428 lines
16 KiB
Rust
428 lines
16 KiB
Rust
// Copyright 2013-2014 The CGMath Developers. For a full listing of the authors,
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// refer to the AUTHORS file at the top-level directory of this distribution.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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use std::fmt;
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use std::mem;
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use std::num::{Zero, zero, One, one};
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use angle::{Rad, atan2, acos};
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use approx::ApproxEq;
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use array::Array1;
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use num::{BaseNum, BaseFloat};
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/// A trait that specifies a range of numeric operations for vectors. Not all
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/// of these make sense from a linear algebra point of view, but are included
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/// for pragmatic reasons.
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pub trait Vector<S: BaseNum>: Array1<S>
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+ Neg<Self>
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+ Zero
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+ One {
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/// Add a scalar to this vector, returning a new vector.
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fn add_s(&self, s: S) -> Self;
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/// Subtract a scalar from this vector, returning a new vector.
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fn sub_s(&self, s: S) -> Self;
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/// Multiply this vector by a scalar, returning a new vector.
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fn mul_s(&self, s: S) -> Self;
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/// Divide this vector by a scalar, returning a new vector.
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fn div_s(&self, s: S) -> Self;
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/// Take the remainder of this vector by a scalar, returning a new vector.
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fn rem_s(&self, s: S) -> Self;
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/// Add this vector to another, returning a new vector.
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fn add_v(&self, v: &Self) -> Self;
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/// Subtract another vector from this one, returning a new vector.
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fn sub_v(&self, v: &Self) -> Self;
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/// Multiply this vector by another, returning a new vector.
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fn mul_v(&self, v: &Self) -> Self;
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/// Divide this vector by another, returning a new vector.
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fn div_v(&self, v: &Self) -> Self;
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/// Take the remainder of this vector by another, returning a new scalar.
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fn rem_v(&self, v: &Self) -> Self;
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/// Negate this vector in-place.
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fn neg_self(&mut self);
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/// Add a scalar to this vector in-place.
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fn add_self_s(&mut self, s: S);
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/// Subtract a scalar from this vector, in-place.
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fn sub_self_s(&mut self, s: S);
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/// Multiply this vector by a scalar, in-place.
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fn mul_self_s(&mut self, s: S);
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/// Divide this vector by a scalar, in-place.
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fn div_self_s(&mut self, s: S);
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/// Take the remainder of this vector by a scalar, in-place.
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fn rem_self_s(&mut self, s: S);
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/// Add another vector to this one, in-place.
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fn add_self_v(&mut self, v: &Self);
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/// Subtract another vector from this one, in-place.
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fn sub_self_v(&mut self, v: &Self);
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/// Multiply this matrix by another, in-place.
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fn mul_self_v(&mut self, v: &Self);
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/// Divide this matrix by anothor, in-place.
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fn div_self_v(&mut self, v: &Self);
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/// Take the remainder of this vector by another, in-place.
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fn rem_self_v(&mut self, v: &Self);
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/// The sum of each component of the vector.
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fn comp_add(&self) -> S;
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/// The product of each component of the vector.
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fn comp_mul(&self) -> S;
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/// Vector dot product.
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#[inline]
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fn dot(&self, v: &Self) -> S { self.mul_v(v).comp_add() }
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/// The minimum component of the vector.
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fn comp_min(&self) -> S;
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/// The maximum component of the vector.
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fn comp_max(&self) -> S;
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}
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/// Dot product of two vectors.
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#[inline] pub fn dot<S: BaseNum, V: Vector<S>>(a: V, b: V) -> S { a.dot(&b) }
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// Utility macro for generating associated functions for the vectors
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macro_rules! vec(
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($Self:ident <$S:ident> { $($field:ident),+ }, $n:expr) => (
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#[deriving(PartialEq, Eq, Clone, Hash)]
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pub struct $Self<S> { $(pub $field: S),+ }
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impl<$S> $Self<$S> {
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/// Construct a new vector, using the provided values.
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#[inline]
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pub fn new($($field: $S),+) -> $Self<$S> {
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$Self { $($field: $field),+ }
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}
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}
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impl<$S: Clone> $Self<$S> {
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/// Construct a vector from a single value, replicating it.
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#[inline]
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pub fn from_value(value: $S) -> $Self<$S> {
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$Self { $($field: value.clone()),+ }
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}
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}
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impl<$S: BaseNum> $Self<$S> {
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/// The additive identity of the vector.
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#[inline]
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pub fn zero() -> $Self<$S> { $Self::from_value(zero()) }
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/// The multiplicative identity of the vector.
