1 use fpnum::{fp, integral_sqrt, FPNum, FPPoint};

     2 use std::{

     3     cmp::{max, min},

     4     ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, RangeInclusive, Sub, SubAssign},

     5 };

     6 

     7 #[derive(PartialEq, Eq, Clone, Copy, Debug)]

     8 pub struct Point {

     9     pub x: i32,

    10     pub y: i32,

    11 }

    12 

    13 impl Point {

    14     pub const ZERO: Self = Self::new(0, 0);

    15 

    16     #[inline]

    17     pub const fn new(x: i32, y: i32) -> Self {

    18         Self { x, y }

    19     }

    20 

    21     #[inline]

    22     pub const fn diag(v: i32) -> Self {

    23         Self::new(v, v)

    24     }

    25 

    26     #[inline]

    27     pub fn signum(self) -> Self {

    28         Self::new(self.x.signum(), self.y.signum())

    29     }

    30 

    31     #[inline]

    32     pub fn abs(self) -> Self {

    33         Self::new(self.x.abs(), self.y.abs())

    34     }

    35 

    36     #[inline]

    37     pub const fn dot(self, other: Point) -> i32 {

    38         self.x * other.x + self.y * other.y

    39     }

    40 

    41     #[inline]

    42     pub fn max_norm(self) -> i32 {

    43         std::cmp::max(self.x.abs(), self.y.abs())

    44     }

    45 

    46     #[inline]

    47     pub fn integral_norm(self) -> u32 {

    48         let sqr = (self.x as u64).pow(2) + (self.y as u64).pow(2);

    49         integral_sqrt(sqr) as u32

    50     }

    51 

    52     #[inline]

    53     pub const fn transform(self, matrix: &[i32; 4]) -> Self {

    54         Point::new(

    55             matrix[0] * self.x + matrix[1] * self.y,

    56             matrix[2] * self.x + matrix[3] * self.y,

    57         )

    58     }

    59 

    60     #[inline]

    61     pub const fn rotate90(self) -> Self {

    62         Point::new(self.y, -self.x)

    63     }

    64 

    65     #[inline]

    66     pub const fn cross(self, other: Point) -> i32 {

    67         self.dot(other.rotate90())

    68     }

    69 

    70     #[inline]

    71     pub fn clamp(self, rect: &Rect) -> Point {

    72         Point::new(rect.x_range().clamp(self.x), rect.y_range().clamp(self.y))

    73     }

    74 

    75     #[inline]

    76     pub const fn line_to(self, end: Point) -> Line {

    77         Line::new(self, end)

    78     }

    79 

    80     #[inline]

    81     pub const fn ray_with_dir(self, direction: Point) -> Ray {

    82         Ray::new(self, direction)

    83     }

    84 

    85     #[inline]

    86     pub const fn tangent_mul(self, x: i32) -> i32 {

    87         x * self.y / self.x

    88     }

    89 

    90     #[inline]

    91     pub const fn cotangent_mul(self, y: i32) -> i32 {

    92         y * self.x / self.y

    93     }

    94 

    95     #[inline]

    96     pub fn to_fppoint(self) -> FPPoint {

    97         FPPoint::new(self.x.into(), self.y.into())

    98     }

    99 

   100     #[inline]

   101     pub fn from_fppoint(p: &FPPoint) -> Self {

   102         Self::new(p.x().round(), p.y().round())

   103     }

   104 }

   105 

   106 #[derive(PartialEq, Eq, Clone, Copy, Debug)]

   107 pub struct Size {

   108     pub width: usize,

   109     pub height: usize,

   110 }

   111 

   112 impl Size {

   113     pub const EMPTY: Self = Self::square(0);

   114 

   115     #[inline]

   116     pub const fn new(width: usize, height: usize) -> Self {

   117         Self { width, height }

   118     }

   119 

   120     #[inline]

   121     pub const fn square(size: usize) -> Self {

   122         Self {

   123             width: size,

   124             height: size,

   125         }

   126     }

   127 

   128     #[inline]

