4f9f987099
# Objective - Add some useful methods to `Ellipse` ## Solution - Added `Ellipse::perimeter()` and `::focal_length()` --------- Co-authored-by: IQuick 143 <IQuick143cz@gmail.com>
1059 lines
34 KiB
Rust
1059 lines
34 KiB
Rust
use std::f32::consts::PI;
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use super::{Primitive2d, WindingOrder};
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use crate::{Dir2, Vec2};
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/// A circle primitive
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#[derive(Clone, Copy, Debug, PartialEq)]
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#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
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pub struct Circle {
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/// The radius of the circle
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pub radius: f32,
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}
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impl Primitive2d for Circle {}
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impl Default for Circle {
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/// Returns the default [`Circle`] with a radius of `0.5`.
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fn default() -> Self {
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Self { radius: 0.5 }
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}
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}
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impl Circle {
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/// Create a new [`Circle`] from a `radius`
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#[inline(always)]
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pub const fn new(radius: f32) -> Self {
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Self { radius }
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}
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/// Get the diameter of the circle
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#[inline(always)]
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pub fn diameter(&self) -> f32 {
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2.0 * self.radius
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}
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/// Get the area of the circle
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#[inline(always)]
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pub fn area(&self) -> f32 {
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PI * self.radius.powi(2)
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}
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/// Get the perimeter or circumference of the circle
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#[inline(always)]
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#[doc(alias = "circumference")]
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pub fn perimeter(&self) -> f32 {
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2.0 * PI * self.radius
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}
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/// Finds the point on the circle that is closest to the given `point`.
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///
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/// If the point is outside the circle, the returned point will be on the perimeter of the circle.
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/// Otherwise, it will be inside the circle and returned as is.
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#[inline(always)]
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pub fn closest_point(&self, point: Vec2) -> Vec2 {
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let distance_squared = point.length_squared();
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if distance_squared <= self.radius.powi(2) {
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// The point is inside the circle.
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point
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} else {
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// The point is outside the circle.
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// Find the closest point on the perimeter of the circle.
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let dir_to_point = point / distance_squared.sqrt();
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self.radius * dir_to_point
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}
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}
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}
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/// An ellipse primitive
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#[derive(Clone, Copy, Debug, PartialEq)]
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#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
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pub struct Ellipse {
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/// Half of the width and height of the ellipse.
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///
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/// This corresponds to the two perpendicular radii defining the ellipse.
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pub half_size: Vec2,
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}
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impl Primitive2d for Ellipse {}
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impl Default for Ellipse {
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/// Returns the default [`Ellipse`] with a half-width of `1.0` and a half-height of `0.5`.
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fn default() -> Self {
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Self {
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half_size: Vec2::new(1.0, 0.5),
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}
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}
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}
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impl Ellipse {
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/// Create a new `Ellipse` from half of its width and height.
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///
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/// This corresponds to the two perpendicular radii defining the ellipse.
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#[inline(always)]
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pub const fn new(half_width: f32, half_height: f32) -> Self {
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Self {
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half_size: Vec2::new(half_width, half_height),
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}
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}
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/// Create a new `Ellipse` from a given full size.
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///
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/// `size.x` is the diameter along the X axis, and `size.y` is the diameter along the Y axis.
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#[inline(always)]
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pub fn from_size(size: Vec2) -> Self {
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Self {
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half_size: size / 2.0,
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}
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}
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#[inline(always)]
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/// Returns the [eccentricity](https://en.wikipedia.org/wiki/Eccentricity_(mathematics)) of the ellipse.
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/// It can be thought of as a measure of how "stretched" or elongated the ellipse is.
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///
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/// The value should be in the range [0, 1), where 0 represents a circle, and 1 represents a parabola.
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pub fn eccentricity(&self) -> f32 {
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let a = self.semi_major();
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let b = self.semi_minor();
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(a * a - b * b).sqrt() / a
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}
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#[inline(always)]
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/// Get the focal length of the ellipse. This corresponds to the distance between one of the foci and the center of the ellipse.
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///
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/// The focal length of an ellipse is related to its eccentricity by `eccentricity = focal_length / semi_major`
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pub fn focal_length(&self) -> f32 {
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let a = self.semi_major();
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let b = self.semi_minor();
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(a * a - b * b).sqrt()
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}
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#[inline(always)]
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/// Get an approximation for the perimeter or circumference of the ellipse.
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///
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/// The approximation is reasonably precise with a relative error less than 0.007%, getting more precise as the eccentricity of the ellipse decreases.
