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plane.rs
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plane.rs
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// Copyright 2013-2014 The CGMath Developers. For a full listing of the authors,
// refer to the AUTHORS file at the top-level directory of this distribution.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
use std::fmt;
use std::num::Zero;
use approx::ApproxEq;
use intersect::Intersect;
use num::BaseFloat;
use point::{Point, Point3};
use ray::Ray3;
use vector::{Vector3, Vector4};
use vector::{Vector, EuclideanVector};
/// A 3-dimensional plane formed from the equation: `A*x + B*y + C*z - D = 0`.
///
/// # Fields
///
/// - `n`: a unit vector representing the normal of the plane where:
/// - `n.x`: corresponds to `A` in the plane equation
/// - `n.y`: corresponds to `B` in the plane equation
/// - `n.z`: corresponds to `C` in the plane equation
/// - `d`: the distance value, corresponding to `D` in the plane equation
///
/// # Notes
///
/// The `A*x + B*y + C*z - D = 0` form is preferred over the other common
/// alternative, `A*x + B*y + C*z + D = 0`, because it tends to avoid
/// superfluous negations (see _Real Time Collision Detection_, p. 55).
#[deriving(Clone, PartialEq)]
pub struct Plane<S> {
pub n: Vector3<S>,
pub d: S,
}
impl<S: BaseFloat> Plane<S> {
/// Construct a plane from a normal vector and a scalar distance. The
/// plane will be perpendicular to `n`, and `d` units offset from the
/// origin.
pub fn new(n: Vector3<S>, d: S) -> Plane<S> {
Plane { n: n, d: d }
}
/// # Arguments
///
/// - `a`: the `x` component of the normal
/// - `b`: the `y` component of the normal
/// - `c`: the `z` component of the normal
/// - `d`: the plane's distance value
pub fn from_abcd(a: S, b: S, c: S, d: S) -> Plane<S> {
Plane { n: Vector3::new(a, b, c), d: d }
}
/// Construct a plane from the components of a four-dimensional vector
pub fn from_vector4(v: Vector4<S>) -> Plane<S> {
match v {
Vector4 { x, y, z, w } => Plane { n: Vector3::new(x, y, z), d: w },
}
}
/// Constructs a plane that passes through the the three points `a`, `b` and `c`
pub fn from_points(a: Point3<S>, b: Point3<S>, c: Point3<S>) -> Option<Plane<S>> {
// create two vectors that run parallel to the plane
let v0 = b.sub_p(&a);
let v1 = c.sub_p(&a);
// find the normal vector that is perpendicular to v1 and v2
let mut n = v0.cross(&v1);
if n.approx_eq(&Vector3::zero()) { None }
else {
// compute the normal and the distance to the plane
n.normalize_self();
let d = -a.dot(&n);
Some(Plane::new(n, d))
}
}
}
impl<S: BaseFloat> Intersect<Option<Point3<S>>> for (Plane<S>, Ray3<S>) {
fn intersection(&self) -> Option<Point3<S>> {
match *self {
(ref p, ref r) => {
let t = -(p.d + r.origin.dot(&p.n)) / r.direction.dot(&p.n);
if t < Zero::zero() { None }
else { Some(r.origin.add_v(&r.direction.mul_s(t))) }
}
}
}
}
impl<S: BaseFloat> Intersect<Option<Ray3<S>>> for (Plane<S>, Plane<S>) {
fn intersection(&self) -> Option<Ray3<S>> {
fail!("Not yet implemented");
}
}
impl<S: BaseFloat> Intersect<Option<Point3<S>>> for (Plane<S>, Plane<S>, Plane<S>) {
fn intersection(&self) -> Option<Point3<S>> {
fail!("Not yet implemented");
}
}
impl<S: BaseFloat + ApproxEq<S>>
ApproxEq<S> for Plane<S> {
#[inline]
fn approx_eq_eps(&self, other: &Plane<S>, epsilon: &S) -> bool {
self.n.approx_eq_eps(&other.n, epsilon) &&
self.d.approx_eq_eps(&other.d, epsilon)
}
}
impl<S: BaseFloat> fmt::Show for Plane<S> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "{:f}x + {:f}y + {:f}z - {:f} = 0",
self.n.x, self.n.y, self.n.z, self.d)
}
}