Struct cgmath::Basis2
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pub struct Basis2<S> {
// some fields omitted
}A two-dimensional rotation matrix.
The matrix is guaranteed to be orthogonal, so some operations can be
implemented more efficiently than the implementations for math::Matrix2. To
enforce orthogonality at the type level the operations have been restricted
to a subset of those implemented on Matrix2.
Example
Suppose we want to rotate a vector that lies in the x-y plane by some angle. We can accomplish this quite easily with a two-dimensional rotation matrix:
use cgmath::rad; use cgmath::Vector2; use cgmath::{Matrix, Matrix2}; use cgmath::{Rotation, Rotation2, Basis2}; use cgmath::ApproxEq; use std::f64; // For simplicity, we will rotate the unit x vector to the unit y vector -- // so the angle is 90 degrees, or π/2. let unit_x: Vector2<f64> = Vector2::unit_x(); let rot: Basis2<f64> = Rotation2::from_angle(rad(0.5f64 * f64::consts::PI)); // Rotate the vector using the two-dimensional rotation matrix: let unit_y = rot.rotate_vector(&unit_x); // Since sin(π/2) may not be exactly zero due to rounding errors, we can // use cgmath's approx_eq() feature to show that it is close enough. assert!(unit_y.approx_eq(&Vector2::unit_y())); // This is exactly equivalent to using the raw matrix itself: let unit_y2: Matrix2<_> = rot.into(); let unit_y2 = unit_y2.mul_v(&unit_x); assert_eq!(unit_y2, unit_y); // Note that we can also concatenate rotations: let rot_half: Basis2<f64> = Rotation2::from_angle(rad(0.25f64 * f64::consts::PI)); let unit_y3 = rot_half.concat(&rot_half).rotate_vector(&unit_x); assert!(unit_y3.approx_eq(&unit_y2));