Untangle mat macros
This commit is contained in:
Brendan Zabarauskas
parent
1819846a4c
commit
c91b0747b3
2 changed files with 972 additions and 853 deletions
1281
src/mat.rs
1281
src/mat.rs
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// Copyright 2013 The Lmath 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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#[macro_escape];
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macro_rules! impl_mat(
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($Mat:ident, $Vec:ident) => (
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impl<T> $Mat<T> {
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#[inline]
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pub fn col<'a>(&'a self, i: uint) -> &'a $Vec<T> {
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self.index(i)
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}
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#[inline]
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pub fn col_mut<'a>(&'a mut self, i: uint) -> &'a mut $Vec<T> {
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self.index_mut(i)
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}
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#[inline]
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pub fn elem<'a>(&'a self, i: uint, j: uint) -> &'a T {
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self.index(i).index(j)
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}
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#[inline]
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pub fn elem_mut<'a>(&'a mut self, i: uint, j: uint) -> &'a mut T {
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self.index_mut(i).index_mut(j)
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}
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}
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)
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)
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macro_rules! impl_mat_clonable(
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($Mat:ident, $Vec:ident) => (
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impl<T:Clone> $Mat<T> {
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#[inline]
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pub fn row(&self, i: uint) -> $Vec<T> {
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$Vec::from_slice(self.map(|c| c.index(i).clone()))
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}
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#[inline]
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pub fn swap_cols(&mut self, a: uint, b: uint) {
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let tmp = self.col(a).clone();
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*self.col_mut(a) = self.col(b).clone();
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*self.col_mut(b) = tmp;
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}
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#[inline]
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pub fn swap_rows(&mut self, a: uint, b: uint) {
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self.map_mut(|x| x.swap(a, b))
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}
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#[inline]
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pub fn swap_elem(&mut self, (ai, aj): (uint, uint), (bi, bj): (uint, uint)) {
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let tmp = self.elem(ai, aj).clone();
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*self.elem_mut(ai, aj) = self.elem(bi, bj).clone();
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*self.elem_mut(bi, bj) = tmp;
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}
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#[inline] pub fn transpose(&self) -> $Mat<T> { mat_transpose!($Mat) }
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#[inline] pub fn transpose_self(&mut self) { mat_transpose_self!($Mat) }
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}
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)
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)
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macro_rules! mat_transpose(
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(Mat2) => (
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Mat2::new(self.elem(0, 0).clone(), self.elem(1, 0).clone(),
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self.elem(0, 1).clone(), self.elem(1, 1).clone())
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);
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(Mat3) => (
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Mat3::new(self.elem(0, 0).clone(), self.elem(1, 0).clone(), self.elem(2, 0).clone(),
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self.elem(0, 1).clone(), self.elem(1, 1).clone(), self.elem(2, 1).clone(),
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self.elem(0, 2).clone(), self.elem(1, 2).clone(), self.elem(2, 2).clone())
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);
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(Mat4) => (
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Mat4::new(self.elem(0, 0).clone(), self.elem(1, 0).clone(), self.elem(2, 0).clone(), self.elem(3, 0).clone(),
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self.elem(0, 1).clone(), self.elem(1, 1).clone(), self.elem(2, 1).clone(), self.elem(3, 1).clone(),
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self.elem(0, 2).clone(), self.elem(1, 2).clone(), self.elem(2, 2).clone(), self.elem(3, 2).clone(),
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self.elem(0, 3).clone(), self.elem(1, 3).clone(), self.elem(2, 3).clone(), self.elem(3, 3).clone())
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);
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)
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macro_rules! mat_transpose_self(
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(Mat2) => (
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self.swap_elem((0, 1), (1, 0));
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self.swap_elem((1, 0), (0, 1));