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pub fn perimeter(&self) -> f32 {
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let a = self.semi_major();
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let b = self.semi_minor();
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// In the case that `a == b`, the ellipse is a circle
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if a / b - 1. < 1e-5 {
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return PI * (a + b);
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};
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// In the case that `a` is much larger than `b`, the ellipse is a line
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if a / b > 1e4 {
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return 4. * a;
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};
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// These values are the result of (0.5 choose n)^2 where n is the index in the array
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// They could be calculated on the fly but hardcoding them yields more accurate and faster results
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// because the actual calculation for these values involves factorials and numbers > 10^23
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const BINOMIAL_COEFFICIENTS: [f32; 21] = [
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1.,
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0.25,
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0.015625,
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0.00390625,
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0.0015258789,
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0.00074768066,
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0.00042057037,
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0.00025963783,
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0.00017140154,
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0.000119028846,
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0.00008599834,
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0.00006414339,
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0.000049109784,
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0.000038430585,
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0.000030636627,
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0.000024815668,
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0.000020380836,
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0.000016942893,
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0.000014236736,
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0.000012077564,
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0.000010333865,
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];
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// The algorithm used here is the Gauss-Kummer infinite series expansion of the elliptic integral expression for the perimeter of ellipses
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// For more information see https://www.wolframalpha.com/input/?i=gauss-kummer+series
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// We only use the terms up to `i == 20` for this approximation
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let h = ((a - b) / (a + b)).powi(2);
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PI * (a + b)
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* (0..=20)
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.map(|i| BINOMIAL_COEFFICIENTS[i] * h.powi(i as i32))
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.sum::<f32>()
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}
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/// Returns the length of the semi-major axis. This corresponds to the longest radius of the ellipse.
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#[inline(always)]
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pub fn semi_major(&self) -> f32 {
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self.half_size.max_element()
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}
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/// Returns the length of the semi-minor axis. This corresponds to the shortest radius of the ellipse.
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#[inline(always)]
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pub fn semi_minor(&self) -> f32 {
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self.half_size.min_element()
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}
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/// Get the area of the ellipse
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#[inline(always)]
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pub fn area(&self) -> f32 {
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PI * self.half_size.x * self.half_size.y
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}
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}
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/// A primitive shape formed by the region between two circles, also known as a ring.
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#[derive(Clone, Copy, Debug, PartialEq)]
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#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
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#[doc(alias = "Ring")]
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pub struct Annulus {
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/// The inner circle of the annulus
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pub inner_circle: Circle,
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/// The outer circle of the annulus
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pub outer_circle: Circle,
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}
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impl Primitive2d for Annulus {}
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impl Default for Annulus {
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/// Returns the default [`Annulus`] with radii of `0.5` and `1.0`.
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fn default() -> Self {
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Self {
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inner_circle: Circle::new(0.5),
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outer_circle: Circle::new(1.0),
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}
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}
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}
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impl Annulus {
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/// Create a new [`Annulus`] from the radii of the inner and outer circle
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#[inline(always)]
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pub const fn new(inner_radius: f32, outer_radius: f32) -> Self {
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Self {
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inner_circle: Circle::new(inner_radius),
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outer_circle: Circle::new(outer_radius),
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}
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}
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/// Get the diameter of the annulus
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#[inline(always)]
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pub fn diameter(&self) -> f32 {
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self.outer_circle.diameter()
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}
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/// Get the thickness of the annulus
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#[inline(always)]
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pub fn thickness(&self) -> f32 {
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self.outer_circle.radius - self.inner_circle.radius
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}
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/// Get the area of the annulus
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#[inline(always)]
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pub fn area(&self) -> f32 {
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PI * (self.outer_circle.radius.powi(2) - self.inner_circle.radius.powi(2))
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}
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/// Get the perimeter or circumference of the annulus,
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/// which is the sum of the perimeters of the inner and outer circles.
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#[inline(always)]
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#[doc(alias = "circumference")]
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pub fn perimeter(&self) -> f32 {
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2.0 * PI * (self.outer_circle.radius + self.inner_circle.radius)
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}
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/// Finds the point on the annulus that is closest to the given `point`:
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///
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/// - If the point is outside of the annulus completely, the returned point will be on the outer perimeter.
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/// - If the point is inside of the inner circle (hole) of the annulus, the returned point will be on the inner perimeter.
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/// - Otherwise, the returned point is overlapping the annulus and returned as is.
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#[inline(always)]
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pub fn closest_point(&self, point: Vec2) -> Vec2 {
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let distance_squared = point.length_squared();
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if self.inner_circle.radius.powi(2) <= distance_squared {
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if distance_squared <= self.outer_circle.radius.powi(2) {
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// The point is inside the annulus.
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point
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} else {
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// The point is outside the annulus and closer to the outer perimeter.
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// Find the closest point on the perimeter of the annulus.
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let dir_to_point = point / distance_squared.sqrt();
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self.outer_circle.radius * dir_to_point
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}
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} else {
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// The point is outside the annulus and closer to the inner perimeter.
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// Find the closest point on the perimeter of the annulus.
