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use std::convert::{AsRef, AsMut, From};
use std::cell::{Cell, RefCell};
use std::marker::PhantomData;
use std::fmt::{Debug, Formatter};
use std::ops::Range;
use super::{BezCurve, Point2d, Float, Point, lerp};
#[derive(Copy, Clone)]
struct RangeSlice {
start: usize,
end: usize
}
impl RangeSlice {
#[inline]
fn new(start: usize, end: usize) -> RangeSlice {
RangeSlice {
start: start,
end: end
}
}
fn as_range(&self) -> Range<usize> {
self.start..self.end
}
fn len(&self) -> usize {
self.end - self.start
}
}
fn combination(n: u64, k: u64) -> u64 {
factorial(n) / (factorial(k) * factorial(n - k))
}
fn factorial(mut n: u64) -> u64 {
let mut accumulator: u64 = 1;
while n > 0 {
accumulator = accumulator.checked_mul(n).expect("Attempted to create Bézier curve with combination that overflow u64; decrease curve order");
n -= 1;
}
accumulator
}
fn update_factors(order: usize, factors: &Cell<RangeSlice>, dfactors: &Cell<RangeSlice>, vec: &RefCell<Vec<u64>>) {
if factors.get().len() != order + 1 {
let mut vec = vec.borrow_mut();
unsafe{ vec.set_len(0) };
let new_len = (order + 1) * 2 - 1;
if vec.capacity() < new_len {
let reserve_amount = new_len - vec.capacity();
vec.reserve(reserve_amount);
}
{
let order = order as u64;
for k in 0..order + 1 {
vec.push(combination(order, k));
}
for k in 0..order {
vec.push(combination(order - 1, k));
}
}
factors.set(RangeSlice::new(0, order + 1));
dfactors.set(RangeSlice::new(order + 1, vec.len()));
}
}
#[derive(Clone)]
pub struct NBez<F, P = Point2d<F>, C = Vec<P>>
where F: Float,
P: Point<F>,
C: AsRef<[P]> + AsMut<[P]> {
points: C,
factor_vec: RefCell<Vec<u64>>,
factors: Cell<RangeSlice>,
dfactors: Cell<RangeSlice>,
phantom: PhantomData<(F, P)>
}
impl<F, P, C> From<C> for NBez<F, P, C>
where F: Float,
P: Point<F>,
C: AsRef<[P]> + AsMut<[P]> {
fn from(container: C) -> NBez<F, P, C> {
NBez::from_container(container)
}
}
impl<F, P, C> NBez<F, P, C>
where F: Float,
P: Point<F>,
C: AsRef<[P]> + AsMut<[P]> {
#[inline]
pub fn from_container(points: C) -> NBez<F, P, C> {
if points.as_ref().len() >= 22 {
panic!("Cannot create Bézier polynomials with an order >= 21")
}
NBez {
points: points,
factor_vec: RefCell::new(Vec::new()),
factors: Cell::new(RangeSlice::new(0, 0)),
dfactors: Cell::new(RangeSlice::new(0, 0)),
phantom: PhantomData
}
}
#[inline]
pub fn unwrap(self) -> C {
self.points
}
}
impl<F, P, C> BezCurve<F> for NBez<F, P, C>
where F: Float,
P: Point<F>,
C: AsRef<[P]> + AsMut<[P]> {
type Point = P;
type Elevated = NBez<F, P, Vec<P>>;
fn from_slice(_: &[P]) -> Option<NBez<F, P, C>> {
None
}
fn interp_unbounded(&self, t: F) -> P {
let points = self.points.as_ref();
update_factors(self.order(), &self.factors, &self.dfactors, &self.factor_vec);
let factors = &self.factor_vec.borrow()[self.factors.get().as_range()];
let t1 = F::from_f32(1.0).unwrap() - t;
let order = factors.len() - 1;
let mut acc = P::zero();
let mut factor = 0;
for point in points.iter() {
acc = acc + *point *
t.powi(factor as i32) *
t1.powi((order - factor) as i32) *
F::from_u64(factors[factor]).unwrap();
factor += 1;
}
acc
}
fn slope_unbounded(&self, t: F) -> P::Vector {
let points = self.points.as_ref();
update_factors(self.order(), &self.factors, &self.dfactors, &self.factor_vec);
let dfactors = &self.factor_vec.borrow()[self.dfactors.get().as_range()];
let t1 = F::from_f32(1.0).unwrap() - t;
let order = dfactors.len() - 1;
let mut acc = P::zero();
let mut factor = 0;
let mut point_last = points[0].clone();
for point in points[1..].iter().map(|p| *p) {
acc = acc + (point - point_last) *
t.powi(factor as i32) *
t1.powi((order-factor) as i32) *
F::from_u64(dfactors[factor] * (order + 1) as u64).unwrap();
point_last = point;
factor += 1;
}
acc.into()
}
fn elevate(&self) -> NBez<F, P, Vec<P>> {
let points = self.points.as_ref();
let order = self.order() + 1;
let order_f = F::from_usize(order).unwrap();
let mut el_points = Vec::with_capacity(order + 1);
el_points.push(points[0]);
let mut prev_p = points[0];
for (i, p) in points.iter().map(|p| *p).enumerate().skip(1) {
el_points.push(lerp(p, prev_p, F::from_usize(i).unwrap()/order_f));
prev_p = p;
}
el_points.push(points[self.order()]);
NBez::from_container(el_points)
}
fn split(&self, _: F) -> Option<(NBez<F, P, C>, NBez<F, P, C>)> {
None
}
fn split_unbounded(&self, _: F) -> (NBez<F, P, C>, NBez<F, P, C>) {
unimplemented!()
}
fn order(&self) -> usize {
self.points.as_ref().len()-1
}
}
impl<F, P, C> AsRef<C> for NBez<F, P, C>
where F: Float,
P: Point<F>,
C: AsRef<[P]> + AsMut<[P]> {
fn as_ref(&self) -> &C {
&self.points
}
}
impl<F, P, C> AsMut<C> for NBez<F, P, C>
where F: Float,
P: Point<F>,
C: AsRef<[P]> + AsMut<[P]> {
fn as_mut(&mut self) -> &mut C {
&mut self.points
}
}
impl<F, P, C> AsRef<[P]> for NBez<F, P, C>
where F: Float,
P: Point<F>,
C: AsRef<[P]> + AsMut<[P]> {
fn as_ref(&self) -> &[P] {
self.points.as_ref()
}
}
impl<F, P, C> AsMut<[P]> for NBez<F, P, C>
where F: Float,
P: Point<F>,
C: AsRef<[P]> + AsMut<[P]> {
fn as_mut(&mut self) -> &mut [P] {
self.points.as_mut()
}
}
impl<F, P, C> Debug for NBez<F, P, C>
where F: Float,
P: Point<F>,
C: AsRef<[P]> + AsMut<[P]> + Debug {
fn fmt(&self, f: &mut Formatter) -> Result<(), ::std::fmt::Error> {
f.debug_tuple("NBez")
.field(&self.points)
.finish()
}
}