Cubic Spline Calculator

x is the independent variable and y is the dependent variable. quadratic spline interpolation calculator Sx is a cubic interpolating spline function, and more. Natural Cubic Spline Function Interpolation Examples 1 Recall from the Natural Cubic Spline Function Interpolation page that we can construct a natural cubic. În matematică, prin funcție algebrică de gradul al treilea sau, mai scurt, funcție cubică se înțelege orice funcție polinomială de următoarea formă: = + + +,în care singura condiție obligatorie se referă la coeficientul a, care trebuie să nu fie zero. We created new PrusaPrinters website for all Prusa and RepRap fans. Originally, spline was a term for elastic rulers that were bent to pass through a number of predefined points ("knots"). Cubic Spline ÖThe idea of spline interpolation is reminiscent of very old mechanical devices used by draftsmen to get a smooth shape. Cubic spline interpolation lets you pass a curve through a set of points in such a way that the first and second derivatives of the curve are continuous across each point. This "quick start" guide shows you how to carry out Poisson regression using SPSS Statistics, as well as interpret and report the results from this test. 1 Motivating Example: Curve Interpolation Curve interpolation is a problem that arises frequently in computer graphics and in robotics (path planning). Further, a smoothing technique is applied to ensure that the forward rate curve is smooth. For the data set x x 0 x 1 x n y f 0 f 1 f n where a= x. The "Spline Calculator" software calculates the inspection dimensions of spline profiles with serration flanks and of involute gearing (straight or helical). Interpolation Calculator. Rutherford 1 Michael J. FRENCO Spline Calculator. And we can connect these 4 points with 3 lines (shown in red). % MATLAB permits us to solve for the "spline" curve in a relatively simple approach when we call upon the spline() function. Cubic Splines Typically, piecewise polynomials are used to t smooth functions, and therefore are required to have a certain number of continuous derivatives. In this example, I'll show you a weighted averaging technique that uses a cubic spline interpolation kernel designed to approximate a Gaussian kernel. 2 Linear Interpolating Splines A simple piecewise polynomial fit is the continuous linear interpolating spline. Spline functions include Cubic spline, bessel spline, and 'OneWay' spline (which is a monotonic spline). pp = pchip(x, f(x)) pchip takes a vector of nodes x and the corresponding function values f(x), and produces a cubic Hermite spline in Matlab’s internal format. Involute calculator. Cubic spline Again, the basic idea of the cubic spline is that we represent the function by a di erent cubic function on each interval between data points. 512 free download, review. In the discussion below, we will focus first on the case where the robot’s trajectory is defined by just two points (with appropriate selections of course and speed). The Davies equation gives reasonable estimates up to I ~0. This illustrates that cubic spline interpolation is essentially local. i = 1 for all i, then it reduces to a standard B-Spline. detrino on Oct 18, 2015 Ya, B-spline, as the article defines it: Cubic(1, 0), is an example of a very blurry cubic filter. 8 CubicSplineDifferentiate: A natural cubic spline with continuous second derivative in the interior and zero second derivative at the end points. CERCHACOEF Spline coefficients (ref. #crackthemaths Concept of Cubic Spline (Topic under the Subject Applied Numerical method) is Explained in a simple and easy way. In this example, I'll show you a weighted averaging technique that uses a cubic spline interpolation kernel designed to approximate a Gaussian kernel. The cubic parabola is a simple function of the form of y = f(x) and is based on the acknowledgment that its length is equal to its projection on axis X. 0 There are many xls cubic spline wav man 1. 3 Cubic Spline Interpolation The goal of cubic spline interpolation is to get an interpolation formula that is continuous in both the first and second derivatives, both within the intervals and at the interpolating nodes. quadratic spline interpolation matlab code. SRS1 Cubic Spline for Excel v. What is filtering/smoothing? Smoothing is an operation which removes high-frequency fluctuations from a signal. 7 in the text. Use curve fit functions like four parameter logistic, five parameter logistic and Passing Bablok in Excel, Libreoffice, Python, R and online to create a calibration curve and calculate unknown values. An interactive guide to Robert Penner's Easing Functions. Inline chevy 6 performance, Turbocharging, Custom parts, 12 bolt rebuilding. Attached is a sample data set. For vector data calculators enter the data as X,Z pairs separated. Given two (x, y) pairs and an additional x or y, compute the missing value. I think you mean the "B-spline" filter. Function approximation with regression analysis. B-spline Basis Functions: Computation Examples. Register Now! It is Free Math Help Boards We are an online community that gives free mathematics help any time of the day about any problem, no matter what the level. 