Drawing a spiraling half circle

Question

Örs Istok 2020-5-22

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/530253-drawing-a-spiraling-half-circle

评论： Örs Istok 2020-5-22

Dear all,

I hit a wall while trying to solve this problem I have. I am trying to draw a spiraling half-circle (as seen in figure below, B) with n turns and extracting the x,y coordinates for the lines.

For now, I managed to draw something like (A), but I need to get the B. I atempted to do B myself, but I can only solve it by having the vertical lines slightly angled. Then I got an ideea to draw the geometry using something like iamfreehand function. Found a good code here(https://www.mathworks.com/matlabcentral/answers/320227-how-can-i-draw-with-mouse-as-we-do-in-paint) that does some of the job for the straight lines, but then I need to also draw the arcs that have a descending radius each turn and also displace the x middle coordinate of the n-th turn.

This is my attempt to solve B, but my problem is that... say the starting position(x2,y2) for arc n = 2 is not the same as ending position(x1,y2) for arc n = 1;

I haven't included yet the vertical lines.

clear all, close all
s = 0.01;
cx = 0; %arc center coordinate for x-axis
cy = 0; %arc center coordinate for y-axis
N = 51; %number of points / arc
d = 0.15; %circle diameter
r = d/2; % radius
ncoil = 3; %number of arcs
length = 2*pi*r + 2*r; %total length of coil 1 in meters
length_arc = 2*pi*r; 
a = length_arc/1000; 
a1 = (a:a:a*ncoil)'; 
sin_alfa(:,1) = a1./r;
alfa = asin(sin_alfa);
for i = 1 : ncoil
    for j = 1 : N
        th1(:,i) = linspace(-pi/2, pi/2-alfa(i,1),N);
        x_right(j,i) = ((r-10*a1(i,1)/2) .* cos(th1(j,i)) + cx + a1(i,1));
        y_right(j,i) = ((r-10*a1(i,1)/2) .* sin(th1(j,i)) + cy);
    end
end
for i = 1 : 1
figure(1)
plot(x_right, y_right)
hold on
daspect([1,1,1])
end
hold off

I know some of you have great ideeas to solve this, so please help me out. Any solution is wellcomed :)!

Thank you!

Ors.

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Answer 1

darova 2020-5-22

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/530253-drawing-a-spiraling-half-circle#answer_436303

在 MATLAB Online 中打开

Try polyxpoly. Here is a start

clc,clear
cla
[x,y] = pol2cart(-pi/2:.1:pi/2,1);    
for i = 3:5    
    r = 5+i;
    [xc,yc] = polyxpoly(r*x,r*y,[1 1]*(10-i),[-1 1]*10);
    line(r*x,r*y)
    line(xc,yc,'marker','.')
    pause(0.5)
end
axis equal