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let dir_to_point = point / distance_squared.sqrt();
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self.inner_circle.radius * dir_to_point
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}
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}
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}
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/// An unbounded plane in 2D space. It forms a separating surface through the origin,
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/// stretching infinitely far
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#[derive(Clone, Copy, Debug, PartialEq)]
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#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
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pub struct Plane2d {
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/// The normal of the plane. The plane will be placed perpendicular to this direction
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pub normal: Dir2,
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}
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impl Primitive2d for Plane2d {}
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impl Default for Plane2d {
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/// Returns the default [`Plane2d`] with a normal pointing in the `+Y` direction.
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fn default() -> Self {
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Self { normal: Dir2::Y }
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}
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}
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impl Plane2d {
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/// Create a new `Plane2d` from a normal
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///
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/// # Panics
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///
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/// Panics if the given `normal` is zero (or very close to zero), or non-finite.
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#[inline(always)]
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pub fn new(normal: Vec2) -> Self {
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Self {
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normal: Dir2::new(normal).expect("normal must be nonzero and finite"),
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}
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}
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}
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/// An infinite line along a direction in 2D space.
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///
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/// For a finite line: [`Segment2d`]
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#[derive(Clone, Copy, Debug, PartialEq)]
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#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
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pub struct Line2d {
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/// The direction of the line. The line extends infinitely in both the given direction
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/// and its opposite direction
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pub direction: Dir2,
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}
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impl Primitive2d for Line2d {}
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/// A segment of a line along a direction in 2D space.
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#[derive(Clone, Copy, Debug, PartialEq)]
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#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
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#[doc(alias = "LineSegment2d")]
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pub struct Segment2d {
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/// The direction of the line segment
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pub direction: Dir2,
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/// Half the length of the line segment. The segment extends by this amount in both
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/// the given direction and its opposite direction
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pub half_length: f32,
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}
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impl Primitive2d for Segment2d {}
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impl Segment2d {
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/// Create a new `Segment2d` from a direction and full length of the segment
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#[inline(always)]
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pub fn new(direction: Dir2, length: f32) -> Self {
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Self {
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direction,
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half_length: length / 2.0,
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}
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}
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/// Create a new `Segment2d` from its endpoints and compute its geometric center
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///
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/// # Panics
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///
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/// Panics if `point1 == point2`
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#[inline(always)]
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pub fn from_points(point1: Vec2, point2: Vec2) -> (Self, Vec2) {
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let diff = point2 - point1;
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let length = diff.length();
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(
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// We are dividing by the length here, so the vector is normalized.
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Self::new(Dir2::new_unchecked(diff / length), length),
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(point1 + point2) / 2.,
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)
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}
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/// Get the position of the first point on the line segment
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#[inline(always)]
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pub fn point1(&self) -> Vec2 {
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*self.direction * -self.half_length
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}
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/// Get the position of the second point on the line segment
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#[inline(always)]
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pub fn point2(&self) -> Vec2 {
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*self.direction * self.half_length
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}
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}
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/// A series of connected line segments in 2D space.
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///
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/// For a version without generics: [`BoxedPolyline2d`]
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#[derive(Clone, Debug, PartialEq)]
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#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
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pub struct Polyline2d<const N: usize> {
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/// The vertices of the polyline
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#[cfg_attr(feature = "serialize", serde(with = "super::serde::array"))]
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pub vertices: [Vec2; N],
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}
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impl<const N: usize> Primitive2d for Polyline2d<N> {}
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impl<const N: usize> FromIterator<Vec2> for Polyline2d<N> {
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fn from_iter<I: IntoIterator<Item = Vec2>>(iter: I) -> Self {
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let mut vertices: [Vec2; N] = [Vec2::ZERO; N];
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for (index, i) in iter.into_iter().take(N).enumerate() {
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vertices[index] = i;
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}
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Self { vertices }
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}
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}
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impl<const N: usize> Polyline2d<N> {
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/// Create a new `Polyline2d` from its vertices
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pub fn new(vertices: impl IntoIterator<Item = Vec2>) -> Self {
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Self::from_iter(vertices)
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}
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}
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/// A series of connected line segments in 2D space, allocated on the heap
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/// in a `Box<[Vec2]>`.
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///
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/// For a version without alloc: [`Polyline2d`]
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#[derive(Clone, Debug, PartialEq)]
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#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
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pub struct BoxedPolyline2d {
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/// The vertices of the polyline
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pub vertices: Box<[Vec2]>,
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}
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impl Primitive2d for BoxedPolyline2d {}
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impl FromIterator<Vec2> for BoxedPolyline2d {
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fn from_iter<I: IntoIterator<Item = Vec2>>(iter: I) -> Self {
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let vertices: Vec<Vec2> = iter.into_iter().collect();
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Self {
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vertices: vertices.into_boxed_slice(),
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}
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}
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}
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impl BoxedPolyline2d {
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/// Create a new `BoxedPolyline2d` from its vertices
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pub fn new(vertices: impl IntoIterator<Item = Vec2>) -> Self {
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Self::from_iter(vertices)
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}
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}
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/// A triangle in 2D space
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#[derive(Clone, Copy, Debug, PartialEq)]
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#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
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pub struct Triangle2d {
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/// The vertices of the triangle
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pub vertices: [Vec2; 3],
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}
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impl Primitive2d for Triangle2d {}
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impl Default for Triangle2d {
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/// Returns the default [`Triangle2d`] with the vertices `[0.0, 0.5]`, `[-0.5, -0.5]`, and `[0.5, -0.5]`.