   129     pub const fn area(&self) -> usize {

   130         self.width * self.height

   131     }

   132 

   133     #[inline]

   134     pub const fn linear_index(&self, x: usize, y: usize) -> usize {

   135         y * self.width + x

   136     }

   137 

   138     #[inline]

   139     pub fn is_power_of_two(&self) -> bool {

   140         self.width.is_power_of_two() && self.height.is_power_of_two()

   141     }

   142 

   143     #[inline]

   144     pub fn next_power_of_two(&self) -> Self {

   145         Self {

   146             width: self.width.next_power_of_two(),

   147             height: self.height.next_power_of_two(),

   148         }

   149     }

   150 

   151     #[inline]

   152     pub const fn transpose(&self) -> Self {

   153         Self::new(self.height, self.width)

   154     }

   155 

   156     #[inline]

   157     pub fn to_mask(&self) -> SizeMask {

   158         SizeMask::new(*self)

   159     }

   160 

   161     #[inline]

   162     pub fn to_square(&self) -> Self {

   163         Self::square(max(self.width, self.height))

   164     }

   165 

   166     pub fn to_grid_index(&self) -> GridIndex {

   167         GridIndex::new(*self)

   168     }

   169 

   170     #[inline]

   171     pub fn contains(&self, other: Self) -> bool {

   172         self.width >= other.width && self.height >= other.height

   173     }

   174 }

   175 

   176 #[derive(PartialEq, Eq, Clone, Copy, Debug)]

   177 pub struct SizeMask {

   178     size: Size,

   179 }

   180 

   181 impl SizeMask {

   182     #[inline]

   183     pub fn new(size: Size) -> Self {

   184         debug_assert!(size.is_power_of_two());

   185         let size = Size {

   186             width: !(size.width - 1),

   187             height: !(size.height - 1),

   188         };

   189         Self { size }

   190     }

   191 

   192     #[inline]

   193     pub fn contains_x<T: Into<usize>>(&self, x: T) -> bool {

   194         (self.size.width & x.into()) == 0

   195     }

   196 

   197     #[inline]

   198     pub fn contains_y<T: Into<usize>>(&self, y: T) -> bool {

   199         (self.size.height & y.into()) == 0

   200     }

   201 

   202     #[inline]

   203     pub fn contains(&self, point: Point) -> bool {

   204         self.contains_x(point.x as usize) && self.contains_y(point.y as usize)

   205     }

   206 }

   207 

   208 pub struct GridIndex {

   209     shift: Point,

   210 }

   211 

   212 impl GridIndex {

   213     pub fn new(size: Size) -> Self {

   214         assert!(size.is_power_of_two());

   215         let shift = Point::new(

   216             size.width.trailing_zeros() as i32,

   217             size.height.trailing_zeros() as i32,

   218         );

   219         Self { shift }

   220     }

   221 

   222     pub fn map(&self, position: Point) -> Point {

   223         Point::new(position.x >> self.shift.x, position.y >> self.shift.y)

   224     }

   225 }

   226 

   227 macro_rules! bin_op_impl {

   228     ($op: ty, $name: tt) => {

   229         impl $op for Point {

   230             type Output = Self;

   231 

   232             #[inline]

   233             fn $name(self, rhs: Self) -> Self::Output {

   234                 Self::new(self.x.$name(rhs.x), self.y.$name(rhs.y))

   235             }

   236         }

   237     };

   238 }

   239 

   240 macro_rules! scalar_bin_op_impl {

   241     ($($op: tt)::+, $name: tt) => {

   242         impl $($op)::+<i32> for Point {

   243             type Output = Self;

   244 

   245             #[inline]

   246             fn $name(self, rhs: i32) -> Self::Output {

   247                 Self::new(self.x.$name(rhs), self.y.$name(rhs))

   248             }

   249         }

   250     };

   251 }

   252 

   253 macro_rules! bin_assign_op_impl {

   254     ($op: ty, $name: tt) => {

   255         impl $op for Point {

   256             #[inline]