5 INCHES = D 2 D 2 = 6. Compute and plot the natural cubic spline for. It is simple to use because the new functions work just like all other existing Excel functions. Interpolate at point t. Data can be entered in two ways: x values in the first line and y values in the second line, or. There are many ways of tackling this problem and in this section we will describe a solution using cubic splines. TriLookup 2. 512 This is free software that adds several spline and linear interpolation functions to Microsoft Excel. , by its values and first derivatives at the end points of the corresponding domain interval. Solution: Let the cubic spline in the interval from x =2 to x =4 be the polynomial S1(x) =0. "Approximating a Circle or an Ellipse Using Four Bezier Cubic Splines. 41 Advanced Sci/Eng calculator. Cubic Interpolation: CERCHA Cubic spline interpolation. Array Output - If you want to calculate the spline values for many values, all based on the same source data set, then you can make the cubic spline solve faster by using an array formula. When the interpolation finished the map in the gulf was created very well but a value is also created around the island. In addition to conventional two-dimensional Cartesian plots, McPlot provides the capability to display three-dimensional data in spherical perspective. It is the same powerful curve fitting engine as used and verified in DataFit software. Assayfit Pro is a curve fitting API for laboratory assays and other scientific data. B-spline Basis Functions: Computation Examples. For the first G5 command in a series of G5 commands, I and J must both be specified. For that reason we have made available for you a variety of online calculators to help you with your installation and other configurations. The word "natural" means that the second derivatives of the spline polynomials are set. we stop? There is an almost universal consensus that cubic is the optimal degree for splines and so we focus the rest of the lecture on cubic splines. 2 The parametric model is the SVI (“stochastic volatility inspired”) model published by Professor Jim. The endpoint conditions are. That makes points and intervals between them. natural spline. Q&A for cartographers, geographers and GIS professionals. You can fit higher-order polynomial equations, but it is very unlikely that you would want to use anything more than the cubic in biology. It would be preferable to have a situation in which adding an extra term merely refine the model in the sense that by increasing the order, we do not need to do all the calculations from the scratch. In the discussion below, we will focus first on the case where the robot’s trajectory is defined by just two points (with appropriate selections of course and speed). These were used to make technical drawings for shipbuilding and construction by hand, as illustrated by Figure 1. This simple editor demonstrates the various methods of spline interpolation supported by Protovis. CubicSpline(). We will show that this is not always possible with cubic splines. In addition to conventional two-dimensional Cartesian plots, McPlot provides the capability to display three-dimensional data in spherical perspective. A quick googling showed me that there is no "closed form" solution. Spline functions include cubic spline, bessel spline, and 'OneWay' spline (which is a monotonic. You should confirm all information before relying on it. CERCHACI Initial second derivative of the first spline. ÖThe final shape is quite smooth. cubic-bezier(0, 0,. A cubic Hermite spline is a spline with each polynomial in Hermite form. Read and follow all label directions before using this product. This is an implementation of cubic spline interpolation based on the Wikipedia articles Spline Interpolation and Tridiagonal Matrix Algorithm. Calculation instructions for many commercial assay kits recommend the use of a cubic regression curve-fit (also known as 3rd order polynomial regression). With everything from interesting interviews, guides and forums. Kalkulator latest version: Scientific/engineering calculator. Now let's get into the math behind them. a cubic model etc. Example Let f x cos x2 , x0 0, x1 0. Gaussian quadrature 1 Gaussian quadrature In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration. B-splines are a more general type of curve than Bezier curves. ÖIt is like securing a strip of elastic material (metal or plastic ruler) between knots (or nails). Class Cubic A cubic spline is a piecewise cubic polynomial such that the function, its derivative and its second derivative are continuous at the interpolation nodes. The cubic spline is given by the function values in the nodes and derivative values on the edges of the interpolation interval (either of the first or second derivatives). Trajectory