Thanks @jijinbei.
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use super::*;
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impl Plane {
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/// Creates a new plane from three points.
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#[inline(always)]
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pub const fn new(origin: Point3, one: Point3, another: Point3) -> Plane {
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Plane {
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o: origin,
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p: one,
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q: another,
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}
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}
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/// Returns the origin
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#[inline(always)]
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pub const fn origin(&self) -> Point3 { self.o }
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/// Returns the u-axis
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#[inline(always)]
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pub fn u_axis(&self) -> Vector3 { self.p - self.o }
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/// Returns the v-axis
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#[inline(always)]
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pub fn v_axis(&self) -> Vector3 { self.q - self.o }
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/// Returns the normal
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/// # Examples
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/// ```
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/// use truck_geometry::prelude::*;
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/// let plane = Plane::new(
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/// Point3::new(0.0, 0.0, 0.0),
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/// Point3::new(1.0, 0.0, 0.0),
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/// Point3::new(0.0, 1.0, 0.0),
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/// );
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/// assert_near!(plane.normal(), Vector3::unit_z());
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/// ```
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#[inline(always)]
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pub fn normal(&self) -> Vector3 { self.u_axis().cross(self.v_axis()).normalize() }
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/// Gets the parameter of `pt` in plane's matrix.
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/// # Examples
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/// ```
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/// use truck_geometry::prelude::*;
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/// let plane = Plane::new(
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/// Point3::new(1.0, 2.0, 3.0),
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/// Point3::new(2.0, 1.0, 3.0),
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/// Point3::new(3.0, 4.0, -1.0),
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/// );
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///
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/// let pt = Point3::new(2.1, -6.5, 4.7);
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/// let prm = plane.get_parameter(pt);
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/// let rev = plane.origin()
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/// + prm[0] * plane.u_axis()
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/// + prm[1] * plane.v_axis()
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/// + prm[2] * plane.normal();
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/// assert_near!(pt, rev);
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/// ```
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#[inline(always)]
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pub fn get_parameter(&self, pt: Point3) -> Vector3 {
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let a = self.u_axis();
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let b = self.v_axis();
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let c = self.normal();
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let mat = Matrix3::from_cols(a, b, c).invert().unwrap();
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mat * (pt - self.o)
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}
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/// into B-spline surface
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/// # Examples
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/// ```
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/// use truck_geometry::prelude::*;
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/// let pt0 = Point3::new(0.0, 1.0, 2.0);
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/// let pt1 = Point3::new(1.0, 1.0, 3.0);
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/// let pt2 = Point3::new(0.0, 2.0, 3.0);
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/// let plane: Plane = Plane::new(pt0, pt1, pt2);
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/// let surface: BSplineSurface<Point3> = plane.into_bspline();
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/// assert_eq!(surface.range_tuple(), ((0.0, 1.0), (0.0, 1.0)));
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///
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/// const N: usize = 100;
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/// for i in 0..=N {
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/// for j in 0..=N {
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/// let u = i as f64 / N as f64;
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/// let v = j as f64 / N as f64;
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/// let res = surface.subs(u, v);
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/// let ans = plane.subs(u, v);
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/// assert_near!(ans, res);
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/// }
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/// }
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/// ```
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#[inline(always)]
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pub fn into_bspline(&self) -> BSplineSurface<Point3> {
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let o = self.o;
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let p = self.p;
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let q = self.q;
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BSplineSurface::debug_new(
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(KnotVec::bezier_knot(1), KnotVec::bezier_knot(1)),
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vec![vec![o, q], vec![p, p + (q - o)]],
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)
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}
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/// into NURBS surface
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/// # Examples
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/// ```
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/// use truck_geometry::prelude::*;
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/// let pt0 = Point3::new(0.0, 1.0, 2.0);
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/// let pt1 = Point3::new(1.0, 1.0, 3.0);
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/// let pt2 = Point3::new(0.0, 2.0, 3.0);
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/// let plane: Plane = Plane::new(pt0, pt1, pt2);
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/// let surface: NurbsSurface<Vector4> = plane.into_nurbs();
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/// assert_eq!(surface.range_tuple(), ((0.0, 1.0), (0.0, 1.0)));
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///
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/// const N: usize = 100;
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/// for i in 0..=N {
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/// for j in 0..=N {
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/// let u = i as f64 / N as f64;
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/// let v = j as f64 / N as f64;
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/// let res = surface.subs(u, v);
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/// let ans = plane.subs(u, v);
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/// assert_near!(ans, res);
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/// }
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/// }
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/// ```
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#[inline(always)]
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pub fn into_nurbs(&self) -> NurbsSurface<Vector4> {
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let o = self.o.to_homogeneous();
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let p = self.p.to_homogeneous();
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let q = self.q.to_homogeneous();
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NurbsSurface::new(BSplineSurface::debug_new(
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(KnotVec::bezier_knot(1), KnotVec::bezier_knot(1)),