   257             fn $name(&mut self, rhs: Self) {

   258                 self.x.$name(rhs.x);

   259                 self.y.$name(rhs.y);

   260             }

   261         }

   262     };

   263 }

   264 

   265 macro_rules! fp_scalar_bin_op_impl {

   266     ($($op: tt)::+, $name: tt) => {

   267         impl $($op)::+<FPNum> for Point {

   268             type Output = FPPoint;

   269 

   270             #[inline]

   271             fn $name(self, rhs: FPNum) -> Self::Output {

   272                 FPPoint::new(rhs.$name(self.x), rhs.$name(self.y))

   273             }

   274         }

   275     };

   276 }

   277 

   278 macro_rules! left_fp_scalar_bin_op_impl {

   279     ($($op: tt)::+, $name: tt) => {

   280         impl $($op)::+<Point> for FPNum {

   281             type Output = FPPoint;

   282 

   283             #[inline]

   284             fn $name(self, rhs: Point) -> Self::Output {

   285                 FPPoint::new(self.$name(rhs.x), self.$name(rhs.y))

   286             }

   287         }

   288     };

   289 }

   290 

   291 bin_op_impl!(Add, add);

   292 bin_op_impl!(Sub, sub);

   293 bin_op_impl!(Mul, mul);

   294 bin_op_impl!(Div, div);

   295 scalar_bin_op_impl!(Mul, mul);

   296 scalar_bin_op_impl!(Div, div);

   297 fp_scalar_bin_op_impl!(Mul, mul);

   298 fp_scalar_bin_op_impl!(Div, div);

   299 left_fp_scalar_bin_op_impl!(Mul, mul);

   300 left_fp_scalar_bin_op_impl!(Div, div);

   301 bin_assign_op_impl!(AddAssign, add_assign);

   302 bin_assign_op_impl!(SubAssign, sub_assign);

   303 bin_assign_op_impl!(MulAssign, mul_assign);

   304 bin_assign_op_impl!(DivAssign, div_assign);

   305 

   306 #[derive(PartialEq, Eq, Clone, Copy, Debug)]

   307 pub struct Rect {

   308     top_left: Point,

   309     bottom_right: Point,

   310 }

   311 

   312 impl Rect {

   313     pub const EMPTY: Self = Self {

   314         top_left: Point::ZERO,

   315         bottom_right: Point::diag(-1),

   316     };

   317 

   318     #[inline]

   319     pub fn new(top_left: Point, bottom_right: Point) -> Self {

   320         debug_assert!(top_left.x <= bottom_right.x + 1);

   321         debug_assert!(top_left.y <= bottom_right.y + 1);

   322         Self {

   323             top_left,

   324             bottom_right,

   325         }

   326     }

   327 

   328     pub fn from_box(left: i32, right: i32, top: i32, bottom: i32) -> Self {

   329         Self::new(Point::new(left, top), Point::new(right, bottom))

   330     }

   331 

   332     pub fn from_size(top_left: Point, size: Size) -> Self {

   333         Self::new(

   334             top_left,

   335             top_left + Point::new(size.width as i32 - 1, size.height as i32 - 1),

   336         )

   337     }

   338 

   339     pub fn from_size_coords(x: i32, y: i32, width: usize, height: usize) -> Self {

   340         Self::from_size(Point::new(x, y), Size::new(width, height))

   341     }

   342 

   343     pub fn at_origin(size: Size) -> Self {

   344         Self::from_size(Point::ZERO, size)

   345     }

   346 

   347     #[inline]

   348     pub const fn width(&self) -> usize {

   349         (self.right() - self.left() + 1) as usize

   350     }

   351 

   352     #[inline]

   353     pub const fn height(&self) -> usize {

   354         (self.bottom() - self.top() + 1) as usize

   355     }

   356 

   357     #[inline]

   358     pub const fn size(&self) -> Size {

   359         Size::new(self.width(), self.height())

   360     }

   361 

   362     #[inline]

