Add Plane::from_points constructor and impl ApproxEq for Plane

src/cgmath/plane.rs

@@ -14,25 +14,67 @@
 // limitations under the License.
 
 use intersect::Intersect;
-use point::Point3;
+use point::{Point, Point3};
 use ray::Ray3;
-use vector::Vec3;
+use vector::{Vector, EuclideanVector, Vec3};
 
 use std::fmt;
 
-/// A 3-dimendional plane formed from the equation: `Ax + Bx + Cx + D = 0`
+/// A 3-dimendional plane formed from the equation: `a*x + b*y + c*z - d = 0`.
 ///
 /// # Fields
 ///
-/// - `normal`: the normal of the plane where:
-///   - `normal.x`: corresponds to `A` in the plane equation
-///   - `normal.y`: corresponds to `B` in the plane equation
-///   - `normal.z`: corresponds to `C` in the plane equation
-/// - `distance`: the distance value, corresponding to `D` in the plane equation
+/// - `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, Eq)]
 pub struct Plane<S> {
-    normal: Vec3<S>,
-    distance: S,
+    n: Vec3<S>,
+    d: S,
+}
+
+impl<S: Float> Plane<S> {
+    /// Construct a plane from a normal vector and a scalar distance
+    pub fn new(n: Vec3<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: Vec3::new(a, b, c), d: d }
+    }
+
+    /// 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(&Vec3::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: Float> Intersect<Option<Point3<S>>> for (Plane<S>, Ray3<S>) {
@@ -53,12 +95,32 @@ impl<S: Float> Intersect<Option<Point3<S>>> for (Plane<S>, Plane<S>, Plane<S>) {
     }
 }
 
-impl<S: Clone + fmt::Float> ToStr for Plane<S> {
-    fn to_str(&self) -> ~str {
-        format!("{:f}x + {:f}y + {:f}z + {:f} = 0",
-                self.normal.x,
-                self.normal.y,
-                self.normal.z,
-                self.distance)
+impl<S: Float> ApproxEq<S> for Plane<S> {
+    #[inline]
+    fn approx_epsilon() -> S {
+        // TODO: fix this after static methods are fixed in rustc
+        fail!(~"Doesn't work!");
+    }
+
+    #[inline]
+    fn approx_eq(&self, other: &Plane<S>) -> bool {
+        self.n.approx_eq(&other.n) &&
+        self.d.approx_eq(&other.d)
+    }
+
+    #[inline]
+    fn approx_eq_eps(&self, other: &Plane<S>, approx_epsilon: &S) -> bool {
+        self.n.approx_eq_eps(&other.n, approx_epsilon) &&
+        self.d.approx_eq_eps(&other.d, approx_epsilon)
+    }
+}
+
+impl<S: Clone + fmt::Float> ToStr for Plane<S> {
+    fn to_str(&self) -> ~str {
+        format!("{:f}x + {:f}y + {:f}z - {:f} = 0",
+                self.n.x,
+                self.n.y,
+                self.n.z,
+                self.d)
     }
 }

src/cgmath/point.rs

@@ -74,6 +74,12 @@ pub trait Point
     #[inline] fn rem_self_s(&mut self, s: S) { self.each_mut(|_, x| *x = x.rem(&s)) }
 
     #[inline] fn add_self_v(&mut self, other: &V) { self.each_mut(|i, x| *x = x.add(other.i(i))) }
+
+    /// This is a weird one, but its useful for plane calculations
+    #[inline]
+    fn dot(&self, v: &V) -> S {
+        build::<S, Slice, V>(|i| self.i(i).mul(v.i(i))).comp_add()
+    }
 }
 
 array!(impl<S> Point2<S> -> [S, ..2] _2)