Struct Point

pub struct Point<T> { /* private fields */ }

A point is defined by a x and y coordinate in the euclidean plane.

Implementations

impl<T> Point<T>

pub fn new(x: T, y: T) -> Point<T>

Create a new point with x and y coordinates.

impl<T> Point<T>

where T: Copy,

pub fn v(&self) -> Vector<T>

Return the location of this point as a vector.

pub fn get(&self, coord: Orientation2D) -> T

Get a specific coordinate of the point.

pub fn set(&mut self, coord: Orientation2D, value: T)

Set a specific coordinate of the point.

impl<T> Point<T>

where T: Zero,

pub fn zero() -> Point<T>

Get zero-Point.

Examples

use iron_shapes::point::Point;

let a = Point::zero();
let b = Point::new(0, 0);

assert_eq!(a, b);

pub fn is_zero(&self) -> bool

Check if this is the zero-Point.

Examples

use iron_shapes::point::*;

assert!(Point::<usize>::zero().is_zero());

impl<T> Point<T>

where T: Add<Output = T> + Copy + Sub<Output = T> + Mul<Output = T>,

pub fn distance_sq(self, other: &Point<T>) -> T

Compute the squared distance to the other point.

Examples

use iron_shapes::point::*;

let a = Point::new(0, 0);
let b = Point::new(2, 0);
assert_eq!(a.distance_sq(&b), 2*2);

pub fn cross_prod3(&self, b: Point<T>, c: Point<T>) -> T

Calculate the cross product of the two vectors defined by three points.

A positive value implies that self → a → b is counter-clockwise, negative implies clockwise.

(b - self) x (c - b)

Examples

use iron_shapes::point::Point;

let a = Point::new(1,0);
let b = Point::new(1,1);
let c = Point::new(0,1);

let p = a.cross_prod3(b, c);

assert_eq!(p, (b-a).cross_prod(c - b));

impl<T> Point<T>

where T: Copy + Sub<Output = T> + NumCast,

pub fn distance<F>(self, other: &Point<T>) -> F

where F: Float,

Compute the Euclidean distance betwen two points.

impl<T> Point<T>

where T: Copy + NumCast,

pub fn cast_to_float<F>(&self) -> Point<F>

where F: Float + NumCast,

Convert Point into a Point with floating point data type.

Methods from Deref<Target = Vector<T>>

pub fn norm1(&self) -> T

Get 1-norm of vector, i.e. the sum of the absolute values of its components.

Examples

use iron_shapes::vector::Vector;
let a = Vector::new(-2, 3);
assert_eq!(a.norm1(), 5);

pub fn orientation_of(&self, other: Vector<T>) -> Orientation

Check if other is oriented clockwise or counter-clockwise respective to self.

Examples

use iron_shapes::vector::Vector;
use iron_shapes::types::Orientation;

let a = Vector::new(1, 0);
let b = Vector::new(1, 1);
let c = Vector::new(1, -1);
let d = Vector::new(2, 0);

assert_eq!(a.orientation_of(b), Orientation::CounterClockWise);
assert_eq!(a.orientation_of(c), Orientation::ClockWise);
assert_eq!(a.orientation_of(d), Orientation::Straight);

pub fn norm2_squared(&self) -> T

Get squared 2-norm of vector.

Examples

use iron_shapes::vector::Vector;
let a = Vector::new(2, 3);
assert_eq!(a.norm2_squared(), 2*2+3*3);

pub fn dot(&self, other: Vector<T>) -> T

Calculate scalar product.

Examples

use iron_shapes::vector::Vector;

let a = Vector::new(1, 2);
let b = Vector::new(3, 4);

assert_eq!(a.dot(b), 1*3 + 2*4);

pub fn cross_prod(&self, other: Vector<T>) -> T

Calculate cross product.

Examples

use iron_shapes::vector::Vector;

let a = Vector::new(2, 0);
let b = Vector::new(0, 2);

assert_eq!(a.cross_prod(b), 4);
assert_eq!(b.cross_prod(a), -4);

pub fn cast_to_float<F>(&self) -> Vector<F>

where F: Float + NumCast,

Convert vector into a vector with floating point data type.

pub fn norm2(&self) -> T

Get 2-norm of vector (length of vector).