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#[inline]
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pub fn ident() -> $Self<$S> { $Self::from_value(one()) }
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}
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impl<S: Copy> Array1<S> for $Self<S> {
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#[inline]
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fn ptr<'a>(&'a self) -> &'a S { &self.x }
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#[inline]
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fn mut_ptr<'a>(&'a mut self) -> &'a mut S { &mut self.x }
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#[inline]
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fn i(&self, i: uint) -> S {
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let slice: &[S, ..$n] = unsafe { mem::transmute(self) };
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slice[i]
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}
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#[inline]
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fn mut_i<'a>(&'a mut self, i: uint) -> &'a mut S {
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let slice: &'a mut [S, ..$n] = unsafe { mem::transmute(self) };
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&mut slice[i]
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}
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#[inline]
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fn map(&mut self, op: |S| -> S) -> $Self<S> { $(self.$field = op(self.$field);)+ *self }
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}
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impl<S: BaseNum> Vector<S> for $Self<S> {
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#[inline] fn add_s(&self, s: S) -> $Self<S> { $Self::new($(self.$field + s),+) }
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#[inline] fn sub_s(&self, s: S) -> $Self<S> { $Self::new($(self.$field - s),+) }
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#[inline] fn mul_s(&self, s: S) -> $Self<S> { $Self::new($(self.$field * s),+) }
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#[inline] fn div_s(&self, s: S) -> $Self<S> { $Self::new($(self.$field / s),+) }
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#[inline] fn rem_s(&self, s: S) -> $Self<S> { $Self::new($(self.$field % s),+) }
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#[inline] fn add_v(&self, v: &$Self<S>) -> $Self<S> { $Self::new($(self.$field + v.$field),+) }
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#[inline] fn sub_v(&self, v: &$Self<S>) -> $Self<S> { $Self::new($(self.$field - v.$field),+) }
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#[inline] fn mul_v(&self, v: &$Self<S>) -> $Self<S> { $Self::new($(self.$field * v.$field),+) }
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#[inline] fn div_v(&self, v: &$Self<S>) -> $Self<S> { $Self::new($(self.$field / v.$field),+) }
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#[inline] fn rem_v(&self, v: &$Self<S>) -> $Self<S> { $Self::new($(self.$field % v.$field),+) }
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#[inline] fn neg_self(&mut self) { $(self.$field = -self.$field;)+ }
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#[inline] fn add_self_s(&mut self, s: S) { $(self.$field = self.$field + s;)+ }
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#[inline] fn sub_self_s(&mut self, s: S) { $(self.$field = self.$field - s;)+ }
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#[inline] fn mul_self_s(&mut self, s: S) { $(self.$field = self.$field * s;)+ }
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#[inline] fn div_self_s(&mut self, s: S) { $(self.$field = self.$field / s;)+ }
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#[inline] fn rem_self_s(&mut self, s: S) { $(self.$field = self.$field % s;)+ }
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#[inline] fn add_self_v(&mut self, v: &$Self<S>) { $(self.$field = self.$field + v.$field;)+ }
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#[inline] fn sub_self_v(&mut self, v: &$Self<S>) { $(self.$field = self.$field - v.$field;)+ }
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#[inline] fn mul_self_v(&mut self, v: &$Self<S>) { $(self.$field = self.$field * v.$field;)+ }
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#[inline] fn div_self_v(&mut self, v: &$Self<S>) { $(self.$field = self.$field / v.$field;)+ }
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#[inline] fn rem_self_v(&mut self, v: &$Self<S>) { $(self.$field = self.$field % v.$field;)+ }
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#[inline] fn comp_add(&self) -> S { fold!(&add, { $(self.$field),+ }) }
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#[inline] fn comp_mul(&self) -> S { fold!(&mul, { $(self.$field),+ }) }
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#[inline] fn comp_min(&self) -> S { fold!(partial_min, { $(self.$field),+ }) }
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#[inline] fn comp_max(&self) -> S { fold!(partial_max, { $(self.$field),+ }) }
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}
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impl<S: BaseNum> Add<$Self<S>, $Self<S>> for $Self<S> {
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#[inline] fn add(&self, v: &$Self<S>) -> $Self<S> { self.add_v(v) }
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}
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impl<S: BaseNum> Sub<$Self<S>, $Self<S>> for $Self<S> {
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#[inline] fn sub(&self, v: &$Self<S>) -> $Self<S> { self.sub_v(v) }
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}
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impl<S: BaseNum> Zero for $Self<S> {
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#[inline] fn zero() -> $Self<S> { $Self::from_value(zero()) }
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#[inline] fn is_zero(&self) -> bool { *self == zero() }
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}
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impl<S: BaseNum> Neg<$Self<S>> for $Self<S> {
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#[inline] fn neg(&self) -> $Self<S> { $Self::new($(-self.$field),+) }
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}
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impl<S: BaseNum> Mul<$Self<S>, $Self<S>> for $Self<S> {
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#[inline] fn mul(&self, v: &$Self<S>) -> $Self<S> { self.mul_v(v) }
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}
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impl<S: BaseNum> One for $Self<S> {
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#[inline] fn one() -> $Self<S> { $Self::from_value(one()) }
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}
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impl<S: BaseFloat> ApproxEq<S> for $Self<S> {
