How to plot specified semi-circle, rectangle ?

Hi all

I have 2 points, and need to plot semi-circle, rectangle as folowing picture.

semi-circle need to perpendiculars with slope of 2 points line.

In Case A - simple case which Ay = By. I created code as:

A = [2,2];
B = [5,2];

plot([A(1) B(1)],[A(2) B(2)],'-og');
hold on;

x_centerCircle = A(1);
y_centerCircle = A(2);
r=1; % Radius 1m

theta = linspace(pi/2, 3*pi/2, 100);
xCirc = r * cos(theta) + x_centerCircle;
yCirc = r * sin(theta) + y_centerCircle;

plot(xCirc, yCirc, 'r');

plot([xCirc(1), xCirc(end)], [yCirc(1), yCirc(end)], 'r');
rectangle('Position',[x_centerCircle x_centerCircle-0.075 5 0.15], 'EdgeColor', 'r');
grid on;
xlim([0 8]);
ylim([0 4]);

But when line AB does not parallel with Ox (Case B), becomes more difficult.

Do anyone show me how to plot for all cases?

Thank you so much

Answer 1

[Voss]

You can create shapes of that type as a single patch object.

Below is a function that does it, and here are some examples of its usage:

create_semi_rect_patch();%[2 2],[5 2],0.15,1)
axis equal

figure();
create_semi_rect_patch([2 2],[2+sqrt(7.56) 3.2],0.15,1);
axis equal

figure();
create_semi_rect_patch([0 2],[0 10],2,1.5);
axis equal

figure();
create_semi_rect_patch([-2 2],[0 0],1,1.5,4);
axis equal

function p = create_semi_rect_patch(A,B,h,r,Npts_semi)

if ~nargin || isempty(A) % if no A specified, use [2 2]
    A = [2 2];
end
if nargin < 2 || isempty(B) % if no B specified, use [5 2]
    B = [5 2];
end
if nargin < 3 || isempty(h) % if no h specified, use 0.15
    h = 0.15;               % (half-height of the rectangle)
end
if nargin < 4 || isempty(r) % if no r specified, use 1
    r = 1;                  % (radius of the semi-circle)
end
if nargin < 5 || isempty(Npts_semi) % if no Npts_semi specified, use 100
    Npts_semi = 100;                % (number of points along semi-circle)
end

% angle from A to B:
theta = atan2(B(2)-A(2),B(1)-A(1));

% coordinates of the corners of the rectangle:
corner_offset = h*[1;-1]*[cos(theta+pi/2) sin(theta+pi/2)];
rect_points = [A+corner_offset; B+corner_offset];

% coordinates of the points along the semi-circle:
theta_semi = linspace(theta+pi/2,theta+3*pi/2,Npts_semi).';
semi_points = A+r*[cos(theta_semi) sin(theta_semi)];

% create the patch:
p = patch( ...
    'XData',[semi_points(:,1); rect_points([2 4 3 1],1)], ...
    'YData',[semi_points(:,2); rect_points([2 4 3 1],2)], ...
    'FaceColor','flat', ...
    'EdgeColor','none', ...
    'FaceVertexCData',[1 0 0], ...
    'FaceAlpha',0.2);

end

[galaxy]

@Voss

Thank you for your answer.

I had idea about rotation position for each points.

clc;
clear all;


A = [8,1];
B = [5,2];

plot([A(1) B(1)],[A(2) B(2)],'-og');
hold on;

x_centerCircle = A(1);
y_centerCircle = A(2);
r=1; % Radius 1m

theta = linspace(pi/2, 3*pi/2, 100);
xCirc = r * cos(theta) + x_centerCircle;
yCirc = r * sin(theta) + y_centerCircle;

xyCirc = zeros(2, length(xCirc));
for cnt = 1:length(xCirc)
    xyCirc(:,cnt) = RotationPoint(A, B, [xCirc(cnt), yCirc(cnt)]);
end

xCirc = xyCirc(1,:);
yCirc = xyCirc(2,:);
            
plot(xCirc, yCirc, 'r', 'Tag', 'pos_shape');
plot([xCirc(1), xCirc(end)], [yCirc(1), yCirc(end)], 'r', 'Tag', 'pos_shape');

bbox = [A(1) A(2)-0.075 5 0.15];
points = bbox2points(bbox);

rec_points = zeros(2, length(points));
for cnt = 1:length(points)
    rec_points(:,cnt) = RotationPoint(A, B, [points(cnt,1), points(cnt,2)]);
end

points2 = horzcat(rec_points(1,:)', rec_points(2,:)');
points2(end+1,:) = points2(1,:);
plot(points2(:,1),points2(:,2), '*-');

grid on;
xlim([-10 10]);
ylim([-10 10]);

function [rotated_Point] = RotationPoint(point1, point2, rotationPointIn)
    
    AB = point2-point1;
    
    theta = atan2(AB(2), AB(1));
    
    Rot_by_theta=[cos(theta) -sin(theta) ; sin(theta) cos(theta)];
    
    AC_ = [rotationPointIn(1) - point1(1); rotationPointIn(2) - point1(2)];

    A_ = [point1(1); point1(2)];
    
    rotated_Point = Rot_by_theta * AC_ + A_;   
end

It is Ok for me.

But your idea also fantastic. I will consider to use your function.

Thank you so much.