Question

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How can I parametrize a line with many points. let, P1(X1,Y1),P2(X2,Y2),P3(X3,Y3),......Pn(Xn,Yn). then I want to find the two intersection points with a circle and this circle has radius 4 and the center P3(X3.Y3) which is on the line.

Answer 1

dalvoron, can you help me?

Answer 2

Step 1: Pick any 2 points on the line,
Step 2: Find the slope of the line:\[m=\frac{y_2-y_1}{x_2-x_1}\]Step 3: Find the equation of the line:\[m=\frac{y-y_1}{x-x_1}\]
Step 3a:Optionally, rearrange it into the form \(y=mx+c\)
Step 4: Find the equation of the circle:
\[(x-X3)^2+(y-Y3)^2=r^2\]
Step 5: Simultaneous equations! Substitution is probably the method to go with.

Answer 3

Do you Know
How can I parametrize a line with many points. let, P1(X1,Y1),P2(X2,Y2),P3(X3,Y3),......Pn(Xn,Yn).

Answer 4

IF i can parametrize the line then I can find it
What do you think?

Answer 5

The beautiful thing about a line is that the paramaterisation is exactly the same everywhere along the line. It doesn't matter how many points there are, you can paramaterise it by just picking 2 of them.

Answer 6

thanks for the information. I don't know that. Whole day I am searching for that.

Answer 7

I parametrize the line using two points. Then I found the value of parameter then I plug the value to find x and y for the intersect but I got wrong ans

Answer 8

Could you post your method?

Answer 9

I am gonna posting my data file

Answer 10

line = span{v}+b

maybe

Answer 11

what is span{v}+b

Answer 12

span{v} is just the basis for parallel line thru the origin; vector you add to move it to the actual points

Answer 13

I took two points P1(7 1) and P2(7 2). then I used parametric equation line=P1+t(P2-P1)
i got (7 1)+t(0 1) then (0*t+7, 1*t+1) = (7, t+1)

Answer 14

t(slope) = span{v} but thats just semantics

Answer 15

your slope is undefined

Answer 16

i spose 0,1 is good as any

Answer 17

amistre64 I have no idea about your method. Can you explain more easily. I need to solve this and then need to write a fortran code for this. I am writing code for the first time.

Answer 18

your method is good, perse. what issues are you running up on?

Answer 19

\[\vec{v}={{0}\choose{1}};\vec{b}={{7}\choose{0}}\]
\[\vec{x}=t\vec{v}+\vec{b}\]

Answer 20

I took two points P1(7 1) and P2(7 2). then I used parametric equation line=P1+t(P2-P1) i got (7 1)+t(0 1) then (0*t+7, 1*t+1) = (7, t+1)
where x = 7 and y = t+1. then I put this value into circle equation
(x-XC)^2+(y-YC)^2=R^2 and solve for t

Answer 21

you need to end up with: (7,t)

which is a vertical line thru x=7

Answer 22

I have attach a file for my data.