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);
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(Mat3) => (
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self.swap_elem((0, 1), (1, 0));
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self.swap_elem((0, 2), (2, 0));
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self.swap_elem((1, 0), (0, 1));
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self.swap_elem((1, 2), (2, 1));
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self.swap_elem((2, 0), (0, 2));
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self.swap_elem((2, 1), (1, 2));
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);
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(Mat4) => (
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self.swap_elem((0, 1), (1, 0));
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self.swap_elem((0, 2), (2, 0));
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self.swap_elem((0, 3), (3, 0));
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self.swap_elem((1, 0), (0, 1));
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self.swap_elem((1, 2), (2, 1));
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self.swap_elem((1, 3), (3, 1));
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self.swap_elem((2, 0), (0, 2));
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self.swap_elem((2, 1), (1, 2));
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self.swap_elem((2, 3), (3, 2));
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self.swap_elem((3, 0), (0, 3));
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self.swap_elem((3, 1), (1, 3));
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self.swap_elem((3, 2), (2, 3));
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);
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)
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macro_rules! impl_mat_numeric(
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($Mat:ident, $Vec:ident) => (
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impl<T:Clone + Num> $Mat<T> {
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#[inline]
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pub fn from_value(value: T) -> $Mat<T> { mat_from_value!($Mat) }
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#[inline]
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pub fn identity() -> $Mat<T> { $Mat::from_value(one!(T)) }
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#[inline]
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pub fn zero() -> $Mat<T> { $Mat::from_value(zero!(T)) }
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#[inline]
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pub fn mul_t(&self, value: T) -> $Mat<T> {
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$Mat::from_slice(self.map(|&c| c.mul_t(value.clone())))
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}
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#[inline]
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pub fn mul_v(&self, vec: &$Vec<T>) -> $Vec<T> {
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mat_mul_v!($Mat)
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}
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#[inline]
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pub fn mul_m(&self, other: &$Mat<T>) -> $Mat<T> {
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mat_mul_m!($Mat)
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}
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#[inline]
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pub fn add_m(&self, other: &$Mat<T>) -> $Mat<T> {
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$Mat::from_slice(self.zip(other, |a, b| a.add_v(b)))
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}
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#[inline]
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pub fn sub_m(&self, other: &$Mat<T>) -> $Mat<T> {
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$Mat::from_slice(self.zip(other, |a, b| a.sub_v(b)))
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}
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#[inline]
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pub fn mul_self_t(&mut self, value: T) {
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self.map_mut(|x| x.mul_self_t(value.clone()))
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}
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#[inline]
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pub fn add_self_m(&mut self, other: &$Mat<T>) {
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self.zip_mut(other, |a, b| a.add_self_v(b))
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}
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#[inline]
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pub fn sub_self_m(&mut self, other: &$Mat<T>) {
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self.zip_mut(other, |a, b| a.sub_self_v(b))
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}
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pub fn dot(&self, other: &$Mat<T>) -> T {
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other.transpose().mul_m(self).trace()
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}
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pub fn determinant(&self) -> T {
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mat_determinant!($Mat)
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}
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pub fn trace(&self) -> T {
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mat_trace!($Mat)
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}
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#[inline]
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pub fn to_identity(&mut self) {
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*self = $Mat::identity();
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}
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#[inline]
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pub fn to_zero(&mut self) {
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*self = $Mat::zero();
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}