Examples

use iron_shapes::vector::Vector;
let a = Vector::new(2.0, 3.0);
let norm2 = a.norm2();
let norm2_sq = norm2 * norm2;
let expected = a.norm2_squared();
assert!(norm2_sq < expected + 1e-12);
assert!(norm2_sq > expected - 1e-12);

pub fn normalized(&self) -> Vector<T>

Return a vector with the same direction but length 1.

Panics

Panics if the vector has length 0.

pub fn normal(&self) -> Vector<T>

Return the normal vector onto this vector. The normal has length 1.

Panics

Panics if the vector has length 0.

pub fn length<F>(&self) -> F

where F: Float,

Calculate length of vector.

Similar to Vector::norm2 but does potentially return another data type for the length.

Examples

use iron_shapes::vector::Vector;
let a = Vector::new(2.0, 3.0);
let length: f64 = a.length();
let norm2_sq = length * length;
let expected = a.norm2_squared();
assert!(norm2_sq < expected + 1e-12);
assert!(norm2_sq > expected - 1e-12);

Trait Implementations

impl<T, V> Add<V> for Point<T>

where T: Copy + Add<Output = T>, V: Into<Point<T>>,

Point addition.

type Output = Point<T>

The resulting type after applying the + operator.

fn add(self, rhs: V) -> Point<T>

Performs the + operation.

impl<T, V> AddAssign<V> for Point<T>

where T: Copy + AddAssign, V: Into<Vector<T>>,

fn add_assign(&mut self, rhs: V)

Performs the += operation.

impl<T> BoundingBox<T> for Point<T>

where T: Copy,

fn bounding_box(&self) -> Rect<T>

Return the bounding box of this geometry.

impl<T> Clone for Point<T>

where T: Clone,

fn clone(&self) -> Point<T>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T> Debug for Point<T>

where T: Debug,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<T> Default for Point<T>

where T: Default,

fn default() -> Point<T>

Returns the “default value” for a type.

impl<T> Deref for Point<T>

type Target = Vector<T>

The resulting type after dereferencing.

fn deref(&self) -> &<Point<T> as Deref>::Target

Dereferences the value.

impl<T> DerefMut for Point<T>

fn deref_mut(&mut self) -> &mut <Point<T> as Deref>::Target

Mutably dereferences the value.

impl<T> Display for Point<T>

where T: Display,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<T> Div<T> for Point<T>

where T: Copy + Div<Output = T>,

Scalar division.

type Output = Point<T>

The resulting type after applying the / operator.

fn div(self, rhs: T) -> Point<T>

Performs the / operation.

impl<'a, T> From<&'a (T, T)> for Point<T>

where T: Copy,

fn from(coords: &'a (T, T)) -> Point<T>

Converts to this type from the input type.

impl<'a, T> From<&'a Point<T>> for Point<T>

where T: Copy,

fn from(v: &'a Point<T>) -> Point<T>

Converts to this type from the input type.

impl<T> From<&Point<T>> for Vector<T>

where T: Copy,

fn from(p: &Point<T>) -> Vector<T>

Converts to this type from the input type.

impl<T> From<&Vector<T>> for Point<T>

where T: Copy,

fn from(v: &Vector<T>) -> Point<T>

Converts to this type from the input type.

impl<T> From<[T; 2]> for Point<T>

where T: Copy,

fn from(coords: [T; 2]) -> Point<T>

Converts to this type from the input type.

impl<T> From<(T, T)> for Point<T>

where T: Copy,

fn from(coords: (T, T)) -> Point<T>

Converts to this type from the input type.

impl<T> From<Point<T>> for Geometry<T>

fn from(x: Point<T>) -> Geometry<T>

Converts to this type from the input type.

impl<T> From<Point<T>> for Vector<T>

fn from(p: Point<T>) -> Vector<T>

Converts to this type from the input type.

impl<T> From<Vector<T>> for Point<T>

fn from(v: Vector<T>) -> Point<T>

Converts to this type from the input type.

impl<T> Hash for Point<T>

where T: Hash,

fn hash<__H>(&self, state: &mut __H)

where __H: Hasher,

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T> MapPointwise<T> for Point<T>

where T: Copy,

Point wise transformation for a single point.

fn transform<F>(&self, transformation: F) -> Point<T>

where F: Fn(Point<T>) -> Point<T>,

Point wise transformation.

impl<T> Mul<T> for Point<T>

where T: Copy + Mul<Output = T>,

Scalar multiplication.

type Output = Point<T>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Point<T>

Performs the * operation.

impl<T> MulAssign<T> for Point<T>

where T: Copy + MulAssign,

In-place scalar multiplication.