Generation Path points : Initial, final and via points • cubic splines -- change set of coefficients at the end of each segment • linear with. Performs curve fitting, regression, interpolation, and cubic spline ; This worksheet helps to differentiate between regression and interpolation. The natural cubic spline has zero second derivatives at the endpoints. To do this, instead of setting "input_x" to a single value, you set it to a array of values. Library Import Export. It is simple to use because the new functions work just like all other existing Excel functions. Statistics Definitions > Standardized Residuals. • Let z i = S00(x i) ,i = 0 ··· n. Is there a better and more documented type of curve I could use to achieve this? My goal is to move an object along the smooth curve going through the control points. The second derivative of each polynomial is commonly set to zero at the endpoints, since this provides a boundary condition that completes the system of equations. SRS1 Cubic Spline for Excel 2. How to abbreviate Cubic Feet? The most popular abbreviation for Cubic Feet is: CF. 1987 & 6 HP, 2-Stroke, Includes Merc 6 Mercury Outboard (Thru Hub Exhaust & 8 Tooth Spline). Technical information speeds feeds, material removal rates, Depth of cut and chip per tooth load, cutting speed, cross reference information. Two of the four conditions required to specify a cubic are taken by placement of ‘control points. The use of spline functions in non-parametric density estimation and spectral estimation is surveyed. It is possible to retain the interpolating cubic spline in a form suitable for subsequent evaluation, or for calculating its derivatives, or for other manipulations. Select Currency and click on Detail icon. Volume of a cube = side times side times side. A cubic function is one of the most challenging types of polynomial equation you may have to solve by hand. Returns the Y which lies on an interpolated curve at the given X Interp. By a cute trick the cosine interpolation reverts to linear if applied independently to each coordinate. Select the appropriate “Int. Year-End Deals at Amazon. Figure 1 – A trajectory based on third-degree polynomials. com, any file sharing sites. Class Cubic A cubic spline is a piecewise cubic polynomial such that the function, its derivative and its second derivative are continuous at the interpolation nodes. Lambert 1;2 1Department of Health Sciences, University of Leicester, UK. B-spline Curves: Computing the Coefficients. This class contains the constructor and method for performing a multi-dimensional cubic spline interpolation, i. Using this function might give an even better approximation of the area under the actual function f, but you need to have access to a method for determining the best cubic spline. For mathematical background, see course handouts on Lagrange interpolation , cubic Bezier curves , cubic spline curves , and nonuniform splines. Length factors can be supplied both in curve units and normalized units. find the corresponding cubic spline and evaluate it at x =3. SRS1 Cubic Spline for Excel v. 1) What is a good source (besides ESL which I read but am still uncertain) to learn about splines for regression? 2) How would you calculate the basis of a given natural cubic spline solution on new data? Specifically if one were to do the following:. Origin provides four options for data interpolation: Linear, Cubic spline, Cubic B-spline, Akima Spline. For the data set x x 0 x 1 x n y f 0 f 1 f n where a= x. You can make the process of transfering the application to your calculator sweet and simple with Texas Instrument’s handy TI connect software. Find Gifts for Everyone with Amazon. The KaleidaGraph Guide to Curve Fitting 6 1. A Primer on Bézier Curves A free, online book for when you really need to know how to do Bézier things. Using Stata 9 to Model Complex Nonlinear Relationships with Restricted Cubic Splines William D. Cubic spline curve fitting Overview. Luckily, this is easy to get. My question is, does anyone know something about Cubic Spline Interpolation? To be more specific, does anyone know any working algorithm for Cubic Splines that actually calculates as it should? I tried with CubicSpline function (inside of Scipy library), but it turns out it returns wrong numbers - or I used it wrong way. The cubic spline is simply a polynomial spline of order 3; cubic splines are the most common form of spline. NURBS is the most general and popular representation. Is says it''s the maximum eigenvalue of A, that is lambda_max(A). In this post I am sharing with you a C program that performs cubic spline interpolation. The best place to find and install add-ons for SketchUp! Categories. liquid zero rate curve based on Cubic Spline approach is generated. Final Words. Given an X vector, this function interpolates a vector Y based on the input curve (XY Range). com, rapidshare. Time - Multiplication - Sim to Sim - 9. Crowther 1 Paul C. A cubic spline is a function f : → constructed by piecing together cubic polynomials p k (x) on different intervals [x [k], x [k+1]]. 