivative at the two nearest tabulated points.
		NAME: SPLINE_SMOOTH PURPOSE: Compute a cubic smoothing spline to (weighted) data EXPLANATION: Construct cubic smoothing spline (or give regression solution) to given data with minimum "roughness" (measured by the energy in the second derivatives) while restricting the weighted mean square distance of the approximation from the data.
	lasco-www.nrl.navy.mil /doc/astrolib/math.html (7281 words)

	DFT-Library
		May be used by itself for Hermite interpolation, or as an evaluator for PCHIM or PCHIC.
		Evaluate the definite integral of a piecewise cubic Hermite func tion over an interval whose endpoints are data points.
		Set derivatives needed to determine the Hermite represen- tation of the cubic spline interpolant to given data, with specified boundary conditions.
	www.physics.rutgers.edu /~happel/lib/slatec/p.html (692 words)

	SLATEC Keylist Index
		May be used by itself for Hermite interpolation, or as an evaluator for DPCHIM or DPCHIC.
		While designed for use by PCHFE, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance.
		While designed for use by DPCHFE, it may be useful directly as an evaluator for a piecewise cubic Hermite function in applications, such as graphing, where the interval is known in advance.
	www.cs.yorku.ca /~roumani/fortran/labs/slatecIndex.htm (11408 words)

	Graphics assignment due April 28 (Site not responding. Last check: 2007-10-09)
		In our last class we briefly discussed Hermite Splines, which were used for building the Noise function.
		A Hermite Spline produces a smooth curve (actually a cubic polynomial), when you give it a value and gradient at the beginning and end of an interval (usually the interval from 0.0 to 1.0).
		In any case, your Hermite Spline routine should take four floating point values, and return four floating point values.
	mrl.nyu.edu /~perlin/courses/spring97/assignment6.html (308 words)

	[music-dsp] Hermite (Site not responding. Last check: 2007-10-09)
		I have a cross-platform ready Hermite spline plotter all done, along with an "audio ready" version of the HSpline class.
		In case anyone was confused, the version of the class I posted yesterday was more like a 2D drawing class than something for audio; it demonstrated coding Hermite splines simply, but wasn't appropriate for audio transfer functions.
		I'm thinking of making this a code-generator: you design some transfer curves, and it spits out C code for a waveshaper that might look like void wavshape(int curve_index, float blend, float xin, float *yout); It would blend between curves based on the curve_index and blend.
	shoko.calarts.edu /pipermail/music-dsp/2001-February/007908.html (238 words)

	BU CAS CS 580: Advanced Computer Graphics---Programming Assignment 1 (Site not responding. Last check: 2007-10-09)
		You will develop a spline editor that allows a user to create, modify, and display a 2-D cubic Hermite spline.
		The resulting spline editor will become part of your keyframe animation tool in programming assignment 1.
		You are welcome to use this program as a starting point for your Hermite spline editor; however, this is not required.
	www.cs.bu.edu /fac/sclaroff/courses/cs580-97/p0 (383 words)

	Documentation for PCHIPD
		C C DPCHIM -- Piecewise Cubic Hermite Interpolation to Monotone C data.
		C C DPCHSP -- Piecewise Cubic Hermite Spline.
		C C DPCHFD -- Piecewise Cubic Hermite Function and Derivative C Evaluator.
	orion.math.iastate.edu /docs/cmlib/pchipd.html (935 words)

	IDL Help (Site not responding. Last check: 2007-10-09)
		It may be preferable to Lagrangian interpolation ; (QUADTERP) when either (1) the first derivatives are known, or (2) ; one desires continuity of the first derivative of the interpolated ; values.
		HERMITE() will numerically compute the necessary ; derivatives, if they are not supplied.
		; The FDERIV keyword is useful either when (1) the derivative ; values are (somehow) known to better accuracy than can be ; computed numerically, or (2) when HERMITE() is called repeatedly ; with the same tabulated function, so that the derivatives ; need be computed only once.
	www.astro.washington.edu /deutsch-bin/getpro/library32.html?HERMITE (160 words)

	C4D Tutorial - Ears (Site not responding. Last check: 2007-10-09)
		We want to add our original Ear Spline to this new Object Group, but, as we noticed before, if you open the group, there is another Ear Spline (as well as an Ear Spline.1).
		Now lets fiddle with the points on the middle spline to create the major contour of the ear.
		This will allow you to edit the points (this is the same as selecting the spline and hitting the Points Tool button).
	members.aol.com /RogN/Pg9.html (478 words)

	[No title]
		C*DESCRIPTION C C PCHIP: Piecewise Cubic Hermite Interpolation Package C C This document contains the specifications for PCHIP, a new C Fortran package for piecewise cubic Hermite** interpolation of data.
		As is demonstrated in Reference 1, C such an interpolant may be more reasonable than a cubic spline if C the data contains both "steep" and "flat" sections.
		C C PCHMC -- Piecewise Cubic Hermite Monotonicity Checker.
	www.umbc.edu /doc/cmlib/doc/pchips/pchdoc.html (935 words)

	SLATEC Routines for Interpolation
		Thus, the principle is that increasing the continuity of derivatives decreases the number of free parameters and conversely.
		Monotone splines (reference 7) can help curb this undulating tendency but constrained least squares is more likely to give an acceptable fit with fewer parameters.
		Sets derivatives needed to determine a monotone piecewise cubic Hermite interpolant to the data given in X and F. Default boundary conditions are provided which are compatible with monotonicity.
	www.stats.bris.ac.uk /~marp/slatec/routin-e.htm (15308 words)

	Hermite cubic spline collocation methods with upwind features (Site not responding. Last check: 2007-10-09)
		In this paper, we present an eigenvalue analysis of the first-order Hermite cubic spline collocation differentiation matrices with arbitrary collocation points.
		Some important features are explored and the method is compared with some other discrete methods, such as finite difference methods.
		A class of spline collocation methods with upwind features is proposed for solving singular perturbation problems.
	anziamj.austms.org.au /V42/CTAC99/Sun (99 words)

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