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}
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)
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)
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macro_rules! mat_from_value(
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(Mat2) => (
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Mat2::new(value.clone(), zero!(T),
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zero!(T), value.clone())
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);
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(Mat3) => (
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Mat3::new(value.clone(), zero!(T), zero!(T),
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zero!(T), value.clone(), zero!(T),
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zero!(T), zero!(T), value.clone())
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);
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(Mat4) => (
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Mat4::new(value.clone(), zero!(T), zero!(T), zero!(T),
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zero!(T), value.clone(), zero!(T), zero!(T),
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zero!(T), zero!(T), value.clone(), zero!(T),
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zero!(T), zero!(T), zero!(T), value.clone())
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);
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)
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macro_rules! mat_mul_v(
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(Mat2) => (
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Vec2::new(self.row(0).dot(vec),
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self.row(1).dot(vec))
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);
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(Mat3) => (
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Vec3::new(self.row(0).dot(vec),
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self.row(1).dot(vec),
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self.row(2).dot(vec))
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);
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(Mat4) => (
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Vec4::new(self.row(0).dot(vec),
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self.row(1).dot(vec),
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self.row(2).dot(vec),
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self.row(3).dot(vec))
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);
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)
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macro_rules! mat_mul_m(
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(Mat2) => (
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Mat2::new(self.row(0).dot(other.col(0)), self.row(1).dot(other.col(0)),
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self.row(0).dot(other.col(1)), self.row(1).dot(other.col(1)))
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);
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(Mat3) => (
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Mat3::new(self.row(0).dot(other.col(0)),
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self.row(1).dot(other.col(0)),
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self.row(2).dot(other.col(0)),
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self.row(0).dot(other.col(1)),
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self.row(1).dot(other.col(1)),
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self.row(2).dot(other.col(1)),
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self.row(0).dot(other.col(2)),
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self.row(1).dot(other.col(2)),
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self.row(2).dot(other.col(2)))
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);
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(Mat4) => (
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Mat4::new(self.row(0).dot(other.col(0)),
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self.row(1).dot(other.col(0)),
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self.row(2).dot(other.col(0)),
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self.row(3).dot(other.col(0)),
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self.row(0).dot(other.col(1)),
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self.row(1).dot(other.col(1)),
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self.row(2).dot(other.col(1)),
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self.row(3).dot(other.col(1)),
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self.row(0).dot(other.col(2)),
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self.row(1).dot(other.col(2)),
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self.row(2).dot(other.col(2)),
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self.row(3).dot(other.col(2)),
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self.row(0).dot(other.col(3)),
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self.row(1).dot(other.col(3)),
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self.row(2).dot(other.col(3)),
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self.row(3).dot(other.col(3)))
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);
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)
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macro_rules! mat_determinant(
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(Mat2) => (
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*self.elem(0, 0) *
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*self.elem(1, 1) -
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*self.elem(1, 0) *
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*self.elem(0, 1)
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);
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(Mat3) => (
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self.col(0).dot(&self.col(1).cross(self.col(2)))
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);
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(Mat4) => ({