1: Cubic Splines Interpolating cubic splines need two additional conditions to be uniquely defined Definition. • The requirement that it is to be a cubic spline gives us 3(n −1) equations. Input the set of points, choose one of the following interpolation methods (Linear interpolation, Lagrange interpolation or Cubic Spline interpolation) and click "Interpolate". The Kochanek-Bartels Splines (also called TCB-Splines) Now we're going down to the guts of curve interpolation. e, divide the interval into smaller sub-intervals, and construct different low degree polynomial approximations (with small oscillations) on the sub-intervals. Re: Cubic Spline VBA code Hey shg I have this code that i use for finding out y for any x using the data of x's and y's that i have (in my case it is the yield curve which i pasted above - tenor and yield points). Natural cubic splines vs. I wrote a thesis on expanding a model with cubic truncated power basis and B-spline. Then we will see how the Laplace transform and its inverse interact with the said construct. Piecewise linear interpolation • Same format as all other interpolants • Function diff finds difference of elements in a vector • Find appropriate sub-interval •Evaluate • Jargon: x is called a “knot” for the linear spline interpolant function v = piecelin(x,y,u) %PIECELIN Piecewise linear interpolation. •Challenge: If 𝑓′(𝑥 ) are not known, can we still generate interpolating polynomial with continuous derivatives? 8. There are all kinds of cubic curves available. Function approximation with regression analysis. SPLINE INTERPOLATION Spline Background Problem: high degree interpolating polynomials often have extra oscillations. After reading this chapter, you should be able to: 1. find the corresponding cubic spline and evaluate it at x =3. A second problem is the Hermite interpolant is smooth, but not smooth enough. A third degree polynomial and its derivative:. Cubic Spline Calculator shareware, freeware, demos: SRS1 Cubic Spline for Excel by SRS1 Software LLC, FRENCO Spline Calculator by FRENCO GmbH, NMath Core by CenterSpace Software etc. Catmull-Rom, Cardinal, and Kochanek-Bartels splines use four control points for each interval (that is the two immediately surrounding control points, and an extra control point on each side, for each interval). x n), using a natural cubic splines and where n may take any integer value. Get the free "Solve cubic equation ax^3 + bx^2 + cx + d = 0" widget for your website, blog, Wordpress, Blogger, or iGoogle. CERCHAP Slope in well-known data. Please help. • In addition we require that S(x i) = y i, i = 0,··· ,n which gives n +1 equations. By default, they are the range of the non-NA data. Free cubic spline: (I) Set up the 3 3matrixA and the 3 1 vector v: h0 0. 5, SL5, Win8, WP8, PCL 47 and. In general, a cubic spline with K knots uses cubic spline with a total of 4 + K degrees of freedom. Assayfit Pro is a curve fitting API for laboratory assays and other scientific data. Evaluate Length (Eval) Evaluate a curve at a certain factor along its length. This is shown on the right for 3 dimensions for all but the cosine interpolation. The method of cubic spline interpolation presented here is widely used in finance. We often want to know the values of a function, f, at various points but do not need to know them. The BoxWrench Engine Specs Database is a community resource for mechanics of all skill levels to access a reference library of Firing Orders, Distributor Rotation Directions and Block-Cylinder Numbering as well as Torque Specs, Timing Settings and Cylinder Head Tightening Sequences among other engine specs. C++ cubic spline interpolation. gauss_spline (x, n) Gaussian approximation to B-spline basis function of order n. Differentiate at point t. Square, Cube, Square Root and Cubic Root. Interpolation at x 0 through x n provides n + 1 equations. The second derivative of each polynomial is commonly set to zero at the endpoints, since this provides a boundary condition that completes the system of equations. Kernel smoothing. Figure 1 – A trajectory based on third-degree polynomials. În matematică, prin funcție algebrică de gradul al treilea sau, mai scurt, funcție cubică se înțelege orice funcție polinomială de următoarea formă: = + + +,în care singura condiție obligatorie se referă la coeficientul a, care trebuie să nu fie zero. For example second line of matrix (8,4,2,1,0,0,0,0) after matrix multiplication means this:. Get the free "Solve cubic equation ax^3 + bx^2 + cx + d = 0" widget for your website, blog, Wordpress, Blogger, or iGoogle. P and Q must both be specified for every G5 command. The idea of a spline interpolation is to extend the single polynomial of linear interpolation to higher degrees. For example (where "LogT_t1" is the log transformed concentration value of the first testosterone sample): mkspline Agesp = Age, cubic displayknots nknots(3) regress LogT_t1 Agesp*. You piecewise fit cubic polynomials using 4 data values (two points and two tangents) in order to create a smooth spline that passes from all given points. 