Question

Please write code in MATLAB. This is an ungraded HW assignment

(5pts). The percentage of light (L) passing through the sea surface that penetrates to specific depths (D) in clean ocean water is as follows: 3. D (m0 2 10 50 100 L(96) | 100 | 45 0.5 39 Use the interpl function to produce piecewise linear, spline and cubic Hermite interpolations, and compute the percentage of light at 30m below the surface. Use the subplot function to present your findings in a 3-by-1 grid. Each plot should contain: a) the original data points (denoted with a circle marker); b) interpolation (denoted with a dash-dotted line); c) a data point corresponding to a calculated solution (denoted by a diamond marker). In each plot display your computed value for percent transmittance next to the diamond marker.

Answer 1

Code:

clear
clc

D = [0 1 2 10 50 100];
L = [100 45 39 22 5 0.5];
Dq = 0:100; % Query points
p1 = interp1(D, L, Dq, 'linear');
p2 = interp1(D, L, Dq, 'spline');
p3 = interp1(D, L, Dq, 'pchip');

L1 = p1(Dq == 30);
L2 = p2(Dq == 30);
L3 = p3(Dq == 30);

figure('Renderer', 'painters', 'Position', [10 10 900 700])
subplot(3, 1, 1)
plot(D, L, 'ro');
hold on
plot(Dq, p1, '-.');
plot(Dq(Dq == 30), L1, 'dk');
xlabel('D(m)');
ylabel('L(%)');
title("Piecewise Linear interpolation");
legend('data', 'interpolated points', 'L at D = 30m');

subplot(3, 1, 2)
plot(D, L, 'ro');
hold on
plot(Dq, p2, '-.');
plot(Dq(Dq == 30), L2, 'dk');
xlabel('D(m)');
ylabel('L(%)');
title("Spline interpolation");
legend('data', 'interpolated points', 'L at D = 30m');

subplot(3, 1, 3)
plot(D, L, 'ro');
hold on
plot(Dq, p3, '-.');
plot(Dq(Dq == 30), L3, 'dk');
xlabel('D(m)');
ylabel('L(%)');
title("Cubic Hermite interpolation");
legend('data', 'interpolated points', 'L at D = 30m');

Output:

Piecewise Linear interpolation rte pelted poirts LatD 30m . 60 100 20 40 TU 90 Dim) Spline interpolation data LatD- 30m 100 10 D(m) Cubic Hermite interpolation data -..inte.pclded porte 20 40 BC 90 Dim)