   363     pub const fn area(&self) -> usize {

   364         self.size().area()

   365     }

   366 

   367     #[inline]

   368     pub const fn left(&self) -> i32 {

   369         self.top_left().x

   370     }

   371 

   372     #[inline]

   373     pub const fn top(&self) -> i32 {

   374         self.top_left().y

   375     }

   376 

   377     #[inline]

   378     pub const fn right(&self) -> i32 {

   379         self.bottom_right().x

   380     }

   381 

   382     #[inline]

   383     pub const fn bottom(&self) -> i32 {

   384         self.bottom_right().y

   385     }

   386 

   387     #[inline]

   388     pub const fn top_left(&self) -> Point {

   389         self.top_left

   390     }

   391 

   392     #[inline]

   393     pub const fn bottom_right(&self) -> Point {

   394         self.bottom_right

   395     }

   396 

   397     #[inline]

   398     pub fn center(&self) -> Point {

   399         (self.top_left() + self.bottom_right()) / 2

   400     }

   401 

   402     #[inline]

   403     pub fn with_margin(&self, margin: i32) -> Self {

   404         let offset = Point::diag(margin);

   405         Self::new(self.top_left() + offset, self.bottom_right() - offset)

   406     }

   407 

   408     #[inline]

   409     pub fn x_range(&self) -> RangeInclusive<i32> {

   410         self.left()..=self.right()

   411     }

   412 

   413     #[inline]

   414     pub fn y_range(&self) -> RangeInclusive<i32> {

   415         self.top()..=self.bottom()

   416     }

   417 

   418     #[inline]

   419     pub fn contains(&self, point: Point) -> bool {

   420         self.x_range().contains(&point.x) && self.y_range().contains(&point.y)

   421     }

   422 

   423     #[inline]

   424     pub fn contains_inside(&self, point: Point) -> bool {

   425         point.x > self.left()

   426             && point.x < self.right()

   427             && point.y > self.top()

   428             && point.y < self.bottom()

   429     }

   430 

   431     #[inline]

   432     pub fn contains_rect(&self, other: &Self) -> bool {

   433         self.contains(other.top_left()) && self.contains(other.bottom_right())

   434     }

   435 

   436     #[inline]

   437     pub fn intersects(&self, other: &Rect) -> bool {

   438         self.left() <= other.right()

   439             && self.right() >= other.left()

   440             && self.top() <= other.bottom()

   441             && self.bottom() >= other.top()

   442     }

   443 

   444     #[inline]

   445     pub fn split_at(&self, point: Point) -> [Rect; 4] {

   446         assert!(self.contains_inside(point));

   447         [

   448             Self::from_box(self.left(), point.x, self.top(), point.y),

   449             Self::from_box(point.x, self.right(), self.top(), point.y),

   450             Self::from_box(point.x, self.right(), point.y, self.bottom()),

   451             Self::from_box(self.left(), point.x, point.y, self.bottom()),

   452         ]

   453     }

   454 

   455     #[inline]

   456     pub fn with_margins(&self, left: i32, right: i32, top: i32, bottom: i32) -> Self {

   457         Self::from_box(

   458             self.left() - left,

   459             self.right() + right,

   460             self.top() - top,

   461             self.bottom() + bottom,

   462         )

   463     }

   464 

   465     #[inline]

   466     pub fn quotient(self, x: usize, y: usize) -> Point {

   467         self.top_left() + Point::new((x % self.width()) as i32, (y % self.height()) as i32)

   468     }

   469 }

   470 

   471 trait RangeClamp<T> {

   472     fn clamp(&self, value: T) -> T;

   473 }

   474 

   475 impl<T: Ord + Copy> RangeClamp<T> for RangeInclusive<T> {

   476     fn clamp(&self, value: T) -> T {

   477         if value < *self.start() {

   478             *self.start()

   479         } else if value > *self.end() {

   480             *self.end()