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fn default() -> Self {
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Self {
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vertices: [Vec2::Y * 0.5, Vec2::new(-0.5, -0.5), Vec2::new(0.5, -0.5)],
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}
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}
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}
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impl Triangle2d {
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/// Create a new `Triangle2d` from points `a`, `b`, and `c`
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#[inline(always)]
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pub const fn new(a: Vec2, b: Vec2, c: Vec2) -> Self {
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Self {
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vertices: [a, b, c],
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}
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}
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/// Get the area of the triangle
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#[inline(always)]
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pub fn area(&self) -> f32 {
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let [a, b, c] = self.vertices;
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(a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y)).abs() / 2.0
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}
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/// Get the perimeter of the triangle
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#[inline(always)]
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pub fn perimeter(&self) -> f32 {
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let [a, b, c] = self.vertices;
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let ab = a.distance(b);
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let bc = b.distance(c);
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let ca = c.distance(a);
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ab + bc + ca
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}
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/// Get the [`WindingOrder`] of the triangle
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#[inline(always)]
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#[doc(alias = "orientation")]
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pub fn winding_order(&self) -> WindingOrder {
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let [a, b, c] = self.vertices;
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let area = (b - a).perp_dot(c - a);
|
|
if area > f32::EPSILON {
|
|
WindingOrder::CounterClockwise
|
|
} else if area < -f32::EPSILON {
|
|
WindingOrder::Clockwise
|
|
} else {
|
|
WindingOrder::Invalid
|
|
}
|
|
}
|
|
|
|
/// Compute the circle passing through all three vertices of the triangle.
|
|
/// The vector in the returned tuple is the circumcenter.
|
|
pub fn circumcircle(&self) -> (Circle, Vec2) {
|
|
// We treat the triangle as translated so that vertex A is at the origin. This simplifies calculations.
|
|
//
|
|
// A = (0, 0)
|
|
// *
|
|
// / \
|
|
// / \
|
|
// / \
|
|
// / \
|
|
// / U \
|
|
// / \
|
|
// *-------------*
|
|
// B C
|
|
|
|
let a = self.vertices[0];
|
|
let (b, c) = (self.vertices[1] - a, self.vertices[2] - a);
|
|
let b_length_sq = b.length_squared();
|
|
let c_length_sq = c.length_squared();
|
|
|
|
// Reference: https://en.wikipedia.org/wiki/Circumcircle#Cartesian_coordinates_2
|
|
let inv_d = (2.0 * (b.x * c.y - b.y * c.x)).recip();
|
|
let ux = inv_d * (c.y * b_length_sq - b.y * c_length_sq);
|
|
let uy = inv_d * (b.x * c_length_sq - c.x * b_length_sq);
|
|
let u = Vec2::new(ux, uy);
|
|
|
|
// Compute true circumcenter and circumradius, adding the tip coordinate so that
|
|
// A is translated back to its actual coordinate.
|
|
let center = u + a;
|
|
let radius = u.length();
|
|
|
|
(Circle { radius }, center)
|
|
}
|
|
|
|
/// Reverse the [`WindingOrder`] of the triangle
|
|
/// by swapping the first and last vertices
|
|
#[inline(always)]
|
|
pub fn reverse(&mut self) {
|
|
self.vertices.swap(0, 2);
|
|
}
|
|
}
|
|
|
|
/// A rectangle primitive
|
|
#[derive(Clone, Copy, Debug, PartialEq)]
|
|
#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
|
|
#[doc(alias = "Quad")]
|
|
pub struct Rectangle {
|
|
/// Half of the width and height of the rectangle
|
|
pub half_size: Vec2,
|
|
}
|
|
impl Primitive2d for Rectangle {}
|
|
|
|
impl Default for Rectangle {
|
|
/// Returns the default [`Rectangle`] with a half-width and half-height of `0.5`.
|
|
fn default() -> Self {
|
|
Self {
|
|
half_size: Vec2::splat(0.5),
|
|
}
|
|
}
|
|
}
|
|
|
|
impl Rectangle {
|
|
/// Create a new `Rectangle` from a full width and height
|
|
#[inline(always)]
|
|
pub fn new(width: f32, height: f32) -> Self {
|
|
Self::from_size(Vec2::new(width, height))
|
|
}
|
|
|
|
/// Create a new `Rectangle` from a given full size
|
|
#[inline(always)]
|
|
pub fn from_size(size: Vec2) -> Self {
|
|
Self {
|
|
half_size: size / 2.0,
|
|
}
|
|
}
|
|
|
|
/// Create a new `Rectangle` from two corner points
|
|
#[inline(always)]
|
|
pub fn from_corners(point1: Vec2, point2: Vec2) -> Self {
|
|
Self {
|
|
half_size: (point2 - point1).abs() / 2.0,
|
|
}
|
|
}
|
|
|
|
/// Create a `Rectangle` from a single length.