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#[inline]
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fn approx_eq_eps(&self, other: &$Self<S>, epsilon: &S) -> bool {
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$(self.$field.approx_eq_eps(&other.$field, epsilon))&&+
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}
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}
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)
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)
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macro_rules! fold {
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(&$method:ident, { $x:expr, $y:expr }) => { $x.$method(&$y) };
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(&$method:ident, { $x:expr, $y:expr, $z:expr }) => { $x.$method(&$y).$method(&$z) };
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(&$method:ident, { $x:expr, $y:expr, $z:expr, $w:expr }) => { $x.$method(&$y).$method(&$z).$method(&$w) };
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($method:ident, { $x:expr, $y:expr }) => { $x.$method($y) };
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($method:ident, { $x:expr, $y:expr, $z:expr }) => { $x.$method($y).$method($z) };
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($method:ident, { $x:expr, $y:expr, $z:expr, $w:expr }) => { $x.$method($y).$method($z).$method($w) };
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}
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vec!(Vector2<S> { x, y }, 2)
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vec!(Vector3<S> { x, y, z }, 3)
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vec!(Vector4<S> { x, y, z, w }, 4)
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/// Operations specific to numeric two-dimensional vectors.
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impl<S: BaseNum> Vector2<S> {
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/// A unit vector in the `x` direction.
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#[inline] pub fn unit_x() -> Vector2<S> { Vector2::new(one(), zero()) }
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/// A unit vector in the `y` direction.
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#[inline] pub fn unit_y() -> Vector2<S> { Vector2::new(zero(), one()) }
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/// The perpendicular dot product of the vector and `other`.
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#[inline]
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pub fn perp_dot(&self, other: &Vector2<S>) -> S {
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(self.x * other.y) - (self.y * other.x)
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}
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/// Create a `Vector3`, using the `x` and `y` values from this vector, and the
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/// provided `z`.
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#[inline]
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pub fn extend(&self, z: S)-> Vector3<S> {
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Vector3::new(self.x.clone(), self.y.clone(), z)
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}
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}
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/// Operations specific to numeric three-dimensional vectors.
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impl<S: BaseNum> Vector3<S> {
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/// A unit vector in the `x` direction.
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#[inline] pub fn unit_x() -> Vector3<S> { Vector3::new(one(), zero(), zero()) }
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/// A unit vector in the `y` direction.
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#[inline] pub fn unit_y() -> Vector3<S> { Vector3::new(zero(), one(), zero()) }
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/// A unit vector in the `w` direction.
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#[inline] pub fn unit_z() -> Vector3<S> { Vector3::new(zero(), zero(), one()) }
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/// Returns the cross product of the vector and `other`.
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#[inline]
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pub fn cross(&self, other: &Vector3<S>) -> Vector3<S> {
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Vector3::new((self.y * other.z) - (self.z * other.y),
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(self.z * other.x) - (self.x * other.z),
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(self.x * other.y) - (self.y * other.x))
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}
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/// Calculates the cross product of the vector and `other`, then stores the
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/// result in `self`.
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#[inline]
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pub fn cross_self(&mut self, other: &Vector3<S>) {
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*self = self.cross(other)
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}
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/// Create a `Vector4`, using the `x`, `y` and `z` values from this vector, and the
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/// provided `w`.
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#[inline]
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pub fn extend(&self, w: S)-> Vector4<S> {
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Vector4::new(self.x.clone(), self.y.clone(), self.z.clone(), w)
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}
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/// Create a `Vector2`, dropping the `z` value.
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#[inline]
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pub fn truncate(&self)-> Vector2<S> {
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Vector2::new(self.x.clone(), self.y.clone())
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}
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}
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/// Operations specific to numeric four-dimensional vectors.
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impl<S: BaseNum> Vector4<S> {
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/// A unit vector in the `x` direction.
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#[inline] pub fn unit_x() -> Vector4<S> { Vector4::new(one(), zero(), zero(), zero()) }
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/// A unit vector in the `y` direction.
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#[inline] pub fn unit_y() -> Vector4<S> { Vector4::new(zero(), one(), zero(), zero()) }
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/// A unit vector in the `z` direction.