   481         } else {

   482             value

   483         }

   484     }

   485 }

   486 

   487 pub struct Polygon {

   488     vertices: Vec<Point>,

   489 }

   490 

   491 impl Polygon {

   492     pub fn new(vertices: &[Point]) -> Self {

   493         let mut v = Vec::with_capacity(vertices.len() + 1);

   494         v.extend_from_slice(vertices);

   495         if !v.is_empty() {

   496             let start = v[0];

   497             v.push(start);

   498         }

   499         Self { vertices: v }

   500     }

   501 

   502     pub fn edges_count(&self) -> usize {

   503         self.vertices.len().saturating_sub(1)

   504     }

   505 

   506     pub fn get_edge(&self, index: usize) -> Line {

   507         Line::new(self.vertices[index], self.vertices[index + 1])

   508     }

   509 

   510     pub fn split_edge(&mut self, edge_index: usize, vertex: Point) {

   511         self.vertices.insert(edge_index + 1, vertex);

   512     }

   513 

   514     pub fn iter<'a>(&'a self) -> impl Iterator<Item = &Point> + 'a {

   515         (&self.vertices[..self.edges_count()]).iter()

   516     }

   517 

   518     pub fn iter_mut<'a>(&'a mut self) -> impl Iterator<Item = &mut Point> + 'a {

   519         let edges_count = self.edges_count();

   520         let start = self.vertices.as_mut_ptr();

   521         let end = unsafe { start.add(edges_count) };

   522         PolygonPointsIteratorMut {

   523             source: self,

   524             start,

   525             end,

   526         }

   527     }

   528 

   529     fn force_close(&mut self) {

   530         if !self.vertices.is_empty() {

   531             let edges_count = self.edges_count();

   532             self.vertices[edges_count] = self.vertices[0];

   533         }

   534     }

   535 

   536     pub fn iter_edges<'a>(&'a self) -> impl Iterator<Item = Line> + 'a {

   537         (&self.vertices[0..self.edges_count()])

   538             .iter()

   539             .zip(&self.vertices[1..])

   540             .map(|(s, e)| Line::new(*s, *e))

   541     }

   542 

   543     pub fn bezierize(&mut self, segments_number: u32) {

   544         fn calc_point(p1: Point, p2: Point, p3: Point) -> FPPoint {

   545             let diff13 = (p1 - p3).to_fppoint();

   546             let diff13_norm = diff13.distance();

   547 

   548             if diff13_norm.is_zero() {

   549                 diff13

   550             } else {

   551                 let diff12_norm = (p1 - p2).to_fppoint().distance();

   552                 let diff23_norm = (p2 - p3).to_fppoint().distance();

   553                 let min_distance = min(diff13_norm, min(diff12_norm, diff23_norm));

   554 

   555                 diff13 * min_distance / diff13_norm / 3

   556             }

   557         }

   558 

   559         if self.vertices.len() < 4 {

   560             return;

   561         }

   562 

   563         let delta = fp!(1 / segments_number);

   564         let mut bezierized_vertices = Vec::new();

   565         let mut pi = 0;

   566         let mut i = 1;

   567         let mut ni = 2;

   568         let mut right_point = calc_point(self.vertices[pi], self.vertices[i], self.vertices[ni]);

   569         let mut left_point;

   570 

   571         pi += 1;

   572         while pi != 0 {

   573             pi = i;

   574             i = ni;

   575             ni += 1;

   576             if ni >= self.vertices.len() {

   577                 ni = 0;

   578             }

   579 

   580             left_point = right_point;

   581             right_point = calc_point(self.vertices[pi], self.vertices[i], self.vertices[ni]);

   582 

   583             bezierized_vertices.extend(BezierCurveSegments::new(

   584                 Line::new(self.vertices[pi], self.vertices[i]),

   585                 left_point,

   586                 -right_point,

   587                 delta,

   588             ));

   589         }

   590 

   591         self.vertices = bezierized_vertices;

