Plot an Arc on a 2D Grid by given radius and end points

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TS Low 2017-11-15

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https://ww2.mathworks.cn/matlabcentral/answers/367126-plot-an-arc-on-a-2d-grid-by-given-radius-and-end-points

回答： Navinda Wickramasinghe 2020-9-17

I have one question, how do I plot the arc on a graph by giving the radius and it end points? It start points is the points set by me take example (2,2). I need draw an arc with radius 3 and end point (5,5) How to write the code for this

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Answer 1

Roger Stafford 2017-11-15

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https://ww2.mathworks.cn/matlabcentral/answers/367126-plot-an-arc-on-a-2d-grid-by-given-radius-and-end-points#answer_291194

编辑：Roger Stafford 2017-11-15

在 MATLAB Online 中打开

(Correction made)

Point vectors A and B must be column vectors

   A = randn(2,1); % Point A to be on circle circumference
   B = randn(2,1); % Same with point B
   d = norm(B-A);
   R = d/2+rand; % Choose R radius >= d/2
   C = (B+A)/2+sqrt(R^2-d^2/4)/d*[0,-1;1,0]*(B-A); % Center of circle
   a = atan2(A(2)-C(2),A(1)-C(1));
   b = atan2(B(2)-C(2),B(1)-C(1));
   b = mod(b-a,2*pi)+a; % Ensure that arc moves counterclockwise
   t = linspace(a,b,1000);
   x = C(1)+R*cos(t);
   y = C(2)+R*sin(t);
   plot(x,y,'y-',C(1),C(2),'w*')
   axis equal

Note that another possible center can be obtained by

C2 = (B+A)/2-sqrt(R^2-d^2/4)/d*[0,-1;1,0]*(B-A);

Note 2: If C is chosen, the arc will be <= pi. If C2 is used, arc will be >= pi

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Roger Stafford 2017-11-15

For two given points, A and B, to lie on a circular arc with a given radius, there are two possible centers that can be used. One, in this case C, places the center to the left as you face from A toward B. The other, in this case C2, places the center to the right as you face from A toward B. The way this code is written, the arc always starts at point A with angle a and goes counterclockwise as t increases until reaching point B with angle b, which is always greater than or equal to a. That means if you use center C, you will always get an arc of less than or equal to pi radians. If you use center C2, you will always get an arc of greater than or equal to pi radians.

The user needs to be prompted for three things: point A, point B, and radius R. In this code A and B are each required to be a two-element column vector, that is, a vector with two rows and one column. The first element is to be the x-coordinate and the second the y-coordinate of a point on the circular arc that is to be created. The radius, R, is of course a scalar.

TS Low 2017-11-19