Find intersection of curve and line.

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A Akhilesh
A Akhilesh 2021-4-1
评论： Star Strider 2021-4-5
i have two equations yw and y1 i need to find intersection of both line and curve and then find the distance of the point from origin. i have only points of y and x for making the curve and have used polynomial interpolation for that
clear
syms x1
x=[0;1;2;3];
y=[7;5;11;28];
for i=1:4
for j=1:4
a(i,j)=power(x(i),(j-1));
end
end
b=inv(a)*(y);
yw=tan(deg2rad(10))*x1+20;
y1=b(1,1)+(b(2,1)*x1)+(b(3,1)*x1.^2)+(b(4,1)*x1.^3);
fplot(yw,[0,5])
hold onclc
fplot(y1,[0,5])

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Star Strider
Star Strider 2021-4-1
Try this:
syms x1
x=[0;1;2;3];
y=[7;5;11;28];
for i=1:4
for j=1:4
a(i,j)=power(x(i),(j-1));
end
end
b=inv(a)*(y);
yw=tan(deg2rad(10))*x1+20;
y1=b(1,1)+(b(2,1)*x1)+(b(3,1)*x1.^2)+(b(4,1)*x1.^3);
xv = vpasolve(y1-yw==0,x1) % X-Value At Intersection
yv = subs(yw, x1, xv) % Y-Value At Intersection
figure
fplot(yw,[0,5])
hold on
fplot(y1,[0,5])
plot(double(xv), double(yv), '+r')
hold off
xlim([0 5])
legend('yw','y1','Intersection', 'Location','best')
.
  2 个评论
A Akhilesh
A Akhilesh 2021-4-5
Hey!, thanks for the answer. i would like to know if the same thing would work when i have n points defining my curve, which gives me an nth degree polynomial.
Star Strider
Star Strider 2021-4-5
As always, my pleasure!
Calculating the intersections of lines defined by data (rather than expressions) from two different data sets is similar in concept, although the code differs. See Plot a point of intersection between 2 lines or curves for a typical approach.

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