Non-linear Implicit function plot

Hi I am trying to plot an implicit function. My function contains both scalars and vectors (a*x^3) - (3*b*(norm(-V1+(x+y)*V2)^3)) = 0, where a, b are scalars and V1 and V2 are some unit vectors. I want to plot 'x vs y'. I tried various methods like fimplicit, fplot, ezplot and also mupad (plot(plot::Implicit2d()) But failed Is there is a way to plot this ?

Answer 1

[Star Strider]

There probably is a way to plot it, but you have to tell us (and MATLAB) what you want as your independent variables.

Guessing here. See if this does what you want:

a = 5.5;
b = 2.3;
V1 = [1; 2; 3];
V2 = [2; 4; 7];

f = @(x,y) (a*x.^3) - (3*b*(norm(-V1+(x+y).*V2).^3));

figure(1)
ezsurf(f, [-5 5 -5 5])

[Chaluvadi Kiran]

Hi, I am expecting a 2D plot(x vs y) not 3D. My implicit function is (a*x^3) - (3*b*(norm(-V1+(x+y)*V2)^3)) = 0 (equals to zero)

Answer 2

[Roger Stafford]

You could plot it using a third variable, t:

n = 200;
t = linspace(-2,2,n); % <-- Choose appropriate range for t
for k = 1:n
  x(k) = (3*b/a)^(1/3)*norm(-V1+t(k)*V2);
  y(k) = t(k)-x(k);
end
plot(x,y,’y-‘)
axis equal

The trick is to choose the appropriate range for variable t to get the desired ranges for x and y.