Point2

Point2 is a two-dimensional point in the Cartesian coordinate system.

:::note Point2 is a generic type, which means you can use any type that implements the NumberType trait as the number type. :::

Constructors

You can create a Point2 object using the new method, which takes two arguments: the x and y coordinates of the point.

let point_2 = Point2::new(1.0, 2.0);

Fields

Point2 has two fields: x and y, which represent the x and y coordinates of the point, respectively. You can access these fields using the x and y methods.

let x = point_2.x();
let y = point_2.y();

Methods

Point2 has several methods that allow you to perform common operations on points. Here are some of the most commonly used methods:

• distance: Computes the distance between two points.
• equals: Checks if two points are equal.
• get_vector: Returns a vector from the origin to the point.
• turn: Calculate the TurnDirection of three points.

let point_1 = Point2::new(1.0, 2.0);
let point_2 = Point2::new(3.0, 4.0);
let distance = point_1.distance(&point_2);
let equals = point_1.equals(&point_2);
let vector = point_1.get_vector();
let turn = Point2::turn(&point_1, &point_2, &Point2::new(5.0, 6.0));

:::note Two points are equal if the distance between them is less than the default_eps of the NumberType. :::

Operators

Point2 implements Add and Sub traits because it has very close relationships with Vector2. Add or Sub two points will return a Vector2 object.

let point_1 = Point2::new(1.0, 2.0);
let point_2 = Point2::new(3.0, 4.0);
let vector_add = point_1 + point_2;
let vector_sub = point_1 - point_2;

Others

Points implements Ord traits, which is useful when you need to sort a list of points or store them in some data structures that require ordering.

1. The left point is Greater
2. If the x coordinates are equal, the bottom point is Greater
3. If the x and y coordinates are equal, the two points are equal

impl<T: NumberType> Ord for Point2<T> {
    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
        if self.x().equals(other.x()) {
            if self.y().equals(other.y()) {
                return std::cmp::Ordering::Equal;
            } else {
                if self.y() > other.y() {
                    return std::cmp::Ordering::Less;
                } else {
                    return std::cmp::Ordering::Greater;
                }
            }
        } else {
            if self.x() < other.x() {
                return std::cmp::Ordering::Greater;
            } else {
                return std::cmp::Ordering::Less;
            }
        }
    }
}