|
|
/// The resulting `Rectangle` will be the same size in every direction.
|
|
#[inline(always)]
|
|
pub fn from_length(length: f32) -> Self {
|
|
Self {
|
|
half_size: Vec2::splat(length / 2.0),
|
|
}
|
|
}
|
|
|
|
/// Get the size of the rectangle
|
|
#[inline(always)]
|
|
pub fn size(&self) -> Vec2 {
|
|
2.0 * self.half_size
|
|
}
|
|
|
|
/// Get the area of the rectangle
|
|
#[inline(always)]
|
|
pub fn area(&self) -> f32 {
|
|
4.0 * self.half_size.x * self.half_size.y
|
|
}
|
|
|
|
/// Get the perimeter of the rectangle
|
|
#[inline(always)]
|
|
pub fn perimeter(&self) -> f32 {
|
|
4.0 * (self.half_size.x + self.half_size.y)
|
|
}
|
|
|
|
/// Finds the point on the rectangle that is closest to the given `point`.
|
|
///
|
|
/// If the point is outside the rectangle, the returned point will be on the perimeter of the rectangle.
|
|
/// Otherwise, it will be inside the rectangle and returned as is.
|
|
#[inline(always)]
|
|
pub fn closest_point(&self, point: Vec2) -> Vec2 {
|
|
// Clamp point coordinates to the rectangle
|
|
point.clamp(-self.half_size, self.half_size)
|
|
}
|
|
}
|
|
|
|
/// A polygon with N vertices.
|
|
///
|
|
/// For a version without generics: [`BoxedPolygon`]
|
|
#[derive(Clone, Debug, PartialEq)]
|
|
#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
|
|
pub struct Polygon<const N: usize> {
|
|
/// The vertices of the `Polygon`
|
|
#[cfg_attr(feature = "serialize", serde(with = "super::serde::array"))]
|
|
pub vertices: [Vec2; N],
|
|
}
|
|
impl<const N: usize> Primitive2d for Polygon<N> {}
|
|
|
|
impl<const N: usize> FromIterator<Vec2> for Polygon<N> {
|
|
fn from_iter<I: IntoIterator<Item = Vec2>>(iter: I) -> Self {
|
|
let mut vertices: [Vec2; N] = [Vec2::ZERO; N];
|
|
|
|
for (index, i) in iter.into_iter().take(N).enumerate() {
|
|
vertices[index] = i;
|
|
}
|
|
Self { vertices }
|
|
}
|
|
}
|
|
|
|
impl<const N: usize> Polygon<N> {
|
|
/// Create a new `Polygon` from its vertices
|
|
pub fn new(vertices: impl IntoIterator<Item = Vec2>) -> Self {
|
|
Self::from_iter(vertices)
|
|
}
|
|
}
|
|
|
|
/// A polygon with a variable number of vertices, allocated on the heap
|
|
/// in a `Box<[Vec2]>`.
|
|
///
|
|
/// For a version without alloc: [`Polygon`]
|
|
#[derive(Clone, Debug, PartialEq)]
|
|
#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
|
|
pub struct BoxedPolygon {
|
|
/// The vertices of the `BoxedPolygon`
|
|
pub vertices: Box<[Vec2]>,
|
|
}
|
|
impl Primitive2d for BoxedPolygon {}
|
|
|
|
impl FromIterator<Vec2> for BoxedPolygon {
|
|
fn from_iter<I: IntoIterator<Item = Vec2>>(iter: I) -> Self {
|
|
let vertices: Vec<Vec2> = iter.into_iter().collect();
|
|
Self {
|
|
vertices: vertices.into_boxed_slice(),
|
|
}
|
|
}
|
|
}
|
|
|
|
impl BoxedPolygon {
|
|
/// Create a new `BoxedPolygon` from its vertices
|
|
pub fn new(vertices: impl IntoIterator<Item = Vec2>) -> Self {
|
|
Self::from_iter(vertices)
|
|
}
|
|
}
|
|
|
|
/// A polygon where all vertices lie on a circle, equally far apart.
|
|
#[derive(Clone, Copy, Debug, PartialEq)]
|
|
#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
|
|
pub struct RegularPolygon {
|
|
/// The circumcircle on which all vertices lie
|
|
pub circumcircle: Circle,
|
|
/// The number of sides
|
|
pub sides: usize,
|
|
}
|
|
impl Primitive2d for RegularPolygon {}
|
|
|
|
impl Default for RegularPolygon {
|
|
/// Returns the default [`RegularPolygon`] with six sides (a hexagon) and a circumradius of `0.5`.
