How to map a point inside a circle to circle area in MATLAB?

Hi I have a point inside a circle in MATLAB. I want to map it to circle environment. I did this but it is not always useful!

function [xr,yr] = FindSurroundingPoint(xc,yc,x2,y2,r)
  x=x2-xc;
  y=y2-yc;
  angle=atan(y/x);
  if(x<0 && y<0)||(x<0&&y>0)
       angle = angle + pi;
  end
  xr=cos(angle)*r + xc;
  yr=sin(angle)*r + yc;
end

Answer 1

[Image Analyst]

Not sure what you're after, but perhaps this will help. It looks like you're trying to find where the line between two points intersects a circle around the first point.

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
markerSize = 40;

% Define parameters
xc=2;
yc=2;
x2=3;
y2=4;
r=1;

% Plot diagram of points and circle.
plot(xc, yc, 'b.', 'MarkerSize', markerSize)
grid on;
hold on;
plot(x2, y2, 'b.', 'MarkerSize', markerSize)
viscircles([xc, yc], r);
axis equal
xlim([0, 4]);
ylim([0, 5]);

% Find the point where the circle intersects
% the line going between the two points.
[xr, yr] = FindSurroundingPoint(xc,yc,x2,y2,r)

% Put line at yr to see where line intersects the circle.
yline(yr, 'Color', 'r', 'LineWidth', 2);
% Put line at xr to see where line intersects the circle.
xline(xr, 'Color', 'r', 'LineWidth', 2);
caption = sprintf('(xr, yr) = (%.3f, %.3f)', xr, yr);
title(caption, 'FontSize',fontSize);

%===================================================================
function [xr, yr] = FindSurroundingPoint(xc,yc,x2,y2,r)
deltax = x2 - xc
deltay = y2 - yc
line([xc, x2], [yc, y2], 'Color', 'b')
angle = atand(deltay/deltax)
if(deltax<0 && deltay<0) || (deltax<0&&deltay>0)
    angle = angle + 180
end
xr = cosd(angle) * r + xc
yr = sind(angle) * r + yc
end