MATLAB: Strange slope for points in a curve

gradient; tangent; imaging processing

Dear experts, I want to get the slope for each point from the curve defined below:

x = 1194:1206;
y =[114,115,117,118,119,120,122,123,124,126,127,128,129];

see the attached graph for the curve.

Directly applying the function "gradient" cannt get the correct slope – the slope will jump up an down. It's understandable that I don't have enough data points. I expect the slope changes gradually.

I expect not to use any interpretation or curve fitting method. Any suggestion is welcome. Many thanks

Best Answer

There are two slopes at each point. The left slope and right slope? What you want to do about that?

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Try this:

x=[142;127;181;234];
y=[251;251;261;255];
[x, idx] = sort(x);
y = y(idx);
points = [x y];
xint = linspace(127,234,50)';
spl = spline(x,y);
tangent_vector = zeros(4,2);
for i=1:4
    if i==4 % last polynomial need to evalauted at endpoint
        deri_coef = polyder(spl.coefs(i-1,:));
        tangent_vector(i, :) = [1 polyval(deri_coef, x(end)-x(end-1))];
    else
        deri_coef = polyder(spl.coefs(i,:));
        tangent_vector(i, :) = [1 polyval(deri_coef, 0)];
    end
end
normal_vec = [-tangent_vector(:,2) tangent_vector(:,1)];
start_points = points;
end_points = 10*normal_vec + points;
fig = figure;
ax = axes();
hold(ax);
t = plot(y,x,'.',ppval(spl,xint),xint,'r-');
for i=1:4
    p1 = start_points(i,:);
    p2 = end_points(i,:);
    plot([p1(2) p2(2)], [p1(1) p2(1)], 'r', 'LineWidth', 2);
end
daspect([1 1 1]);
xlim([180 340])
ylim([100 250])

Best Answer

Related Solutions

MATLAB: Alternative to diff(X)

MATLAB: How to draw normal line at given points

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