|
|
fn default() -> Self {
|
|
Self {
|
|
circumcircle: Circle { radius: 0.5 },
|
|
sides: 6,
|
|
}
|
|
}
|
|
}
|
|
|
|
impl RegularPolygon {
|
|
/// Create a new `RegularPolygon`
|
|
/// from the radius of the circumcircle and a number of sides
|
|
///
|
|
/// # Panics
|
|
///
|
|
/// Panics if `circumradius` is non-positive
|
|
#[inline(always)]
|
|
pub fn new(circumradius: f32, sides: usize) -> Self {
|
|
assert!(circumradius > 0.0, "polygon has a non-positive radius");
|
|
assert!(sides > 2, "polygon has less than 3 sides");
|
|
|
|
Self {
|
|
circumcircle: Circle {
|
|
radius: circumradius,
|
|
},
|
|
sides,
|
|
}
|
|
}
|
|
|
|
/// Get the radius of the circumcircle on which all vertices
|
|
/// of the regular polygon lie
|
|
#[inline(always)]
|
|
pub fn circumradius(&self) -> f32 {
|
|
self.circumcircle.radius
|
|
}
|
|
|
|
/// Get the inradius or apothem of the regular polygon.
|
|
/// This is the radius of the largest circle that can
|
|
/// be drawn within the polygon
|
|
#[inline(always)]
|
|
#[doc(alias = "apothem")]
|
|
pub fn inradius(&self) -> f32 {
|
|
self.circumradius() * (PI / self.sides as f32).cos()
|
|
}
|
|
|
|
/// Get the length of one side of the regular polygon
|
|
#[inline(always)]
|
|
pub fn side_length(&self) -> f32 {
|
|
2.0 * self.circumradius() * (PI / self.sides as f32).sin()
|
|
}
|
|
|
|
/// Get the area of the regular polygon
|
|
#[inline(always)]
|
|
pub fn area(&self) -> f32 {
|
|
let angle: f32 = 2.0 * PI / (self.sides as f32);
|
|
(self.sides as f32) * self.circumradius().powi(2) * angle.sin() / 2.0
|
|
}
|
|
|
|
/// Get the perimeter of the regular polygon.
|
|
/// This is the sum of its sides
|
|
#[inline(always)]
|
|
pub fn perimeter(&self) -> f32 {
|
|
self.sides as f32 * self.side_length()
|
|
}
|
|
|
|
/// Get the internal angle of the regular polygon in degrees.
|
|
///
|
|
/// This is the angle formed by two adjacent sides with points
|
|
/// within the angle being in the interior of the polygon
|
|
#[inline(always)]
|
|
pub fn internal_angle_degrees(&self) -> f32 {
|
|
(self.sides - 2) as f32 / self.sides as f32 * 180.0
|
|
}
|
|
|
|
/// Get the internal angle of the regular polygon in radians.
|
|
///
|
|
/// This is the angle formed by two adjacent sides with points
|
|
/// within the angle being in the interior of the polygon
|
|
#[inline(always)]
|
|
pub fn internal_angle_radians(&self) -> f32 {
|
|
(self.sides - 2) as f32 * PI / self.sides as f32
|
|
}
|
|
|
|
/// Get the external angle of the regular polygon in degrees.
|
|
///
|
|
/// This is the angle formed by two adjacent sides with points
|
|
/// within the angle being in the exterior of the polygon
|
|
#[inline(always)]
|
|
pub fn external_angle_degrees(&self) -> f32 {
|
|
360.0 / self.sides as f32
|
|
}
|
|
|
|
/// Get the external angle of the regular polygon in radians.
|
|
///
|
|
/// This is the angle formed by two adjacent sides with points
|
|
/// within the angle being in the exterior of the polygon
|
|
#[inline(always)]
|
|
pub fn external_angle_radians(&self) -> f32 {
|
|
2.0 * PI / self.sides as f32
|
|
}
|
|
|
|
/// Returns an iterator over the vertices of the regular polygon,
|
|
/// rotated counterclockwise by the given angle in radians.
|
|
///
|
|
/// With a rotation of 0, a vertex will be placed at the top `(0.0, circumradius)`.
|
|
pub fn vertices(self, rotation: f32) -> impl IntoIterator<Item = Vec2> {
|
|
// Add pi/2 so that the polygon has a vertex at the top (sin is 1.0 and cos is 0.0)
|
|
let start_angle = rotation + std::f32::consts::FRAC_PI_2;
|
|
let step = std::f32::consts::TAU / self.sides as f32;
|
|
|
|
(0..self.sides).map(move |i| {
|
|
let theta = start_angle + i as f32 * step;
|
|
let (sin, cos) = theta.sin_cos();
|
|
Vec2::new(cos, sin) * self.circumcircle.radius
|
|
})
|
|
}
|
|
}
|
|
|
|
/// A 2D capsule primitive, also known as a stadium or pill shape.