1987 & 6 HP, 2-Stroke, Includes Merc 6 Mercury Outboard (Thru Hub Exhaust & 8 Tooth Spline). Online calculator for linear interpolation and extrapolation. 5 cubic inch pump. Please subscribe this channel for more videos on different topics. In the following we consider approximating between any two consecutive points and by a linear, quadratic, and cubic polynomial (of first, second, and third degree). com''s Gift Finder. We assume that the points are ordered so. Figure 1 – A trajectory based on third-degree polynomials. The syntax is smooth. cubic Software - Free Download cubic - Top 4 Download - Top4Download. In the simplest case, a first-order Bézier curve, the curve is a straight line between the control points. 0 Comments. Compression Ratio Calculator 1. To interpolate the y 2 value: x 1, x 3, y 1 and y 3 need to be entered/copied from the table. , curve interpolation and approximation). These were used to make technical drawings for shipbuilding and construction by hand, as illustrated by Figure 1. Cubic Spline (Piecewise Interpolation) - C PROGRAM | 6 Manas Sharma (c) Bragitoff. Home of the HI-FLOW lump kit. For the spline to interpolate the data, its value at t i must be y i. You can make the process of transfering the application to your calculator sweet and simple with Texas Instrument’s handy TI connect software. Polynomials of degree 3 are cubic functions. Find more Mathematics widgets in Wolfram|Alpha. Instead, the function f(x) will be evaluated at points chosen by the algorithm. Byju's Interpolation Calculator is a tool which makes calculations very simple and interesting. Trajectory Generation Path points : Initial, final and via points • cubic splines -- change set of coefficients at the end of each segment • linear with. Linear interpolant is the straight line between the two known co-ordinate points (x0, y0) and (x1, y1). The \( bs() \) function is used in R to fit a Cubic Spline. The other method used quite often is w:Cubic Hermite spline, this gives us the spline in w:Hermite form. Parameterised (fast) cubic spline calculates the series of constatnts A, B, C and D in the equation y=A + Bx + cx^2 + dx^3. 75 and u 4 = 1. Rutherford 1 Michael J. Though traditional standards for the exact length of an inch have varied, it is equal to exactly 25. Differentiate at point t. Heading angle of each point can be also calculated analytically. They share one thing with the hermite curves: They are still cubic polynomials, but the way they are calculated is different. Performance Ignition Systems, Caltracs Suspension, Cometic Custom Head Gaskets. The idea of a spline interpolation is to extend the single polynomial of linear interpolation to higher degrees. Cubic and Natural Cubic Splines. Spline • Drafting terminology –Spline is a flexible strip that is easily flexed to pass through a series of design points (control points) to produce a smooth curve. ÖIt is like securing a strip of elastic material (metal or plastic ruler) between knots (or nails). One can of this product treats up to 2,000 cubic feet of unobstructed space. As I confirmed today, the kind of spline it uses is not a simple cubic spline like the one described in the Wikipedia spline article ; Excel uses a (third-order) Bezier Spline , which is commonly used in computer. The cubic regression equation is: Cubic regression should not be confused with cubic spline regression. The velocity gradient equation with the as- sumption of a hub-to-shroud mean stream surface is solved along arbitrary quasi-orthogonals in the meridional plane. The interpolation procedure is recursive. A friend asked me for help on a cubic interpolation problem and since that was too easy I expanded it so I can use it on my projects. the end point of segment i is the same as the starting point of segment i + 1. Hi, I am new calculator. I am interested in using cubic splines to do data interpolation and extrapolation in Excel 2010. Restricted cubic splines are a powerful technique for modeling nonlinear relationships by using linear regression models. A quick googling showed me that there is no "closed form" solution. Step Functions. Cubic Interpolation: CERCHA Cubic spline interpolation. It is further shown that recalibration, using a cubic-spline adjustment, can improve performance beyond that currently observed. A cubic spline uses a cubic polynomial. It applies only in one dimension, but is useful for modeling yield curves, forward curves, and other term structures. For mathematical background, see course handouts on Lagrange interpolation , cubic Bezier curves , cubic spline curves , and nonuniform splines. The continuity of a cubic Bézier spline. Direct Method of Interpolation: Cubic Interpolation - Part 1. com offers free software downloads for Windows, Mac, iOS and Android computers and mobile devices. The