Interpolation | Splines (mathematics)
In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is, by its values and first derivatives at the end points of the corresponding domain interval. Cubic Hermite splines are typically used for interpolation of numeric data specified at given argument values , to obtain a continuous function. The data should consist of the desired function value and derivative at each . (If only the values are provided, the derivatives must be estimated from them.) The Hermite formula is applied to each interval separately. The resulting spline will be continuous and will have continuous first derivative. Cubic polynomial splines can be specified in other ways, the Bezier cubic being the most common. However, these two methods provide the same set of splines, and data can be easily converted between the Bézier and Hermite forms; so the names are often used as if they were synonymous. Cubic polynomial splines are extensively used in computer graphics and geometric modeling to obtain curves or motion trajectories that pass through specified points of the plane or three-dimensional space. In these applications, each coordinate of the plane or space is separately interpolated by a cubic spline function of a separate parameter t. Cubic polynomial splines are also used extensively in structural analysis applications, such as Euler–Bernoulli beam theory. Cubic splines can be extended to functions of two or more parameters, in several ways. Bicubic splines (Bicubic interpolation) are often used to interpolate data on a regular rectangular grid, such as pixel values in a digital image or altitude data on a terrain. Bicubic surface patches, defined by three bicubic splines, are an essential tool in computer graphics. Cubic splines are often called csplines, especially in computer graphics. Hermite splines are named after Charles Hermite. (Wikipedia).
Mod-01 Lec-08 Cubic Spline Interpolation
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Cubic Spline Interpolation (Part A) | Lecture 44 | Numerical Methods for Engineers
Derivation of the method of cubic splines for interpolation. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasno
From playlist Numerical Methods for Engineers
The Newton Fractal Explained | Deep Dive Maths
A Newton fractal is obtained by iterating Newton's method to find the roots of a complex function. The iconic picture of this fractal is what I call The Newton Fractal, and is generated from the function f(z)=z^3-1, whose roots are the three cube roots of unity. What is the history of th
From playlist Deep Dive Maths
Lecture 20: Introduction to Animation (CMU 15-462/662)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/
From playlist Computer Graphics (CMU 15-462/662)
Function approximation using Cubic Splines and Natural Cubic Splines including discussion about figuring out if two sets of equations are splines. Important note: around 1:10 the functions also need to go through the points at the ends ax1^3 + bx1^2 + cx1 + d = y1 ex3^3 + fx3^2 + gx3 + h =
From playlist Numerical Methods
Engineering CEE 20: Engineering Problem Solving. Lecture 21
UCI CIvil & Environmental Engineering 20 Engineering Problem Solving (Spring 2013) Lec 21. Engineering Problem Solving View the complete course: http://ocw.uci.edu/courses/cee_20_introduction_to_computational_engineering_problem_solving.html Instructor: Jasper Alexander Vrugt, Ph.D. Licen
From playlist Engineering CEE 20: Engineering Problem Solving
Mod-01 Lec-07 Piecewise Polynomial Approximation
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Interpolations and Mappings with Applications in Image Processing
In this talk, Markus van Almsick reviews the most popular and most advanced interpolation methods and discusses their merits and shortcomings. The Wolfram Language provides many interpolation methods to construct continuous functions from discrete data points. Furthermore, interpolations a
From playlist Wolfram Technology Conference 2020
Cubic splines using calculus | Wild Linear Algebra 25 | NJ Wildberger
In our last video, we talked about de Casteljau Bezier curves, mostly cubics, for design work. In this lecture we discuss another application of cubic splinesto the interpolation problem: finding a smooth curve passing through a finite number of points in the (x,y) plane. Our approach to
From playlist WildLinAlg: A geometric course in Linear Algebra
Hermite interpolation. Numerical methods, chapter 2, additional video no 3. To be viewed after video Ch02n2. Wen Shen, Penn State University, 2018.
From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University
Cubic Spline Interpolation (Part B) | Lecture 45 | Numerical Methods for Engineers
Part B of the cubic spline interpolation method. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirma
From playlist Numerical Methods for Engineers
Engineering CEE 20: Engineering Problem Solving. Lecture 20
UCI CIvil & Environmental Engineering 20 Engineering Problem Solving (Spring 2013) Lec 20. Engineering Problem Solving View the complete course: http://ocw.uci.edu/courses/cee_20_introduction_to_computational_engineering_problem_solving.html Instructor: Jasper Alexander Vrugt, Ph.D. Licen
From playlist Engineering CEE 20: Engineering Problem Solving
Mod-01 Lec-06 Cubic Hermite Interpolation
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
Code - Seminar 15 - Ethan (AstroCode) livecodes Futurama tubes
Ethan (AstroCode) livecodes Futurama tubes using CatRom splines. Ethan's Twitter: https://twitter.com/AstroCodeRblx Roblox profile: https://www.roblox.com/users/4798123/profile The webpage for this seminar is https://metauni.org/code/ You can join this seminar from anywhere, on any dev
From playlist Code seminar
Fourier sine and cosine series | Lecture 50 | Differential Equations for Engineers
Fourier series for even and odd periodic functions. Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov
From playlist Fourier
Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (56 of 92) What is a Hermite Polynomial?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a Hermite polynomial. Previous videos showed the solution best describe the quantum oscillator of the Schrodinger equation is the product of a constant that needed to be normalized, mu
From playlist THE "WHAT IS" PLAYLIST
The (Coarse) Moduli Space of (Complex) Elliptic Curves | The Geometry of SL(2,Z), Section 1.3
We discuss complex elliptic curves, and describe their moduli space. Richard Borcherd's videos: Riemann-Roch Introduction: https://www.youtube.com/watch?v=uRfbnJ2a-Bs&ab_channel=RichardE.BORCHERDS Genus 1 Curves: https://www.youtube.com/watch?v=NDy4J_noKi8&ab_channel=RichardE.BORCHERDS
From playlist The Geometry of SL(2,Z)
Ingrid Daubechies - 4/4 Time-Frequency Localization and Applications
Abstract: In this 250th anniversary year of the birth of Joseph Fourier, it behoves us to talk of frequency and spectral analysis! The lectures shall visit a number of different techniques that have been developed and applied in the last 30 years, to carry out what engineers and applied m
From playlist Hadamard Lectures 2018 - Ingrid DAUBECHIES - Time-Frequency Localization and Applications