|
|
///
|
|
/// A two-dimensional capsule is defined as a neighborhood of points at a distance (radius) from a line
|
|
#[derive(Clone, Copy, Debug, PartialEq)]
|
|
#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
|
|
#[doc(alias = "stadium", alias = "pill")]
|
|
pub struct Capsule2d {
|
|
/// The radius of the capsule
|
|
pub radius: f32,
|
|
/// Half the height of the capsule, excluding the hemicircles
|
|
pub half_length: f32,
|
|
}
|
|
impl Primitive2d for Capsule2d {}
|
|
|
|
impl Default for Capsule2d {
|
|
/// Returns the default [`Capsule2d`] with a radius of `0.5` and a half-height of `0.5`,
|
|
/// excluding the hemicircles.
|
|
fn default() -> Self {
|
|
Self {
|
|
radius: 0.5,
|
|
half_length: 0.5,
|
|
}
|
|
}
|
|
}
|
|
|
|
impl Capsule2d {
|
|
/// Create a new `Capsule2d` from a radius and length
|
|
pub fn new(radius: f32, length: f32) -> Self {
|
|
Self {
|
|
radius,
|
|
half_length: length / 2.0,
|
|
}
|
|
}
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod tests {
|
|
// Reference values were computed by hand and/or with external tools
|
|
|
|
use super::*;
|
|
use approx::assert_relative_eq;
|
|
|
|
#[test]
|
|
fn rectangle_closest_point() {
|
|
let rectangle = Rectangle::new(2.0, 2.0);
|
|
assert_eq!(rectangle.closest_point(Vec2::X * 10.0), Vec2::X);
|
|
assert_eq!(rectangle.closest_point(Vec2::NEG_ONE * 10.0), Vec2::NEG_ONE);
|
|
assert_eq!(
|
|
rectangle.closest_point(Vec2::new(0.25, 0.1)),
|
|
Vec2::new(0.25, 0.1)
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn circle_closest_point() {
|
|
let circle = Circle { radius: 1.0 };
|
|
assert_eq!(circle.closest_point(Vec2::X * 10.0), Vec2::X);
|
|
assert_eq!(
|
|
circle.closest_point(Vec2::NEG_ONE * 10.0),
|
|
Vec2::NEG_ONE.normalize()
|
|
);
|
|
assert_eq!(
|
|
circle.closest_point(Vec2::new(0.25, 0.1)),
|
|
Vec2::new(0.25, 0.1)
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn annulus_closest_point() {
|
|
let annulus = Annulus::new(1.5, 2.0);
|
|
assert_eq!(annulus.closest_point(Vec2::X * 10.0), Vec2::X * 2.0);
|
|
assert_eq!(
|
|
annulus.closest_point(Vec2::NEG_ONE),
|
|
Vec2::NEG_ONE.normalize() * 1.5
|
|
);
|
|
assert_eq!(
|
|
annulus.closest_point(Vec2::new(1.55, 0.85)),
|
|
Vec2::new(1.55, 0.85)
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn circle_math() {
|
|
let circle = Circle { radius: 3.0 };
|
|
assert_eq!(circle.diameter(), 6.0, "incorrect diameter");
|
|
assert_eq!(circle.area(), 28.274334, "incorrect area");
|
|
assert_eq!(circle.perimeter(), 18.849556, "incorrect perimeter");
|
|
}
|
|
|
|
#[test]
|
|
fn annulus_math() {
|
|
let annulus = Annulus::new(2.5, 3.5);
|
|
assert_eq!(annulus.diameter(), 7.0, "incorrect diameter");
|
|
assert_eq!(annulus.thickness(), 1.0, "incorrect thickness");
|
|
assert_eq!(annulus.area(), 18.849556, "incorrect area");
|
|
assert_eq!(annulus.perimeter(), 37.699112, "incorrect perimeter");
|
|
}
|
|
|
|
#[test]
|
|
fn ellipse_math() {
|
|
let ellipse = Ellipse::new(3.0, 1.0);
|
|
assert_eq!(ellipse.area(), 9.424778, "incorrect area");
|
|
|
|
assert_eq!(ellipse.eccentricity(), 0.94280905, "incorrect eccentricity");
|
|
|
|
let line = Ellipse::new(1., 0.);
|
|
assert_eq!(line.eccentricity(), 1., "incorrect line eccentricity");
|
|
|
|
let circle = Ellipse::new(2., 2.);
|
|
assert_eq!(circle.eccentricity(), 0., "incorrect circle eccentricity");
|
|
}
|
|
|
|
#[test]
|
|
fn ellipse_perimeter() {
|
|
let circle = Ellipse::new(1., 1.);
|
|
assert_relative_eq!(circle.perimeter(), 6.2831855);
|
|
|
|
let line = Ellipse::new(75_000., 0.5);
|
|
assert_relative_eq!(line.perimeter(), 300_000.);
|
|
|
|
let ellipse = Ellipse::new(0.5, 2.);
|
|
assert_relative_eq!(ellipse.perimeter(), 8.578423);
|
|
|
|
let ellipse = Ellipse::new(5., 3.);
|
|
assert_relative_eq!(ellipse.perimeter(), 25.526999);
|
|
}
|
|
|
|
#[test]
|
|
fn triangle_math() {
|
|
let triangle = Triangle2d::new(
|
|
Vec2::new(-2.0, -1.0),
|
|
Vec2::new(1.0, 4.0),
|
|
Vec2::new(7.0, 0.0),
|
|
);
|
|
assert_eq!(triangle.area(), 21.0, "incorrect area");
|
|
assert_eq!(triangle.perimeter(), 22.097439, "incorrect perimeter");
|
|
}
|
|
|
|
#[test]
|
|
fn triangle_winding_order() {
|
|
let mut cw_triangle = Triangle2d::new(
|
|
Vec2::new(0.0, 2.0),
|
|
Vec2::new(-0.5, -1.2),
|
|
Vec2::new(-1.0, -1.0),
|
|
);
|
|
assert_eq!(cw_triangle.winding_order(), WindingOrder::Clockwise);
|
|
|
|
let ccw_triangle = Triangle2d::new(
|
|
Vec2::new(-1.0, -1.0),
|
|
Vec2::new(-0.5, -1.2),
|
|
Vec2::new(0.0, 2.0),
|
|
);
|
|