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let m0 = Mat3::new(self.elem(1, 1).clone(), self.elem(2, 1).clone(), self.elem(3, 1).clone(),
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self.elem(1, 2).clone(), self.elem(2, 2).clone(), self.elem(3, 2).clone(),
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self.elem(1, 3).clone(), self.elem(2, 3).clone(), self.elem(3, 3).clone());
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let m1 = Mat3::new(self.elem(0, 1).clone(), self.elem(2, 1).clone(), self.elem(3, 1).clone(),
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self.elem(0, 2).clone(), self.elem(2, 2).clone(), self.elem(3, 2).clone(),
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self.elem(0, 3).clone(), self.elem(2, 3).clone(), self.elem(3, 3).clone());
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let m2 = Mat3::new(self.elem(0, 1).clone(), self.elem(1, 1).clone(), self.elem(3, 1).clone(),
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self.elem(0, 2).clone(), self.elem(1, 2).clone(), self.elem(3, 2).clone(),
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self.elem(0, 3).clone(), self.elem(1, 3).clone(), self.elem(3, 3).clone());
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let m3 = Mat3::new(self.elem(0, 1).clone(), self.elem(1, 1).clone(), self.elem(2, 1).clone(),
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self.elem(0, 2).clone(), self.elem(1, 2).clone(), self.elem(2, 2).clone(),
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self.elem(0, 3).clone(), self.elem(1, 3).clone(), self.elem(2, 3).clone());
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self.elem(0, 0) * m0.determinant() -
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self.elem(1, 0) * m1.determinant() +
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self.elem(2, 0) * m2.determinant() -
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self.elem(3, 0) * m3.determinant()
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});
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)
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macro_rules! mat_trace(
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(Mat2) => (*self.elem(0, 0) + *self.elem(1, 1));
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(Mat3) => (*self.elem(0, 0) + *self.elem(1, 1) + *self.elem(2, 2));
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(Mat4) => (*self.elem(0, 0) + *self.elem(1, 1) + *self.elem(2, 2) + *self.elem(3, 3));
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)
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macro_rules! impl_mat_approx_numeric(
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($Mat:ident) => (
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impl<T:Clone + Real + ApproxEq<T>> $Mat<T> {
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#[inline]
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pub fn inverse(&self) -> Option<$Mat<T>> {
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mat_inverse!($Mat)
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}
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#[inline]
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pub fn invert_self(&mut self) {
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*self = self.inverse().expect("Couldn't invert the matrix!");
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}
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#[inline]
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pub fn is_identity(&self) -> bool {
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self.approx_eq(&$Mat::identity())
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}
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#[inline]
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pub fn is_diagonal(&self) -> bool {
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mat_is_diagonal!($Mat)
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}
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#[inline]
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pub fn is_rotated(&self) -> bool {
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!self.approx_eq(&$Mat::identity())
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}
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#[inline]
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pub fn is_symmetric(&self) -> bool {
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mat_is_symmetric!($Mat)
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}
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#[inline]
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pub fn is_invertible(&self) -> bool {
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!self.determinant().approx_eq(&zero!(T))
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}
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}
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)
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)
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macro_rules! mat_inverse(
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(Mat2) => ({
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let d = self.determinant();
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if d.approx_eq(&zero!(T)) {
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None
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} else {
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Some(Mat2::new(self.elem(1, 1) / d, -self.elem(0, 1) / d,
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-self.elem(1, 0) / d, self.elem(0, 0) / d))
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}
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});
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(Mat3) => ({
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let d = self.determinant();
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if d.approx_eq(&zero!(T)) {
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None
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} else {
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Some(Mat3::from_cols(self.col(1).cross(self.col(2)).div_t(d.clone()),
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self.col(2).cross(self.col(0)).div_t(d.clone()),