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<T> Neg for Point<T>

where T: Copy + Neg<Output = T>,

type Output = Point<T>

The resulting type after applying the - operator.

fn neg(self) -> Point<T>

Performs the unary - operation.

impl<T> Ord for Point<T>

where T: Ord,

Compare points.

The ordering is determined by the x-coordinates. If it is the same for both points the y-coordinate is used.

Point a > Point b iff a.x > b.x || (a.x == b.x && a.y > b.y).

fn cmp(&self, rhs: &Point<T>) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl<T> PartialEq for Point<T>

where T: PartialEq,

fn eq(&self, other: &Point<T>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T> PartialOrd for Point<T>

where T: PartialOrd,

Compare points.

The ordering is determined by the x-coordinates. If it is the same for both points the y-coordinate is used.

Point a > Point b iff a.x > b.x || (a.x == b.x && a.y > b.y).

fn partial_cmp(&self, rhs: &Point<T>) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<C> PointBase<C> for Point<<C as CoordinateBase>::Coord>

where C: CoordinateBase,

fn new( x: <C as CoordinateBase>::Coord, y: <C as CoordinateBase>::Coord, ) -> Point<<C as CoordinateBase>::Coord>

Construct a new point.

fn get(&self, orient: Orientation2D) -> <C as CoordinateBase>::Coord

Get a coordinate value.

fn set(&mut self, orient: Orientation2D, value: <C as CoordinateBase>::Coord)

Set a coordinate value.

fn x(&self) -> <C as CoordinateBase>::Coord

Get the x-coordinate value.

fn y(&self) -> <C as CoordinateBase>::Coord

Get the y-coordinate value.

impl<C> PointConcept<C> for Point<<C as CoordinateBase>::Coord>

where C: CoordinateConcept,

fn projected_distance( &self, other: &Self, orient: Orientation2D, ) -> <C as CoordinateConcept>::CoordinateDifference

Compute the x or y component of the vector from the point to the other point.

fn manhattan_distance( &self, other: &Self, ) -> <C as CoordinateConcept>::CoordinateDifference

Compute the 1-norm of the vector pointing from the point to the other.

fn distance_squared( &self, other: &Self, ) -> <C as CoordinateConcept>::CoordinateDistance

Squared euclidean distance.

fn euclidian_distance( &self, other: &Self, ) -> <C as CoordinateConcept>::CoordinateDistance

Euclidean distance, i.e. 2-norm of the vector from the point to the other.

impl<T> Sub<Vector<T>> for Point<T>

where T: Copy + Sub<Output = T>,

Subtract a vector.

type Output = Point<T>

The resulting type after applying the - operator.

fn sub(self, rhs: Vector<T>) -> <Point<T> as Sub<Vector<T>>>::Output

Performs the - operation.

impl<T> Sub for Point<T>

where T: Copy + Sub<Output = T>,

Subtract a point.

type Output = Vector<T>

The resulting type after applying the - operator.

fn sub(self, rhs: Point<T>) -> <Point<T> as Sub>::Output

Performs the - operation.

impl<T, V> SubAssign<V> for Point<T>

where T: Copy + SubAssign, V: Into<Vector<T>>,

fn sub_assign(&mut self, rhs: V)

Performs the -= operation.

impl<T> Sum for Point<T>

where T: Copy + Zero<Output = T> + Add,

fn sum<I>(iter: I) -> Point<T>

where I: Iterator<Item = Point<T>>,

Compute the sum of all points in the iterator. If the iterator is empty, (0, 0) is returned.

impl<T> TryBoundingBox<T> for Point<T>

where T: Copy,

fn try_bounding_box(&self) -> Option<Rect<T>>

Return the bounding box of this geometry if a bounding box is defined.

impl<T, Dst> TryCastCoord<T, Dst> for Point<T>

where T: Copy + NumCast, Dst: Copy + NumCast,

type Output = Point<Dst>

Output type of the cast. This is likely the same geometrical type just with other coordinate types.

fn try_cast(&self) -> Option<<Point<T> as TryCastCoord<T, Dst>>::Output>

Try to cast to target data type.

fn cast(&self) -> Self::Output

Cast to target data type.

impl<T> Copy for Point<T>

where T: Copy,

impl<T> Eq for Point<T>

where T: Eq,

impl<T> StructuralPartialEq for Point<T>