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Implemented a more efficient orthonormal basis function.

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Algorithm taken from the paper "Building an Orthonormal
Basis, Revisited" by Duff et al.
This commit is contained in:
Nathan Vegdahl 2017-03-29 13:19:51 -07:00
parent 4a86c4122a
commit 7223f69151
1 changed files with 7 additions and 9 deletions
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16
src/math/mod.rs
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@ -130,16 +130,14 @@ pub fn log2_64(value: u64) -> u64 {
/// The input vector, v, becomes the first vector of the /// The input vector, v, becomes the first vector of the
/// returned tuple, with the other two vectors in the returned /// returned tuple, with the other two vectors in the returned
/// tuple defining the orthoganal axes. /// tuple defining the orthoganal axes.
///
/// Algorithm taken from "Building an Orthonormal Basis, Revisited" by Duff et al.
pub fn coordinate_system_from_vector(v: Vector) -> (Vector, Vector, Vector) { pub fn coordinate_system_from_vector(v: Vector) -> (Vector, Vector, Vector) {
let v2 = if v.x().abs() > v.y().abs() { let sign = v.z().signum();
let invlen = 1.0 / ((v.x() * v.x()) + (v.z() * v.z())).sqrt(); let a = -1.0 / (sign + v.z());
Vector::new(-v.z() * invlen, 0.0, v.x() * invlen) let b = v.x() * v.y() * a;
} else { let v2 = Vector::new(1.0 + sign * v.x() * v.x() * a, sign * b, -sign * v.x());
let invlen = 1.0 / ((v.y() * v.y()) + (v.z() * v.z())).sqrt(); let v3 = Vector::new(b, sign + v.y() * v.y() * a, -v.y());
Vector::new(0.0, v.z() * invlen, -v.y() * invlen)
};
let v3 = cross(v, v2);
(v, v2, v3) (v, v2, v3)
} }