How to draw three circles with centers and radii given?

Question

Curious 2022-6-27

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链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1748675-how-to-draw-three-circles-with-centers-and-radii-given

评论： Image Analyst 2022-7-13

I have entered the data in this program and tried to draw three circles on same figure which would then give me their intersection in x and y but I can't cuz there is no command for circles. Kindly assist.

clc
clear all
close all
x1=2; y1=8; r1=10;
x2=5; y2=5; r2=12;
x3=4; y3=9; r3=9;
function circle(x,y,r);
h=plot(x
Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.

Error in connector.internal.fevalMatlab

Error in connector.internal.fevalJSON
drawCircle([x1;x2], r1, 'r');
drawCircle([x2;y2], r2, 'g');
drawCircle([x3;y3], r3, 'b');
x=((y2-y1)*((y2^2-y1^2)+(x2^2-x1^2)+(r1^2-r2^2))- (y1-y2)*((y3^2-y2^2)+(x3^2-x2^2)+(r2^2-r3^2)))/2*((x1-x2)*(y2-y3)-(x2-x3)*(y1-y2))
y=((x2-x3)*((x2^2-x1^2)+(y2^2-y1^2)+(r1^2-r2^2))- (x1-x2)*((x3^2-x2^2)+(y3^2-y2^2)+(r2^2-r3^2)))/2*((y1-y2)*(x2-x3)-(y2-y3)*(x1-x2))
plot(x,y)

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Answer 1

Image Analyst 2022-6-27

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1748675-how-to-draw-three-circles-with-centers-and-radii-given#answer_994470

在 MATLAB Online 中打开

"I can't cuz there is no command for circles" <== there is if you have the Image Processing Toolbox.

x1=2; y1=8; r1=10;

x2=5; y2=5; r2=12;

x3=4; y3=9; r3=9;

viscircles([x1, y1], r1, 'Color', 'r');

viscircles([x2, y2], r2, 'Color', 'g');

viscircles([x3, y3], r3, 'Color', 'b');

As far as determining intersection points, you'll have to use math for that. Or else use a distance formula on your (x,y) arrays.

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Curious 2022-7-13

在 MATLAB Online 中打开

x1=2; y1=8; r1=10;

x2=5; y2=5; r2=12;

x3=4; y3=9; r3=9;

viscircles([x1, y1], r1, 'Color', 'r');

viscircles([x2, y2], r2, 'Color', 'g');

viscircles([x3, y3], r3, 'Color', 'b');

hold on

x=(((x2-x3)*((x2^2-x1^2)+(y2^2-y1^2)+(r1^2-r2^2))-(x1-x2)*((x3^2-x2^2)+(y3^2-y2^2)+(r2^2-r3^2))))/(2*((y1-y2)*(x2-x3)-(y2-y3)*(x1-x2)))

x = -14.8889

y=(((y2-y3)*((y2^2-y1^2)+(x2^2-x1^2)+(r1^2-r2^2))-(y1-y2)*((y3^2-y2^2)+(x3^2-x2^2)+(r2^2-r3^2))))/(2*((x1-x2)*(y2-y3)-(x2-x3)*(y1-y2)))

y = -4.5556

plot(x , y,'r*')

I have tried this code of yours with a mathematical formula for intersection point but it's not giving the intersection. Any thoughts?

Image Analyst 2022-7-13

You have to get the equation of a circle and set them equal to each other, like

(x-x1c).^2 + (y - y1c).^2 - R1^2 = (x-x2c).^2 + (y - y2c).^2 - R2^2

Then solve for x and y. It might be easier to do numerically than analytically but maybe not. You'd have to multiply it out, collect terms, etc. just like you'd solve any equation.

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