   592     }

   593 }

   594 

   595 struct PolygonPointsIteratorMut<'a> {

   596     source: &'a mut Polygon,

   597     start: *mut Point,

   598     end: *mut Point,

   599 }

   600 

   601 impl<'a> Iterator for PolygonPointsIteratorMut<'a> {

   602     type Item = &'a mut Point;

   603 

   604     fn next(&mut self) -> Option<<Self as Iterator>::Item> {

   605         if self.start == self.end {

   606             None

   607         } else {

   608             unsafe {

   609                 let result = &mut *self.start;

   610                 self.start = self.start.add(1);

   611                 Some(result)

   612             }

   613         }

   614     }

   615 }

   616 

   617 impl<'a> Drop for PolygonPointsIteratorMut<'a> {

   618     fn drop(&mut self) {

   619         self.source.force_close();

   620     }

   621 }

   622 

   623 impl From<Vec<Point>> for Polygon {

   624     fn from(mut v: Vec<Point>) -> Self {

   625         if !v.is_empty() && v[0] != v[v.len() - 1] {

   626             let start = v[0];

   627             v.push(start)

   628         }

   629         Self { vertices: v }

   630     }

   631 }

   632 

   633 #[derive(PartialEq, Eq, Clone, Copy, Debug)]

   634 pub struct Ray {

   635     pub start: Point,

   636     pub direction: Point,

   637 }

   638 

   639 impl Ray {

   640     #[inline]

   641     pub const fn new(start: Point, direction: Point) -> Ray {

   642         Self { start, direction }

   643     }

   644 

   645     #[inline]

   646     pub const fn tangent_mul(&self, x: i32) -> i32 {

   647         self.direction.tangent_mul(x)

   648     }

   649 

   650     #[inline]

   651     pub const fn cotangent_mul(&self, y: i32) -> i32 {

   652         self.direction.cotangent_mul(y)

   653     }

   654 

   655     #[inline]

   656     pub fn orientation(&self, point: Point) -> i32 {

   657         (point - self.start).cross(self.direction).signum()

   658     }

   659 }

   660 

   661 #[derive(PartialEq, Eq, Clone, Copy, Debug)]

   662 pub struct Line {

   663     pub start: Point,

   664     pub end: Point,

   665 }

   666 

   667 impl Line {

   668     pub const ZERO: Self = Self::new(Point::ZERO, Point::ZERO);

   669 

   670     #[inline]

   671     pub const fn new(start: Point, end: Point) -> Self {

   672         Self { start, end }

   673     }

   674 

   675     #[inline]

   676     pub fn center(&self) -> Point {

   677         (self.start + self.end) / 2

   678     }

   679 

   680     #[inline]

   681     pub fn scaled_direction(&self) -> Point {

   682         self.end - self.start

   683     }

   684 

   685     #[inline]

   686     pub fn scaled_normal(&self) -> Point {

   687         self.scaled_direction().rotate90()

   688     }

   689 

   690     #[inline]

   691     pub fn to_ray(&self) -> Ray {

   692         Ray::new(self.start, self.scaled_direction())

   693     }

   694 }

   695 

   696 impl IntoIterator for Line {

   697     type Item = Point;

   698     type IntoIter = LinePoints;

   699 

   700     fn into_iter(self) -> Self::IntoIter {

   701         LinePoints::new(self)

   702     }

   703 }

   704 

   705 pub struct LinePoints {

   706     accumulator: Point,

   707     direction: Point,

   708     sign: Point,

   709     current: Point,

   710     total_steps: i32,

   711     step: i32,

   712 }

   713 

   714 impl LinePoints {

   715     pub fn new(line: Line) -> Self {

   716         let dir = line.end - line.start;

   717 

   718         Self {

   719             accumulator: Point::ZERO,

   720             direction: dir.abs(),

   721             sign: dir.signum(),

   722             current: line.start,

   723             total_steps: dir.max_norm(),

   724             step: 0,

   725         }

   726     }

   727 }

   728 

   729 impl Iterator for LinePoints {

   730     type Item = Point;