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#[inline] pub fn unit_z() -> Vector4<S> { Vector4::new(zero(), zero(), one(), zero()) }
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/// A unit vector in the `w` direction.
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#[inline] pub fn unit_w() -> Vector4<S> { Vector4::new(zero(), zero(), zero(), one()) }
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/// Create a `Vector3`, dropping the `w` value.
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#[inline]
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pub fn truncate(&self)-> Vector3<S> {
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Vector3::new(self.x.clone(), self.y.clone(), self.z.clone())
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}
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/// Create a `Vector3`, dropping the nth element
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#[inline]
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pub fn truncate_n(&self, n: int)-> Vector3<S> {
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match n {
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0 => Vector3::new(self.y.clone(), self.z.clone(), self.w.clone()),
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1 => Vector3::new(self.x.clone(), self.z.clone(), self.w.clone()),
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2 => Vector3::new(self.x.clone(), self.y.clone(), self.w.clone()),
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3 => Vector3::new(self.x.clone(), self.y.clone(), self.z.clone()),
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_ => fail!("{} is out of range", n)
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}
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}
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}
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/// Specifies geometric operations for vectors. This is only implemented for
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/// 2-dimensional and 3-dimensional vectors.
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pub trait EuclideanVector<S: BaseFloat>: Vector<S>
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+ ApproxEq<S> {
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/// Returns `true` if the vector is perpendicular (at right angles) to the
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/// other vector.
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fn is_perpendicular(&self, other: &Self) -> bool {
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self.dot(other).approx_eq(&zero())
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}
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/// Returns the squared length of the vector. This does not perform an
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/// expensive square root operation like in the `length` method and can
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/// therefore be more efficient for comparing the lengths of two vectors.
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#[inline]
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fn length2(&self) -> S {
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self.dot(self)
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}
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/// The norm of the vector.
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#[inline]
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fn length(&self) -> S {
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self.dot(self).sqrt()
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}
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/// The angle between the vector and `other`, in radians.
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fn angle(&self, other: &Self) -> Rad<S>;
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/// Returns a vector with the same direction, but with a `length` (or
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/// `norm`) of `1`.
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#[inline]
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fn normalize(&self) -> Self {
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self.normalize_to(one::<S>())
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}
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/// Returns a vector with the same direction and a given `length`.
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#[inline]
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fn normalize_to(&self, length: S) -> Self {
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self.mul_s(length / self.length())
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}
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/// Returns the result of linarly interpolating the length of the vector
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/// towards the length of `other` by the specified amount.
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#[inline]
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fn lerp(&self, other: &Self, amount: S) -> Self {
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self.add_v(&other.sub_v(self).mul_s(amount))
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}
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/// Normalises the vector to a length of `1`.
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#[inline]
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fn normalize_self(&mut self) {
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let rlen = self.length().recip();
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self.mul_self_s(rlen);
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}
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/// Normalizes the vector to `length`.
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#[inline]
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fn normalize_self_to(&mut self, length: S) {
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let n = length / self.length();
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self.mul_self_s(n);
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}
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/// Linearly interpolates the length of the vector towards the length of
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/// `other` by the specified amount.
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fn lerp_self(&mut self, other: &Self, amount: S) {
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let v = other.sub_v(self).mul_s(amount);
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self.add_self_v(&v);
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}
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}
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impl<S: BaseFloat> EuclideanVector<S> for Vector2<S> {
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#[inline]
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fn angle(&self, other: &Vector2<S>) -> Rad<S> {
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atan2(self.perp_dot(other), self.dot(other))
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}
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}
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impl<S: BaseFloat> EuclideanVector<S> for Vector3<S> {
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#[inline]
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fn angle(&self, other: &Vector3<S>) -> Rad<S> {
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atan2(self.cross(other).length(), self.dot(other))
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}
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}
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impl<S: BaseFloat> EuclideanVector<S> for Vector4<S> {
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#[inline]
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fn angle(&self, other: &Vector4<S>) -> Rad<S> {
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acos(self.dot(other) / (self.length() * other.length()))
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}
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}
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impl<S: BaseNum> fmt::Show for Vector2<S> {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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write!(f, "[{}, {}]", self.x, self.y)
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}
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}
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impl<S: BaseNum> fmt::Show for Vector3<S> {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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|
write!(f, "[{}, {}, {}]", self.x, self.y, self.z)
|
|
}
|
|
}
|
|
|
|
impl<S: BaseNum> fmt::Show for Vector4<S> {
|
|
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
|
write!(f, "[{}, {}, {}, {}]", self.x, self.y, self.z, self.w)
|
|
}
|
|
}
|