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vec![vec![o, q], vec![p, p + q - o]],
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))
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}
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}
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impl ParametricSurface for Plane {
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type Point = Point3;
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type Vector = Vector3;
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#[inline(always)]
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fn subs(&self, u: f64, v: f64) -> Point3 {
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self.o + u * (self.p - self.o) + v * (self.q - self.o)
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}
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#[inline(always)]
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fn uder(&self, _: f64, _: f64) -> Vector3 { self.p - self.o }
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#[inline(always)]
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fn vder(&self, _: f64, _: f64) -> Vector3 { self.q - self.o }
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#[inline(always)]
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fn uuder(&self, _: f64, _: f64) -> Vector3 { Vector3::zero() }
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#[inline(always)]
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fn uvder(&self, _: f64, _: f64) -> Vector3 { Vector3::zero() }
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#[inline(always)]
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fn vvder(&self, _: f64, _: f64) -> Vector3 { Vector3::zero() }
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/// as square
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#[inline(always)]
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fn parameter_range(&self) -> (ParameterRange, ParameterRange) {
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let range = (Bound::Included(0.0), Bound::Included(1.0));
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(range, range)
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}
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}
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impl ParametricSurface3D for Plane {
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#[inline(always)]
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fn normal(&self, _: f64, _: f64) -> Vector3 { self.normal() }
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}
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impl BoundedSurface for Plane {}
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impl Invertible for Plane {
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#[inline(always)]
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fn inverse(&self) -> Self {
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Plane {
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o: self.o,
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p: self.q,
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q: self.p,
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}
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}
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#[inline(always)]
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fn invert(&mut self) { *self = self.inverse(); }
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}
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impl IncludeCurve<BSplineCurve<Point3>> for Plane {
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#[inline(always)]
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fn include(&self, curve: &BSplineCurve<Point3>) -> bool {
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let origin = self.origin();
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let normal = self.normal();
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curve
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.control_points()
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.iter()
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.all(|pt| (pt - origin).dot(normal).so_small())
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}
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}
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impl IncludeCurve<NurbsCurve<Vector4>> for Plane {
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fn include(&self, curve: &NurbsCurve<Vector4>) -> bool {
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let origin = self.origin();
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let normal = self.normal();
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let (s, e) = (curve.front(), curve.back());
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if !(s - origin).dot(normal).so_small() || !(e - origin).dot(normal).so_small() {
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return false;
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}
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curve.non_rationalized().control_points().iter().all(|pt| {
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if pt[3].so_small() {
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true
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} else {
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let pt = Point3::from_homogeneous(*pt);
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(pt - origin).dot(normal).so_small()
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}
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})
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}
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}
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impl ParameterDivision2D for Plane {
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#[inline(always)]
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fn parameter_division(&self, range: ((f64, f64), (f64, f64)), _: f64) -> (Vec<f64>, Vec<f64>) {
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(vec![range.0 .0, range.0 .1], vec![range.1 .0, range.1 .1])
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}
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}
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impl<T: Transform3<Scalar = f64>> Transformed<T> for Plane {
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#[inline(always)]
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fn transform_by(&mut self, trans: T) {
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self.o = trans.transform_point(self.o);
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self.p = trans.transform_point(self.p);
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self.q = trans.transform_point(self.q);
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}
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#[inline(always)]
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fn transformed(&self, trans: T) -> Self {
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Plane {
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o: trans.transform_point(self.o),
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p: trans.transform_point(self.p),
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q: trans.transform_point(self.q),
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}
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}
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}
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impl SearchParameter<D2> for Plane {
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type Point = Point3;
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#[inline(always)]
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fn search_parameter<H: Into<SPHint2D>>(
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&self,
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point: Point3,
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_: H,
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_: usize,
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) -> Option<(f64, f64)> {
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let v = self.get_parameter(point);
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match v[2].so_small() {
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true => Some((v[0], v[1])),
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false => None,
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}
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}
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}
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impl SearchNearestParameter<D2> for Plane {
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type Point = Point3;
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#[inline(always)]
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fn search_nearest_parameter<H: Into<SPHint2D>>(
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&self,
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point: Point3,
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_: H,
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_: usize,
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) -> Option<(f64, f64)> {
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let v = self.get_parameter(point);
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Some((v[0], v[1]))
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}
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}
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