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self.col(0).cross(self.col(1)).div_t(d.clone())).transpose())
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}
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});
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(Mat4) => ({
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use std::uint;
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let d = self.determinant();
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if d.approx_eq(&zero!(T)) {
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None
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} else {
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// Gauss Jordan Elimination with partial pivoting
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// So take this matrix, A, augmented with the identity
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// and essentially reduce [A|I]
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let mut A = self.clone();
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let mut I = Mat4::identity::<T>();
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for uint::range(0, 4) |j| {
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// Find largest element in col j
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let mut i1 = j;
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for uint::range(j + 1, 4) |i| {
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if A.elem(j, i).abs() > A.elem(j, i1).abs() {
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i1 = i;
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}
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}
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// Swap columns i1 and j in A and I to
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// put pivot on diagonal
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A.swap_cols(i1, j);
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I.swap_cols(i1, j);
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// Scale col j to have a unit diagonal
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let ajj = A.elem(j, j).clone();
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I.col_mut(j).div_self_t(ajj.clone());
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A.col_mut(j).div_self_t(ajj.clone());
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// Eliminate off-diagonal elems in col j of A,
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// doing identical ops to I
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for uint::range(0, 4) |i| {
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if i != j {
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let ij_mul_aij = I.col(j).mul_t(A.elem(i, j).clone());
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let aj_mul_aij = A.col(j).mul_t(A.elem(i, j).clone());
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I.col_mut(i).sub_self_v(&ij_mul_aij);
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A.col_mut(i).sub_self_v(&aj_mul_aij);
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}
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}
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}
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Some(I)
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}
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});
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)
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macro_rules! mat_is_diagonal(
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(Mat2) => (
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self.elem(0, 1).approx_eq(&zero!(T)) &&
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self.elem(1, 0).approx_eq(&zero!(T))
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||||
);
|
||||
(Mat3) => (
|
||||
self.elem(0, 1).approx_eq(&zero!(T)) &&
|
||||
self.elem(0, 2).approx_eq(&zero!(T)) &&
|
||||
|
||||
self.elem(1, 0).approx_eq(&zero!(T)) &&
|
||||
self.elem(1, 2).approx_eq(&zero!(T)) &&
|
||||
|
||||
self.elem(2, 0).approx_eq(&zero!(T)) &&
|
||||
self.elem(2, 1).approx_eq(&zero!(T))
|
||||
);
|
||||
(Mat4) => (
|
||||
self.elem(0, 1).approx_eq(&zero!(T)) &&
|
||||
self.elem(0, 2).approx_eq(&zero!(T)) &&
|
||||
self.elem(0, 3).approx_eq(&zero!(T)) &&
|
||||
|
||||
self.elem(1, 0).approx_eq(&zero!(T)) &&
|
||||
self.elem(1, 2).approx_eq(&zero!(T)) &&
|
||||
self.elem(1, 3).approx_eq(&zero!(T)) &&
|
||||
|
||||
self.elem(2, 0).approx_eq(&zero!(T)) &&
|
||||
self.elem(2, 1).approx_eq(&zero!(T)) &&
|
||||
self.elem(2, 3).approx_eq(&zero!(T)) &&
|
||||
|
||||
self.elem(3, 0).approx_eq(&zero!(T)) &&
|
||||
self.elem(3, 1).approx_eq(&zero!(T)) &&
|
||||
self.elem(3, 2).approx_eq(&zero!(T))
|
||||
);
|
||||
)
|
||||
|
||||
macro_rules! mat_is_symmetric(
|
||||
(Mat2) => (
|
||||
self.elem(0, 1).approx_eq(self.elem(1, 0)) &&
|
||||
self.elem(1, 0).approx_eq(self.elem(0, 1))
|
||||
);
|
||||
(Mat3) => (
|
||||
self.elem(0, 1).approx_eq(self.elem(1, 0)) &&
|
||||
self.elem(0, 2).approx_eq(self.elem(2, 0)) &&
|
||||
|
||||
self.elem(1, 0).approx_eq(self.elem(0, 1)) &&
|
||||
self.elem(1, 2).approx_eq(self.elem(2, 1)) &&
|
||||
|
||||
self.elem(2, 0).approx_eq(self.elem(0, 2)) &&
|
||||
self.elem(2, 1).approx_eq(self.elem(1, 2))
|
||||
);
|
||||
(Mat4) => (
|
||||
self.elem(0, 1).approx_eq(self.elem(1, 0)) &&
|
||||
self.elem(0, 2).approx_eq(self.elem(2, 0)) &&
|
||||
self.elem(0, 3).approx_eq(self.elem(3, 0)) &&
|
||||
|
||||
self.elem(1, 0).approx_eq(self.elem(0, 1)) &&
|
||||
self.elem(1, 2).approx_eq(self.elem(2, 1)) &&
|
||||
self.elem(1, 3).approx_eq(self.elem(3, 1)) &&
|
||||
|
||||
self.elem(2, 0).approx_eq(self.elem(0, 2)) &&
|
||||
self.elem(2, 1).approx_eq(self.elem(1, 2)) &&
|
||||
self.elem(2, 3).approx_eq(self.elem(3, 2)) &&
|
||||
|
||||
self.elem(3, 0).approx_eq(self.elem(0, 3)) &&
|
||||
self.elem(3, 1).approx_eq(self.elem(1, 3)) &&
|
||||
self.elem(3, 2).approx_eq(self.elem(2, 3))
|
||||
);
|
||||
)
|
||||
|
||||
macro_rules! impl_mat_neg(
|
||||
($Mat:ident) => (
|
||||
impl<T:Clone + Num> Neg<$Mat<T>> for $Mat<T> {
|
||||
#[inline]
|
||||
pub fn neg(&self) -> $Mat<T> {
|
||||
$Mat::from_slice(self.map(|&x| -x))
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
Loading…
Reference in a new issue