   731 

   732     fn next(&mut self) -> Option<Self::Item> {

   733         if self.step <= self.total_steps {

   734             self.accumulator += self.direction;

   735 

   736             if self.accumulator.x > self.total_steps {

   737                 self.accumulator.x -= self.total_steps;

   738                 self.current.x += self.sign.x;

   739             }

   740             if self.accumulator.y > self.total_steps {

   741                 self.accumulator.y -= self.total_steps;

   742                 self.current.y += self.sign.y;

   743             }

   744 

   745             self.step += 1;

   746 

   747             Some(self.current)

   748         } else {

   749             None

   750         }

   751     }

   752 }

   753 

   754 pub struct ArcPoints {

   755     point: Point,

   756     step: i32,

   757 }

   758 

   759 impl ArcPoints {

   760     pub const fn new(radius: i32) -> Self {

   761         Self {

   762             point: Point::new(0, radius),

   763             step: 3 - 2 * radius,

   764         }

   765     }

   766 }

   767 

   768 impl Iterator for ArcPoints {

   769     type Item = Point;

   770 

   771     fn next(&mut self) -> Option<Self::Item> {

   772         if self.point.x < self.point.y {

   773             let result = self.point;

   774 

   775             if self.step < 0 {

   776                 self.step += self.point.x * 4 + 6;

   777             } else {

   778                 self.step += (self.point.x - self.point.y) * 4 + 10;

   779                 self.point.y -= 1;

   780             }

   781 

   782             self.point.x += 1;

   783 

   784             Some(result)

   785         } else if self.point.x == self.point.y {

   786             self.point.x += 1;

   787 

   788             Some(self.point)

   789         } else {

   790             None

   791         }

   792     }

   793 }

   794 

   795 pub struct EquidistantPoints {

   796     vector: Vec<Point>,

   797 }

   798 

   799 impl EquidistantPoints {

   800     pub fn new(vector: Point) -> Self {

   801         Self {

   802             vector: if vector.x == vector.y {

   803                 vec![

   804                     Point::new(vector.x, vector.x),

   805                     Point::new(vector.x, -vector.x),

   806                     Point::new(-vector.x, -vector.x),

   807                     Point::new(-vector.x, vector.x),

   808                 ]

   809             } else {

   810                 vec![

   811                     Point::new(vector.x, vector.y),

   812                     Point::new(vector.x, -vector.y),

   813                     Point::new(-vector.x, -vector.y),

   814                     Point::new(-vector.x, vector.y),

   815                     Point::new(vector.y, vector.x),

   816                     Point::new(vector.y, -vector.x),

   817                     Point::new(-vector.y, -vector.x),

   818                     Point::new(-vector.y, vector.x),

   819                 ]

   820             },

   821         }

   822     }

   823 }

   824 

   825 impl IntoIterator for EquidistantPoints {

   826     type Item = Point;

   827     type IntoIter = std::vec::IntoIter<Point>;

   828 

   829     fn into_iter(self) -> Self::IntoIter {

   830         self.vector.into_iter()

   831     }

   832 }

   833 

   834 pub struct BezierCurveSegments {

   835     segment: Line,

   836     control_point1: FPPoint,

   837     control_point2: FPPoint,

   838     offset: FPNum,

   839     max_offset: FPNum,

   840     delta: FPNum,

   841     have_finished: bool,

   842 }

   843 

   844 impl BezierCurveSegments {

   845     pub fn new(segment: Line, p1: FPPoint, p2: FPPoint, delta: FPNum) -> Self {

   846         Self {

   847             segment,

   848             control_point1: segment.start.to_fppoint() - p1,

   849             control_point2: segment.end.to_fppoint() - p2,

   850             offset: fp!(0),

   851             max_offset: fp!(4095 / 4096),

   852             delta,

   853             have_finished: false,

   854         }

   855     }

   856 }

   857 

   858 impl Iterator for BezierCurveSegments {

   859     type Item = Point;

   860 

   861     fn next(&mut self) -> Option<Self::Item> {

   862         if self.offset < self.max_offset {

   863             let offset_sq = self.offset * self.offset;

