圆的特征有圆心，没有问题。圆结构用2个长度相等、互相垂直的矢量代替变径，我有些看不明白有什么特殊意义。很像椭圆的定义方式。源码如下：

use approx::AbsDiffEq;use crate::{Aabb, Point, Scalar, Transform, Vector};/// n维圆
///
/// 圆的维度由常量泛型“D”参数定义。
#[derive(Clone, Copy, Debug, Default, Eq, PartialEq, Hash, Ord, PartialOrd)]
pub struct Circle<const D: usize> {center: Point<D>,a: Vector<D>,b: Vector<D>,
}impl<const D: usize> Circle<D> {
///构建一个圆 
/// 
///#恐慌 
/// 
///如果不符合以下任何要求，则会出现恐慌： 
/// 
///-圆半径（由“a”和“b”的长度定义）不得为零。 
///-“a”和“b”的长度必须相等。 
///-“a”和“b”必须相互垂直。pub fn new(center: impl Into<Point<D>>,a: impl Into<Vector<D>>,b: impl Into<Vector<D>>,) -> Self {let center = center.into();let a = a.into();let b = b.into();assert_eq!(a.magnitude(),b.magnitude(),"`a` and `b` must be of equal length");assert_ne!(a.magnitude(),Scalar::ZERO,"circle radius must not be zero");// Requiring the vector to be *precisely* perpendicular is not// practical, because of numerical inaccuracy. This epsilon value seems// seems to work for now, but maybe it needs to become configurable.assert!(a.dot(&b) < Scalar::default_epsilon(),"`a` and `b` must be perpendicular to each other");Self { center, a, b }}/// Construct a `Circle` from a center point and a radiuspub fn from_center_and_radius(center: impl Into<Point<D>>,radius: impl Into<Scalar>,) -> Self {let radius = radius.into();let mut a = [Scalar::ZERO; D];let mut b = [Scalar::ZERO; D];a[0] = radius;b[1] = radius;Self::new(center, a, b)}/// Access the center point of the circlepub fn center(&self) -> Point<D> {self.center}/// Access the radius of the circlepub fn radius(&self) -> Scalar {self.a().magnitude()}/// Access the vector that defines the starting point of the circle////// The point where this vector points from the circle center, is the zero/// coordinate of the circle's coordinate system. The length of the vector/// defines the circle's radius.////// Please also refer to [`Self::b`].pub fn a(&self) -> Vector<D> {self.a}/// Access the vector that defines the plane of the circle////// Also defines the direction of the circle's coordinate system. The length/// is equal to the circle's radius, and this vector is perpendicular to/// [`Self::a`].pub fn b(&self) -> Vector<D> {self.b}/// Create a new instance that is reversed#[must_use]pub fn reverse(mut self) -> Self {self.b = -self.b;self}/// Convert a `D`-dimensional point to circle coordinates////// Converts the provided point into circle coordinates between `0.`/// (inclusive) and `PI * 2.` (exclusive).////// Projects the point onto the circle before computing circle coordinate,/// ignoring the radius. This is done to make this method robust against/// floating point accuracy issues.////// Callers are advised to be careful about the points they pass, as the/// point not being on the curve, intentional or not, will not result in an/// error.pub fn point_to_circle_coords(&self,point: impl Into<Point<D>>,) -> Point<1> {let vector = (point.into() - self.center).to_uv();let atan = Scalar::atan2(vector.v, vector.u);let coord = if atan >= Scalar::ZERO {atan} else {atan + Scalar::TAU};Point::from([coord])}/// Convert a point in circle coordinates into a `D`-dimensional pointpub fn point_from_circle_coords(&self,point: impl Into<Point<1>>,) -> Point<D> {self.center + self.vector_from_circle_coords(point.into().coords)}/// Convert a vector in circle coordinates into a `D`-dimensional pointpub fn vector_from_circle_coords(&self,vector: impl Into<Vector<1>>,) -> Vector<D> {let angle = vector.into().t;let (sin, cos) = angle.sin_cos();self.a * cos + self.b * sin}/// Calculate an AABB for the circlepub fn aabb(&self) -> Aabb<D> {let center_to_min_max = Vector::from_component(self.radius());Aabb {min: self.center() - center_to_min_max,max: self.center() + center_to_min_max,}}
}impl Circle<3> {/// # Transform the circlepub fn transform(&self, transform: &Transform) -> Self {Circle::new(transform.transform_point(&self.center()),transform.transform_vector(&self.a()),transform.transform_vector(&self.b()),)}
}#[cfg(test)]
mod tests {use std::f64::consts::{FRAC_PI_2, PI};use crate::{Circle, Point, Vector};#[test]fn point_to_circle_coords() {let circle = Circle {center: Point::from([1., 2., 3.]),a: Vector::from([1., 0., 0.]),b: Vector::from([0., 1., 0.]),};assert_eq!(circle.point_to_circle_coords([2., 2., 3.]),Point::from([0.]),);assert_eq!(circle.point_to_circle_coords([1., 3., 3.]),Point::from([FRAC_PI_2]),);assert_eq!(circle.point_to_circle_coords([0., 2., 3.]),Point::from([PI]),);assert_eq!(circle.point_to_circle_coords([1., 1., 3.]),Point::from([FRAC_PI_2 * 3.]),);}
}