Vector field II: directly defined vectors

In the previous example, we derived a vector field from the gradient of a scalar function. In this example, we'll directly define the vector at each point using a custom formula.

We'll create a vector field where the vector at each point is defined by a normalized combination of the coordinates, creating an interesting rotational pattern.

Let's start by creating a point p:

• Create point

Setting up the variables and the output vector

This part does not change anything on the canvas.

Extract the x and y coordinates from this point:

• Get x coordinate
• Get y coordinate

Define a parameter that will control the vector field:

• Define parameter

Scale the x coordinate by :

• Calculate

To normalize our vector, we need the distance from to the origin :

• Calculate distance

Now we'll construct the vector components. We'll use for one component:

• Negate

Normalize the components by dividing by the distance:

• Normalize component
• Normalize component

Define the output point and draw the vector field

Create the output vector from the normalized components:

• Create output vector

Finally, visualize the vector field:

• Draw vector field

This creates a rotational vector field where vectors are tangent to circles centered at the origin. The parameter a controls the strength in the x-direction.

• Create an array for slider values

Try changing the value of to see how the vector field transforms:

Notice how the vector field changes. When , you get a purely vertical rotational field. As a increases, the field becomes more elliptical.