non-polynomial cubic spline method has been used to solve many PDEs (Ramadan et al. The cubic parabola is a simple function of the form of y = f(x) and is based on the acknowledgment that its length is equal to its projection on axis X. A resource for JMP software users. That is, the function values and derivatives are speci ed at each nodal point. Q&A for cartographers, geographers and GIS professionals. The main menu allows you to enter the gear parameters easily. How to Graph in MATLAB. The spline passes through each data point. com/topics/d. " ↑ Wikipedia: Bezier spline#Approximating circular arcs ↑ Michael Hartl. We can see that a spline method works better than a cubic one in this case, just for extrapolations. When we have nonlinear relations, we often assume an intrinsically linear model (one with transformations of the IVs) and then we fit data to the model using polynomial regression. In the next section I'll show you one based on a cubic spline interpolation kernel. 75 and u 4 = 1. The cubic spline function is embedded in the workbook, which makes redistribution of workbooks that use the function very easy. GitHub Gist: instantly share code, notes, and snippets. of force on a hand brake, and 1200 psi. I NumberofknotsK @fcadb:56 r dbo :5m c b jCubic Spline from the main menu. An interpolated y value on a quadratic spline is found by using the general quadratic equation, y = a*x 2 + b*x + c, with the a, b, and c coefficients previously determined. The illustrations show both quadratic and cubic curves going through three fixed points, but with different t values specified (0. ÖThe final shape is quite smooth. “An LU-fuzzy Calculator for the Basic Fuzzy Calculus" in this paper we build an LU-fuzzy calculator, in order If v = w we obtain the ordinary cubic spline. κ-Curves: Interpolation at Local Maximum Curvature • 129:3 Fig. #crackthemaths Concept of Cubic Spline (Topic under the Subject Applied Numerical method) is Explained in a simple and easy way. For straight line or linear curves (Z = A x + B) the regression is performed directly on the X and Z data values. How do I normalise a quaternion? ----- A quaternion can be normalised in a way similar to vectors. Two of the four conditions required to specify a cubic are taken by placement of ‘control points. Evaluate Length (Eval) Evaluate a curve at a certain factor along its length. By a cute trick the cosine interpolation reverts to linear if applied independently to each coordinate. This generally provides a better fit to the data, and also has. the cubic spline by finding its coefficients. The syntax is smooth. 1 Interpolation of Parametric Curves using Cubic Spline The curve as shown here cannot be expressed as a function of one coordinate variable in terms of the other. The calculated result is correct though. CERCHAP Slope in well-known data. Use a text file to write and edit your R commands. You can see that the spline continuity property holds for the first and second derivatives and violates only for the third derivative. It is not meant to cover every detail of graphing in MATLAB, but should cover enough to get you started. A flash drum is used to separate methanol from water by concentrating the methanol in the vapor phase and the water in the liquid phase exiting the flash drum. For more videos and resources on this topic, please visit http://nm. To interpolate the y 2 value: x 1, x 3, y 1 and y 3 need to be entered/copied from the table. Dimensions over (under) pins, balls or wire for an involute gear. For the first G5 command in a series of G5 commands, I and J must both be specified. The default method is 'linear' (type help interp1 on the Matlab command window to see more details). In addition to spline conditions, one can choose piecewise cubic polyno-mials that satisfy Hermite interpolation conditions (sometimes referred to by the acronym PCHIP or Piecewise Cubic Hermite Interpolating Polynomials). com''s Gift Finder. Thus, the cubic spline has second order or C 2. Cubic spline interpolation • In the following, we want to derive the collocation matrix for cubic spline interpolation. Easy and simple—that’s how we want your differential experience to be. There is enough material in the topic of boundary value problems that we could devote a whole class to it. Spline is a collection of polygonal segments. TriLookup 2. The curve does not have to pass through each data point. com, rapidshare. Donald Schaefer built the below listed apps as Free iOS Apps. 4-5 HP, 2-Stroke Mercury Outboard (12 Tooth Spline). The new functions can be used for data. Assayfit Pro is a curve fitting API for laboratory assays and other scientific data. This page contains a cubic spline interpolation utility. 512 This is free software that adds several spline and linear interpolation functions to Microsoft Excel. 3D Hermite. The question wants me to evaluate a natural cubic spline at different S(x) values. To get that, I have to calculate positions of two control points of cubic bezier curve.