Several tangent vectors on curve

Question

Viktor Karlsson 2021-5-14

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https://ww2.mathworks.cn/matlabcentral/answers/830243-several-tangent-vectors-on-curve

评论： Viktor Karlsson 2021-5-17

采纳的回答： the cyclist

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Hello,

I have the following curve plotted:

Now, I want 10 tangent vectors along this curve and I can't seem to figure out how to write the code for this to work. I wrote the following:

t = linspace(-2.5,2.5,100);
x = t.^3 - 4*t;
y = t.^2;
plot(x,y,'LineWidth',2)
axis equal
hold on
i=1:10:100;  
ts=t(i);
xs=x(i); 
ys=y(i); 
tx = ts.^3 -4*ts;
ty = ts.^2;
quiver(tx,ty,xs,ys,'LineWidth',2,'Color','r')
hold off

and the result is.. not quite it:

Any help or advice is appreciated.

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Answer 1

the cyclist 2021-5-14

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https://ww2.mathworks.cn/matlabcentral/answers/830243-several-tangent-vectors-on-curve#answer_699948

编辑：the cyclist 2021-5-14

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Well, you never actually calculated the tangent, so it is not that surprising you didn't get the correct result.

t = linspace(-2.5,2.5,100);

x = t.^3 - 4*t;

y = t.^2;

dydt = 2*t;

dxdt = 3*t.^2 - 4;

dydx = dydt./dxdt;

i=1:10:100;

ts=t(i);

xs=ones(size(i));

ys=dydx(i);

tx = ts.^3 -4*ts;

ty = ts.^2;

figure

hold on

plot(x,y,'LineWidth',2)

quiver(tx,ty,xs,ys,'LineWidth',2,'Color','r')

axis equal

Apologies for rearranging your code to my liking. See this page for the math of calculating the tangent of a parametric equation. (You'll need to be careful if dx/dt is ever zero, because you divide by that.)

Also, I was lazy and just set the length of the x-component of the tangent vector to (positive) 1, then calculated the y-component. You probably want something less lazy.