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use crate::RealNumber;
use crate::aliases::{TVec, TVec2, TVec3};
use crate::traits::Number;
/// Returns `true` if two vectors are collinear (up to an epsilon).
///
/// # See also:
///
/// * [`are_collinear2d()`]
pub fn are_collinear<T: Number>(v0: &TVec3<T>, v1: &TVec3<T>, epsilon: T) -> bool {
abs_diff_eq!(v0.cross(v1), TVec3::<T>::zeros(), epsilon = epsilon)
}
/// Returns `true` if two 2D vectors are collinear (up to an epsilon).
///
/// # See also:
///
/// * [`are_collinear()`]
pub fn are_collinear2d<T: Number>(v0: &TVec2<T>, v1: &TVec2<T>, epsilon: T) -> bool {
abs_diff_eq!(v0.perp(v1), T::zero(), epsilon = epsilon)
}
/// Returns `true` if two vectors are orthogonal (up to an epsilon).
pub fn are_orthogonal<T: Number, const D: usize>(
v0: &TVec<T, D>,
v1: &TVec<T, D>,
epsilon: T,
) -> bool {
abs_diff_eq!(v0.dot(v1), T::zero(), epsilon = epsilon)
}
//pub fn are_orthonormal<T: Number, const D: usize>(v0: &TVec<T, D>, v1: &TVec<T, D>, epsilon: T) -> bool {
// unimplemented!()
//}
/// Returns `true` if all the components of `v` are zero (up to an epsilon).
pub fn is_comp_null<T: Number, const D: usize>(v: &TVec<T, D>, epsilon: T) -> TVec<bool, D> {
v.map(|x| abs_diff_eq!(x, T::zero(), epsilon = epsilon))
}
/// Returns `true` if `v` has a magnitude of 1 (up to an epsilon).
pub fn is_normalized<T: RealNumber, const D: usize>(v: &TVec<T, D>, epsilon: T) -> bool {
// sqrt(1 + epsilon_{norm²} = 1 + epsilon_{norm}
// ==> epsilon_{norm²} = epsilon_{norm}² + 2*epsilon_{norm}
// For small epsilon, epsilon² is basically zero, so use 2*epsilon.
abs_diff_eq!(v.norm_squared(), T::one(), epsilon = epsilon + epsilon)
}
/// Returns `true` if `v` is zero (up to an epsilon).
pub fn is_null<T: RealNumber, const D: usize>(v: &TVec<T, D>, epsilon: T) -> bool {
abs_diff_eq!(v.norm_squared(), T::zero(), epsilon = epsilon * epsilon)
}