assert_eq!(ccw_triangle.winding_order(), WindingOrder::CounterClockwise);
|
|
|
|
// The clockwise triangle should be the same as the counterclockwise
|
|
// triangle when reversed
|
|
cw_triangle.reverse();
|
|
assert_eq!(cw_triangle, ccw_triangle);
|
|
|
|
let invalid_triangle = Triangle2d::new(
|
|
Vec2::new(0.0, 2.0),
|
|
Vec2::new(0.0, -1.0),
|
|
Vec2::new(0.0, -1.2),
|
|
);
|
|
assert_eq!(invalid_triangle.winding_order(), WindingOrder::Invalid);
|
|
}
|
|
|
|
#[test]
|
|
fn rectangle_math() {
|
|
let rectangle = Rectangle::new(3.0, 7.0);
|
|
assert_eq!(
|
|
rectangle,
|
|
Rectangle::from_corners(Vec2::new(-1.5, -3.5), Vec2::new(1.5, 3.5))
|
|
);
|
|
assert_eq!(rectangle.area(), 21.0, "incorrect area");
|
|
assert_eq!(rectangle.perimeter(), 20.0, "incorrect perimeter");
|
|
}
|
|
|
|
#[test]
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fn regular_polygon_math() {
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let polygon = RegularPolygon::new(3.0, 6);
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assert_eq!(polygon.inradius(), 2.598076, "incorrect inradius");
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assert_eq!(polygon.side_length(), 3.0, "incorrect side length");
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assert_relative_eq!(polygon.area(), 23.38268, epsilon = 0.00001);
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assert_eq!(polygon.perimeter(), 18.0, "incorrect perimeter");
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assert_eq!(
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polygon.internal_angle_degrees(),
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120.0,
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|
"incorrect internal angle"
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|
);
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assert_eq!(
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|
polygon.internal_angle_radians(),
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|
120_f32.to_radians(),
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|
"incorrect internal angle"
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|
);
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|
assert_eq!(
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|
polygon.external_angle_degrees(),
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|
60.0,
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|
"incorrect external angle"
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|
);
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|
assert_eq!(
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|
polygon.external_angle_radians(),
|
|
60_f32.to_radians(),
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|
"incorrect external angle"
|
|
);
|
|
}
|
|
|
|
#[test]
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|
fn triangle_circumcenter() {
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|
let triangle = Triangle2d::new(
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|
Vec2::new(10.0, 2.0),
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|
Vec2::new(-5.0, -3.0),
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|
Vec2::new(2.0, -1.0),
|
|
);
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|
let (Circle { radius }, circumcenter) = triangle.circumcircle();
|
|
|
|
// Calculated with external calculator
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|
assert_eq!(radius, 98.34887);
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|
assert_eq!(circumcenter, Vec2::new(-28.5, 92.5));
|
|
}
|
|
|
|
#[test]
|
|
fn regular_polygon_vertices() {
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|
let polygon = RegularPolygon::new(1.0, 4);
|
|
|
|
// Regular polygons have a vertex at the top by default
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|
let mut vertices = polygon.vertices(0.0).into_iter();
|
|
assert!((vertices.next().unwrap() - Vec2::Y).length() < 1e-7);
|
|
|
|
// Rotate by 45 degrees, forming an axis-aligned square
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|
let mut rotated_vertices = polygon.vertices(std::f32::consts::FRAC_PI_4).into_iter();
|
|
|
|
// Distance from the origin to the middle of a side, derived using Pythagorean theorem
|
|
let side_sistance = std::f32::consts::FRAC_1_SQRT_2;
|
|
assert!(
|
|
(rotated_vertices.next().unwrap() - Vec2::new(-side_sistance, side_sistance)).length()
|
|
< 1e-7,
|
|
);
|
|
}
|
|
}
|