MATLAB -- how to create a parabolic arc?

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Dominic
Dominic 2013-4-15
回答： Melek Cavlak 2022-12-4
Example, I have three points x1, x2, and x3.
x1 is the start point of the arc; x3 is the end point of the arc; x2 is the critical point of the arc (where the tangent slope is zero).
If x2<x1, then the arc is a U-shaped (smiley); If x2>x1, then the arc is a upside-down-U-shaped (upside smiley).
Any ideas?
  1 个评论
Youssef Khmou
Youssef Khmou 2013-4-15
编辑：Youssef Khmou 2013-4-15
that condition is done automatically by the equation ax²+bx+c

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采纳的回答

Youssef Khmou
Youssef Khmou 2013-4-15
编辑：Youssef Khmou 2013-4-15
hi,
The parabola's equation is defined y=ax²+bx+c, you need to set the coefficients a,b,and c so as the line passes through the three points x1,x2 and x3 :
x1=[0,0];
x2=[5,5];
x3=[10,0];
Y=[x1(2);x2(2);x3(2)]
A=[x1(1)^2 x1(1) 1;x2(1)^2 x2(1) 1;x3(1)^2 x3(1) 1]
X=inv(A)*Y
x=x1(1):0.1:x3(1);
Y=X(1)*x.^2+X(2)*x;
figure, plot(x,Y), grid on,
hold on
text(x1(1),x1(2), ' POINT X1')
text(x2(1),x2(2), ' POINT X2')
text(x3(1),x3(2), ' POINT X3')
hold off
  5 个评论
显示 3更早的评论
sushant panhale
sushant panhale 2017-9-29
can you tell me, how to find the values of x if you have y values
Tyler Clausen
Tyler Clausen 2018-2-15
how would you do this with the points (-15,2), (1,4), and (3,5)? I keep getting wrong y coordinates when I plot.

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更多回答（3 个）

Jim Riggs
Jim Riggs 2018-2-15
编辑：Jim Riggs 2018-2-15
This is a simple polynomial curve fit problem. If you have the curve fitting toolbox, the problem is solved by:
x = [0 5 10];
y = [0 5 0];
fit(x,y,'poly2');
This will give the coefficients for the second order polynomial. With only 3 point, the fitted curve will pass exactly through all three points. This function will work for any three points, as long as they are no colinear.
If you do not have the curve fitting toolbox, its not too hard to build a function which will perform polynomial curve fitting. If you are interested, I will help you work out the equations.
Vetrivel
Vetrivel 2022-8-30
x = [0 5 10];
y = [0 5 0];
fit(x,y,'poly2');
Melek Cavlak
Melek Cavlak 2022-12-4
x = [0 5 10];
y = [0 5 0];
fit(x,y,'poly2');

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