   864             let offset_cub = offset_sq * self.offset;

   865 

   866             let r1 = fp!(1) - self.offset * 3 + offset_sq * 3 - offset_cub;

   867             let r2 = self.offset * 3 - offset_sq * 6 + offset_cub * 3;

   868             let r3 = offset_sq * 3 - offset_cub * 3;

   869 

   870             let p = r1 * self.segment.start

   871                 + r2 * self.control_point1

   872                 + r3 * self.control_point2

   873                 + offset_cub * self.segment.end;

   874 

   875             self.offset += self.delta;

   876 

   877             Some(Point::from_fppoint(&p))

   878         } else if !self.have_finished {

   879             self.have_finished = true;

   880 

   881             Some(self.segment.end)

   882         } else {

   883             None

   884         }

   885     }

   886 }

   887 

   888 #[cfg(test)]

   889 mod tests {

   890     use super::*;

   891 

   892     fn get_points(coords: &[(i32, i32)]) -> Vec<Point> {

   893         coords.iter().map(|(x, y)| Point::new(*x, *y)).collect()

   894     }

   895 

   896     #[test]

   897     fn line_basic() {

   898         let line: Vec<Point> = Line::new(Point::new(0, 0), Point::new(3, 3))

   899             .into_iter()

   900             .collect();

   901         let v = get_points(&[(0, 0), (1, 1), (2, 2), (3, 3)]);

   902 

   903         assert_eq!(line, v);

   904     }

   905 

   906     #[test]

   907     fn line_skewed() {

   908         let line: Vec<Point> = Line::new(Point::new(0, 0), Point::new(5, -7))

   909             .into_iter()

   910             .collect();

   911         let v = get_points(&[

   912             (0, 0),

   913             (1, -1),

   914             (2, -2),

   915             (2, -3),

   916             (3, -4),

   917             (4, -5),

   918             (4, -6),

   919             (5, -7),

   920         ]);

   921 

   922         assert_eq!(line, v);

   923     }

   924 

   925     #[test]

   926     fn equidistant_full() {

   927         let n: Vec<Point> = EquidistantPoints::new(Point::new(1, 3))

   928             .into_iter()

   929             .collect();

   930         let v = get_points(&[

   931             (1, 3),

   932             (1, -3),

   933             (-1, -3),

   934             (-1, 3),

   935             (3, 1),

   936             (3, -1),

   937             (-3, -1),

   938             (-3, 1),

   939         ]);

   940 

   941         assert_eq!(n, v);

   942     }

   943 

   944     #[test]

   945     fn equidistant_half() {

   946         let n: Vec<Point> = EquidistantPoints::new(Point::new(2, 2))

   947             .into_iter()

   948             .collect();

   949         let v = get_points(&[(2, 2), (2, -2), (-2, -2), (-2, 2)]);

   950 

   951         assert_eq!(n, v);

   952     }

   953 

   954     #[test]

   955     fn line() {

   956         let l = Line::new(Point::new(1, 1), Point::new(5, 6));

   957 

   958         assert_eq!(l.center(), Point::new(3, 3));

   959     }

   960 

   961     #[test]

   962     fn rect() {

   963         let r = Rect::from_box(10, 100, 0, 70);

   964 

   965         assert!(r.contains_inside(Point::new(99, 69)));

   966         assert!(!r.contains_inside(Point::new(100, 70)));

   967 

   968         assert_eq!(r.top_left(), Point::new(10, 0));

   969         assert_eq!(r.with_margin(12), Rect::from_box(22, 88, 12, 58));

   970     }

   971 

   972     #[test]

   973     fn fit() {

   974         let r = Rect::from_box(10, 100, 0, 70);

   975 

   976         assert_eq!(Point::new(0, -10).clamp(&r), Point::new(10, 0));

   977         assert_eq!(Point::new(1000, 1000).clamp(&r), Point::new(100, 70));

   978     }

   979 }