How to Plot the Trajectory of points on a bendRightAngle when Rotated 90 degrees

I am working on the moving sofa problem in mathematics and am trying to plot the trajectory of several points on an L shape when rotated 90 degrees. I have made a right angle L of unit width (see code below). What I would like to do is define sseveral reference points along the inside of my L. I would like to draw a trajectory of these points as the L is rotated 90 degrees. I would also like the coordinates of the trajectory of the reference points along the rotation. I am not sure if this is asking too much.

RightAngle = bendRightAngle(Name='RightAngle',ReferencePoint=[0,0],Length=[3,3],Width=[1,1])

I greatly appreciate any help.

Steven

[William Rose]

@steven, you said see code below but I don’t see it.

Answer 1

[William Rose]

@Steven Thompson,

Matlab can define a polygon. It could be convenient for your work. The only possible disadvantage is that a polyshape includes the corners only. A polyshape does not include additional points along a straight edge. If you want to track those with polyshape(), you might have to define sub-polygons.

Let's try Matlab's polygon functions:

sofa=polyshape([0,3,3,2,2,0],[0,0,2,2,1,1]);  %vertices of sofa
plot(sofa);

Now rotate the sofa with Matlab's rotate function.

theta=[15,30,45,60,75];     %rotation angles
refpoint=[0.5,0.5];         %point to rotate about
hold on; axis equal         %hold the current plot
for i=1:length(theta)
    plot(rotate(sofa,theta(i),refpoint));
end

[William Rose]

@Steven Thompson,

Here's a fun challenge: Find the right combinaitons of translate(sofa,...) and rotate(sofa,...) to get the sofa from the initial to the final position without intersecting the walls.

sofa=polyshape([0,3,3,2,2,0],[0,0,2,2,1,1]);    %vertices of sofa
plot(sofa,'FaceColor','g');                     %initial position
hold on; axis equal
plot(translate(rotate(sofa,180),[3,6]),'FaceColor','g');    %final position

Add walls and plot them

wall1=polyshape([0,3.8,3.8,-.1,-.1,3.8,3.8,0,0,3,3,0],...
    [0,0,-.1,-.1,6.1,6.1,6,6,3.05,3.05,2.95,2.95]);
wall2=translate(rotate(wall1,180),[7.6,6]);
plot(wall1,'FaceColor','k')
plot(wall2,'FaceColor','k')

[Sam Chak]

@William Rose, 👍 Inspired to make a Tetris game!

[William Rose]

:)

Answer 2

[William Rose]

You can define a nx2 array of points on the sofa

S=[0,0;1,0;2,0;3,0;3,2;2,2;2,1;1,1;0,1;0,0];

And plot it

plot(S(:,1),S(:,2),’-b.’);

Then multiply S by 2x2 rotation matrix R to get a new array with the rotated points. You can also combine with translation of the array of points.

Sorry can’t format this correctly, answering on phone.

R=[cos(t),sin(t);-sin(t),cos(t)];

t=angle to rotate by in radians

S1=S*R; %rotated array of points

Plot S1 like S but with a new color.

[William Rose]

Oh by that was formatted even worse than I expected. All my carriage returns disappeared!