I got the problem with polyshape, please help me

Demand: sketch the domain D be the region bounded by

My code:

x1 = 0:1:30;
y1 = 2-x1;
y2 = sqrt(x1).*(12-x1)./2;
xcut = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 0.5);
x = [x1(x1<=xcut), x1(end)];
y = [sqrt(x1).*(12-x1)./2 (x1<=xcut), 2-x1(end)];
M = polyshape(x,y);
plot(x1,y1,x1,y2,x,y)
hold on
plot(M)
hold off
xlim([0,30])
ylim([0,30])

Error:

Error using polyshape/getXY

x- and y-coordinates must be vectors of the same size with at least 3 elements.

Error in polyshape/checkInput (line 842)

[X, Y, xy2input, next_arg] = polyshape.getXY(varargin{:});

Error in polyshape (line 169)

[X, Y, tc, simpl, collinear] = polyshape.checkInput(param, varargin{:});

Error in bai4 (line 7)

M = polyshape(x,y);

[Matt J]

The domain of the first function is x>=0 and the domain of y=2-x is all .Neither domain is bounded, and therefore cannot be sketched.

[John D'Errico]

As well, you cannot use polyshape on unbounded regions.

[Thai Anh]

@John D'Errico can you help me to fix it

[Thai Anh]

oh I'm sorry.

The demand is sketch the domain D be the region bounded by

Answer 1

[Stephan]

You have to take both points into account to find a closed region:

xcut1 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 0.5);
xcut2 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 20);

I had the code ready here - but homework is homework... I leave the rest to you. It should be easy now...

[Thai Anh]

I appreciate that a lot :3

Thanks

[Thai Anh]

sorry but I still cannot solve it

Is this right ?

x1 = 0:1:30;

y1 = 2-x1;

y2 = sqrt(x1).*(12-x1)./2;

xcut1 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 0.5);

xcut2 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 20);

x = [x1(x1>=xcut1), x1(x1<=xcut2)];

y = [sqrt(x1).*(12-x1)./2 -2+x1(x1>=xcut1),sqrt(x1).*(12-x1)./2 -2+x1(x1<=xcut2)];

M = polyshape(x,y);

plot(x1,y1,x1,y2,x,y)

hold on

plot(M)

hold off

xlim([0,30])

ylim([0,30])

[Thai Anh]

can you explained it clearly or give me some hints please .

Thanks in advance @Stephan

[Stephan]

your x used for the polyshape should look like:

x = xcut1:0.1:xcut2;

then think about the corresponding y values...

Hint: Use the false flag for the simplify option of the polyshape function to suppress warnings:

M = polyshape([YOUR X],[YOUR Y], 'simplify', false);

[Thai Anh]

I tried but it still cannot work.

x1 = 0:1:30;
y1 = 2-x1;
y2 = sqrt(x1).*(12-x1)./2;
xcut1 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 0.5);
xcut2 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 20);
x = xcut1:0.1:xcut2;
ycut1 = fzero(@(x)sqrt(xcut1).*(12-xcut1)./2 - 2+xcut1, 0.5);

Exiting fzero: aborting search for an interval containing a sign change
    because no sign change is detected during search.
Function may not have a root.

ycut2 = fzero(@(x)sqrt(xcut2).*(12-xcut2)./2 - 2+xcut2, 20);

Exiting fzero: aborting search for an interval containing a sign change
    because no sign change is detected during search.
Function may not have a root.

M = polyshape([xcut1 ycut1],[xcut2 ycut2], 'simplify', false);

Warning: Boundaries with less than 3 points were removed.

plot(x1,y1,x1,y2,xcut1,xcut2,ycut1,ycut2)
hold on;
plot(M)
hold on;
grid on;
xlim([0,30])
ylim([0,30])

[Thai Anh]

@Stephan

[Stephan]

ycut1 and ycut2 dont make sense.

Think about how polyshape works:

• you need a closed region --> so far we know closing points in xdirection are xcut1 and xcut2
• inside this interval of x-values of your ROI you need correspondig y-values
• you need several points for the nonlinear part of your region
• the linear part of your region should be able to be described using 2 points --> you can guess which points this will be...
• using this thoughts you can construct a vector pair x,y that describes the ROI properly for the usage of polyshape

[Thai Anh]

I change it into this

x1 = 0:1:30;

y1 = 2-x1;

y2 = sqrt(x1).*(12-x1)./2;

xcut1 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 0.5);

xcut2 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 20);

x = xcut1:0.1:xcut2;

y = 2-x1(x1>=xcut1) :0.1: 2-x1(x1<=xcut2);

M = polyshape([xcut1 y],[xcut2 y], 'simplify', false);

plot(x1,y1,x1,y2,x,y)

hold on;

plot(M)

hold on;

grid on;

xlim([0,30])

ylim([0,30])

But it's still wrong in plot(x1,y1,x1,y2,x,y)

[Thai Anh]

x1 = 0:1:30;

y1 = 2-x1;

y2 = sqrt(x1).*(12-x1)./2;

xcut1 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 0.5);

xcut2 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 20);

x = xcut1:0.1:xcut2;

y = 2-x1(x1>=xcut1) :0.1: 2-x1(x1<=xcut2);

M = polyshape([xcut1 y],[xcut2 y], 'simplify', false);

plot(x1,y1,x1,y2,x,y)

hold on;

plot(M)

hold on;

grid on;

xlim([0,30])

ylim([0,30])

it still doesn't work

[Stephan]

inside this interval of x-values of your ROI you need corresponding y-values - that means to calculate them

rectangle example:

x = [1 5 5 1];
y = [1 1 2 2];
M = polyshape(x,y);
plot(M)
xlim([0 6])
ylim([0 6])

Try to find out how it works - then you get it

[Thai Anh]

x1 = 0:1:30;

y1 = 2-x1;

y2 = sqrt(x1).*(12-x1)./2;

xcut1 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 0.5);

xcut2 = fzero(@(x)sqrt(x).*(12-x)./2 - 2+x, 20);

a=[x1(xcut1<=x1),x1(x1<=xcut2)];

b=[2-x1 (x1>=xcut1), 2-x1 (x1<=xcut2)] ;

M = polyshape(a,b);

plot(M)

hold on;

grid on;

xlim([0,30])

ylim([0,30])

..... I tried but I cannot mark the curve region

[Stephan]

Sorry, last try - i can not make it more clear without doing your homework:

x = -10:1:10;
y1 = -x.^2 + 100;
y2 = 0.*x + 50;

xcut1 = fzero(@(x)-x.^2 + 100 - 50,-7);
xcut2 = fzero(@(x)-x.^2 + 100 - 50,7);

x_linear = [xcut1 xcut2];
y_linear = [50 50];

x_quad = linspace(xcut1, xcut2, 25);
y_quad = -x_quad.^2 + 100;

M = polyshape([x_linear, x_quad], [y_linear, y_quad],'simplify', false);

plot(x,y1,x,y2)
hold on
plot(M)