MATLAB: Tracing an arc on circumfrence of quarter circle

calculuscurve fittingleast square errorminimisation functionobjective-function

As per the given problem I have to place the arc on the circumfrence of quarter circle in the best possible way.....

Radius of Quarter curcle=55

Radius of arc= 9 and arc angle=60

The objective of the problem is that the arc bottom point should touch the green line as shown in figure. The quarter circle is divided into equal section of gap 'a'. we need to put the arc center in each zone in best way such that arc traces the quarter circle in best way as shown.

Data can be changed if desired…..

This problem required calculus to find best position of diffrent arc center

Arc radius=9 and arc angle=60 degrees. ( we only need to adjust the arc centeres x cordinate for all arcs)

All the arcs are identical and even there orientation are same and the arcs cannot be rotated.

a=55/6

b1 (given)=4.55

b2=b1+ 1*(a) = 4.55 +1* (55/6)

b3=b1+2*(a) = 4.55 + 2*(55/6)

b4=b1+3*(a) = 4.55 +3 *(55/6)

b5=b1+4*(a) = 4.55 +4 *(55/6)

b6=b1+5*(a) = 4.55 + 5*(55/6)

Best Answer

Solution:

I used fsolve to find: RedArea - BlueArea = 0

See script

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MATLAB: Draw arc in Matlab

There are no such functions in core MATLAB, but they’re easy enough to write.

This code plots an arc of stars:

circr = @(radius,rad_ang)  [radius*cos(rad_ang);  radius*sin(rad_ang)];         % Circle Function For Angles In Radians
circd = @(radius,deg_ang)  [radius*cosd(deg_ang);  radius*sind(deg_ang)];       % Circle Function For Angles In Degrees
N = 25;                                                         % Number Of Points In Complete Circle
r_angl = linspace(pi/4, 3*pi/4, N);                             % Angle Defining Arc Segment (radians)
radius = 1.5;                                                   % Arc Radius
xy_r = circr(radius,r_angl);                                    % Matrix (2xN) Of (x,y) Coordinates
figure(1)
plot(xy_r(1,:), xy_r(2,:), 'bp')                                % Draw An Arc Of Blue Stars
axis([-1.25*radius  1.25*radius    0  1.25*radius])             % Set Axis Limits
axis equal                                                      % No Distortion With ‘axis equal’

MATLAB: Dividing a circle into six equal parts

You could write a custom function to do this:

function P = plot_arc(a,b,h,k,r)
% Plot a circular arc as a pie wedge.
% a is start of arc in radians, 
% b is end of arc in radians, 
% (h,k) is the center of the circle.
% r is the radius.
% Try this:   plot_arc(pi/4,3*pi/4,9,-4,3)
% Author:  Matt Fig
t = linspace(a,b);
x = r*cos(t) + h;
y = r*sin(t) + k;
x = [x h x(1)];
y = [y k y(1)];
P = fill(x,y,'r');
axis([h-r-1 h+r+1 k-r-1 k+r+1]) 
axis square;
if ~nargout
    clear P
end

Now from the command line:

hold on
for ii = 1:6
   P(ii) = plot_arc(pi/3*(ii-1),pi/3*(ii),9,-4,3); 
end

If this doesn't do it, consider using the LINE function. For example, replace this line:

P = fill(x,y,'r');

with this:

P = line(x,y);

and possibly delete the calls to the AXIS function.

Best Answer

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MATLAB: Draw arc in Matlab

MATLAB: Dividing a circle into six equal parts

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