Let w(t) be a blended piecewise- linear trajectory through the points {wo, w', w} with segment traversal times of {T} and a blend transition time of AT. Then the blend acceleration a is as in Prop. 4-7-2, and the complete trajectory is: w(t) wo + = a - Aw' T₁ 0≤1 ≤T-AT T₁ + AT)² + Aw'(1-T) T₁ + w₁ T₁ AT <
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using by matlab and show me the code
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- B. Suppose we wish to animate a bouncing ball. We are given keyframes for the ball's motion. The key frames are at times T = {0, 3, 9, 15} with associated height values of H = {1, 6, 8, 3}. 1. Plot the graph of height versus time using linear interpolation between key frames. 2. Since the ball's speed changes as it falls and as it bounces, linear interpolation will not give a realistic result. Which method would create the most realistic bounce? And how would the graph look like? H 16- 14- 12- 10- 8- 6- 4- 2- 0- →T 4 6 8. 10 12 14 16A fixed beam is subjected to a uniformly-distributed load with an intensity of f = 10 N/mm length of L = 200 mm. Now determine the support reaction forces, internal shear forces and moments, then plot its internal shear force and moment diagram. f[N/m] L 1. Define the paramters, use L and f as the variables y XLet G= (V, E) be an arbitrary flow network with source s and sink t, and a positive integer capacity c(u, v) for each edge (u, v)∈E. Let us call a flow even if the flow in each edge is an even number. Suppose all capacities of edges in G are even numbers. Then,G has a maximum flow with an even flow value.
- We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b]. Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1,x2,..., X., XN. Each interval is Ax = (b − a)/N. The equation for the Simpson numerical integration rule is derived as: f f(x)dx ≈ [ƒ(x0) + 4 (EN-1,n odd S(x)) + 2 (Σ2²n even f(x)) + f(XN)]. Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is f(x) = 2x³ (Already defined in the function, no need to change). *Complete the function given the variables N, a,b and return the value as "TotalArea"." "Don't change the predefined content' only fill your code in the region *YOUR CODE"" from math import * def InterageSimpson (N, a,…We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b] . Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1, X2, ..., Xn,..., XN. Each interval is Ax = (b – a)/N. The Simpon numerical integration rule is derived as: N-2 Li f(x)dx = * f(x0) + 4 (2n odd f(xn)) + 2 ( En=2,n even N-1 f(x,) + f(xn)] . Now complete the Python function InterageSimpson(N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is f (x) = 2x³ (Already defined, don't change it). In [ ]: # Complete the function given the variables N,a,b and return the value as "TotalArea". # Don't change the predefined content, only fill your code in the region "YOUR CODE" from math import * def InterageSimpson (N, a, b): # n is…We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b] . Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1, x2,.. Xn,..., XN. Each interval is Ax = (b − a)/N. The equation for the Simpson numerical integration rule is derived as: f f(x) dx N-1 Ax [ƒ(x0) + 4 (Σ1,n odd f(xn)) ƒ(x₂)) + f(xx)]. N-2 + 2 (n=2,n even Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is ƒ(x) = 2x³ (Already defined in the function, no need to change).
- Simplify the boolean function using carno map in it.Write a program in Scilab that samples f (x )=3e^−x sinx at x=0,1,2,3,4,5 and then, on the same graph, plots nearest-neighbor, linear and spline interpolations of these data using the interp1 function. The interpolation plots should have 200 samples uniformly spaced over 0≤x≤5 .using matlab 1. Plot the following functions on the same graph for x values from −2π to 2π,selecting spacing to create a smooth plot:y1 = sin(x)y2 = sin(2x)y3 = sin(3x).Adjust the plot so that• Line 1 is red and dashed.• Line 2 is blue and solid.• Line 3 is green and dotted.
- In Sammon mapping, if the mapping is linear, namely, g(x|W) = WTx, how can W that minimizes the Sammon stress be calculated?use a CAS to perform the following steps for the given curve over the closed interval. a. Plot the curve together with the polygonal path approximations for n = 2, 4, 8 partition points over the interval. b. Find the corresponding approximation to the length of the curve by summing the lengths of the line segments. c. Evaluate the length of the curve using an integral. Compare your approximations for n = 2, 4, 8 with the actual length given by the integral. How does the actual length compare with the approximations as n increases? Explain your answer. x = 2t^3 - 16t^2 + 25t + 5, y = t^2 + t - 3, 0 … t … 6Let (X, Y) - Uniform(D) with DC R2 being a disc contered at the point (a, b) (s00 the Figure below). Dofine V(x-a)2 +(Y-6)2 Out of the four random variables X, Y,0, R. find a pair which Y-by = arctan and R is independent. (,4) O (X,Y) O (X, R) O (X, e) O (R,Y) o (e,Y) O (R,e) 1. Out of the four random variables X,Y, R, 0. find a pair which is independent. True O False 2. The random variables X, Y aro uncorrolatod.