How to "color" the closed area bounded by three curves

Hi, I want to color the area between the intersection of three curves. Please suggest a way.

Code Updated by @Sam Chak: (based on info in Comment)

T1 = 180:0.1:270;
x1 = 3*cosd(T1); 
y1 = 3*sind(T1); % circle

T2 = 3.3620:0.001:3.9045;
c1 = 4.3123; c2 = -50.2708; c3 = 193.7277; c4 = -243.8411;
r_6 = c1*T2.^3 + c2*T2.^2 + c3*T2 + c4;
x2 = 1.1998 + r_6.*cos(T2); 
y2 = -0.8840 + r_6.*sin(T2);       % region 4

x0 = 1.8977; 
y0 = 2.3235; 
vr = 4.0678;
beta = atan(y0/x0);
x3 = -2.0591:0.001:-1.8541; 
y3 = y0 + (x0-x3)*cot(beta) - (9.81*(x0-x3).^2)./(2*(vr*sin(beta))^2);   % parabola

pgon1 = polyshape(x1,y1);          % circle
pgon2 = polyshape(x2,y2);          % region 4
pgon3 = polyshape(x3,y3);          % parabola
pgon4 = intersect(pgon1,pgon2);

figure(4)
plot(x1, y1, x2, y2, x3, y3, 'linewidth', 2)
hold on
plot(intersect(pgon3, pgon4), 'EdgeColor', 'none')

grid on
axis equal

[Star Strider]

Problems here.

T1 = 180:0.1:270;
x1 = 3*cosd(T1); y1 = 3*sind(T1); 
T2 = theta_4s2:0.001:theta_4f2;

Unrecognized function or variable 'theta_4s2'.

c1 = 4.3123; c2 = -50.2708; c3 = 193.7277; c4 = -243.8411;
r_6 = c1*T2.^3 + c2*T2.^2 + c3*T2 + c4;
x2 = 1.998 + r_6.*cos(T2); y2 = -0.8840 + r_6.*sin(T2);   
x0 = 1.8977; y0 = 2.3235; vr = 4.0678;
beta = atan(y0/x0);
x3 = s2(1,1):0.001:x_t; y3 = y0 + (x0-x3)*cot(beta) - (9.81*(x0-x3).^2)./(2*(vr*sin(beta))^2);
pgon1 = polyshape(x1,y1);         
pgon2 = polyshape(x2,y2);          
pgon3 = polyshape(x3,y3);
figure (1)
plot(x1,y1,x2,y2,x3,y3)
hold on
plot (intersect(intersect(pgon3,pgon4)), pgon3,'EdgeColor','none')

.

[mukesh bisht]

T2 = 3.3620:0.001:3.9045;

The problem is with this function: plot (intersect(intersect(pgon3,pgon4)), pgon3,'EdgeColor','none')

[Star Strider]

More problems —

T2 = 3.3620:0.001:3.9045;
T1 = 180:0.1:270;
x1 = 3*cosd(T1); y1 = 3*sind(T1); 
T2 = theta_4s2:0.001:theta_4f2;

Unrecognized function or variable 'theta_4s2'.

c1 = 4.3123; c2 = -50.2708; c3 = 193.7277; c4 = -243.8411;
r_6 = c1*T2.^3 + c2*T2.^2 + c3*T2 + c4;
x2 = 1.998 + r_6.*cos(T2); y2 = -0.8840 + r_6.*sin(T2);   
x0 = 1.8977; y0 = 2.3235; vr = 4.0678;
beta = atan(y0/x0);
x3 = s2(1,1):0.001:x_t; y3 = y0 + (x0-x3)*cot(beta) - (9.81*(x0-x3).^2)./(2*(vr*sin(beta))^2);
pgon1 = polyshape(x1,y1);         
pgon2 = polyshape(x2,y2);          
pgon3 = polyshape(x3,y3);
figure (1)
plot(x1,y1,x2,y2,x3,y3)
hold on
plot (intersect(intersect(pgon3,pgon4)), pgon3,'EdgeColor','none')

.

[mukesh bisht]

T2 = 3.3620:0.001:3.9045;
T1 = 180:0.1:270;
x1 = 3*cosd(T1); y1 = 3*sind(T1); 
T2 = 3.3620:0.001:3.9045;
c1 = 4.3123; c2 = -50.2708; c3 = 193.7277; c4 = -243.8411;
r_6 = c1*T2.^3 + c2*T2.^2 + c3*T2 + c4;
x2 = 1.998 + r_6.*cos(T2); y2 = -0.8840 + r_6.*sin(T2);   
x0 = 1.8977; y0 = 2.3235; vr = 4.0678;
beta = atan(y0/x0);
x3 = s2(1,1):0.001:x_t; y3 = y0 + (x0-x3)*cot(beta) - (9.81*(x0-x3).^2)./(2*(vr*sin(beta))^2);
pgon1 = polyshape(x1,y1);         
pgon2 = polyshape(x2,y2);          
pgon3 = polyshape(x3,y3);
figure (1)
plot(x1,y1,x2,y2,x3,y3)
hold on
plot (intersect(intersect(pgon3,pgon4)), pgon3,'EdgeColor','none')

[Star Strider]

... still more problems ...

T2 = 3.3620:0.001:3.9045;
T1 = 180:0.1:270;
x1 = 3*cosd(T1); y1 = 3*sind(T1); 
T2 = 3.3620:0.001:3.9045;
c1 = 4.3123; c2 = -50.2708; c3 = 193.7277; c4 = -243.8411;
r_6 = c1*T2.^3 + c2*T2.^2 + c3*T2 + c4;
x2 = 1.998 + r_6.*cos(T2); y2 = -0.8840 + r_6.*sin(T2);   
x0 = 1.8977; y0 = 2.3235; vr = 4.0678;
beta = atan(y0/x0);
x3 = s2(1,1):0.001:x_t; y3 = y0 + (x0-x3)*cot(beta) - (9.81*(x0-x3).^2)./(2*(vr*sin(beta))^2);

Unrecognized function or variable 's2'.

pgon1 = polyshape(x1,y1);         
pgon2 = polyshape(x2,y2);          
pgon3 = polyshape(x3,y3);
figure (1)
plot(x1,y1,x2,y2,x3,y3)
hold on
plot (intersect(intersect(pgon3,pgon4)), pgon3,'EdgeColor','none')

I would really like to be able to run this in order to see what the problems are.

.

[mukesh bisht]

sorry for my incorrect code. Here, is the final corrected version

T1 = 180:0.1:270;
x1 = 3*cosd(T1); y1 = 3*sind(T1); % circle

T2 = 3.3620:0.001:3.9045;
c1 = 4.3123; c2 = -50.2708; c3 = 193.7277; c4 = -243.8411;
r_6 = c1*T2.^3 + c2*T2.^2 + c3*T2 + c4;
x2 = 1.1998 + r_6.*cos(T2); y2 = -0.8840 + r_6.*sin(T2);   % region 4

x0 = 1.8977; y0 = 2.3235; vr = 4.0678;
beta = atan(y0/x0);
x3 = -2.0591:0.001:-1.8541; y3 = y0 + (x0-x3)*cot(beta) - (9.81*(x0-x3).^2)./(2*(vr*sin(beta))^2);   % parabola

pgon1 = polyshape(x1,y1);          % circle
pgon2 = polyshape(x2,y2);          % region 4
pgon3 = polyshape(x3,y3);          % parabola
pgon4 = intersect(pgon1,pgon2);
figure (4)
plot(x1,y1,x2,y2,x3,y3)
hold on
plot (intersect(pgon3,pgon4),'EdgeColor','none')

I want to color the area of intersection of these threee curves

Answer 1

[Simran]

Hey @mukesh bisht,

The common area between the polygons 'pgon3' and pgon4' isn't being plotted because the 'intersect' function doesn't find any common points between the 2 regions and thus returns an object having an empty matrix for 'Vertices' field, when you run

>> intersect(pgon3,pgon4)

To visualise your plots better, you can try plotting the polygon regions ('pgon1', 'pgon2' etc one after the other) and then decide which polygons to send to the 'intersect' function to compute the common points. You can refer the following code snippet:

>> figure
>> hold on
>> plot(pgon3)
>> plot(pgon1)
>> plot(pgon2)

You can refer to the below documentation links:

'intersect' - https://www.mathworks.com/help/matlab/ref/double.intersect.html

'polyshape' - https://www.mathworks.com/help/matlab/ref/polyshape.html?s_tid=doc_ta