1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784
// Copyright 2016 The CGMath Developers. For a full listing of the authors, // refer to the Cargo.toml file at the top-level directory of this distribution. // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. //! Generic algebraic structures use num_traits::{cast, Float}; use std::cmp; use std::iter; use std::ops::*; use approx; use angle::Rad; use num::{BaseFloat, BaseNum}; pub use num_traits::{Bounded, One, Zero}; /// An array containing elements of type `Element` pub trait Array where // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092 Self: Index<usize, Output = <Self as Array>::Element>, Self: IndexMut<usize, Output = <Self as Array>::Element>, { type Element: Copy; /// Get the number of elements in the array type /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Vector3; /// /// assert_eq!(Vector3::<f32>::len(), 3); /// ``` fn len() -> usize; /// Construct a vector from a single value, replicating it. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Vector3; /// /// assert_eq!(Vector3::from_value(1), /// Vector3::new(1, 1, 1)); /// ``` fn from_value(value: Self::Element) -> Self; /// Get the pointer to the first element of the array. #[inline] fn as_ptr(&self) -> *const Self::Element { &self[0] } /// Get a mutable pointer to the first element of the array. #[inline] fn as_mut_ptr(&mut self) -> *mut Self::Element { &mut self[0] } /// Swap the elements at indices `i` and `j` in-place. #[inline] fn swap_elements(&mut self, i: usize, j: usize) { use std::ptr; // Yeah, ok borrow checker – I know what I'm doing here unsafe { ptr::swap(&mut self[i], &mut self[j]) }; } /// The sum of the elements of the array. fn sum(self) -> Self::Element where Self::Element: Add<Output = <Self as Array>::Element>; /// The product of the elements of the array. fn product(self) -> Self::Element where Self::Element: Mul<Output = <Self as Array>::Element>; /// Whether all elements of the array are finite fn is_finite(&self) -> bool where Self::Element: BaseFloat; } /// Element-wise arithmetic operations. These are supplied for pragmatic /// reasons, but will usually fall outside of traditional algebraic properties. pub trait ElementWise<Rhs = Self> { fn add_element_wise(self, rhs: Rhs) -> Self; fn sub_element_wise(self, rhs: Rhs) -> Self; fn mul_element_wise(self, rhs: Rhs) -> Self; fn div_element_wise(self, rhs: Rhs) -> Self; fn rem_element_wise(self, rhs: Rhs) -> Self; fn add_assign_element_wise(&mut self, rhs: Rhs); fn sub_assign_element_wise(&mut self, rhs: Rhs); fn mul_assign_element_wise(&mut self, rhs: Rhs); fn div_assign_element_wise(&mut self, rhs: Rhs); fn rem_assign_element_wise(&mut self, rhs: Rhs); } /// Vectors that can be [added](http://mathworld.wolfram.com/VectorAddition.html) /// together and [multiplied](https://en.wikipedia.org/wiki/Scalar_multiplication) /// by scalars. /// /// Examples include vectors, matrices, and quaternions. /// /// # Required operators /// /// ## Vector addition /// /// Vectors can be added, subtracted, or negated via the following traits: /// /// - `Add<Output = Self>` /// - `Sub<Output = Self>` /// - `Neg<Output = Self>` /// /// ```rust /// use cgmath::Vector3; /// /// let velocity0 = Vector3::new(1, 2, 0); /// let velocity1 = Vector3::new(1, 1, 0); /// /// let total_velocity = velocity0 + velocity1; /// let velocity_diff = velocity1 - velocity0; /// let reversed_velocity0 = -velocity0; /// ``` /// /// Vector spaces are also required to implement the additive identity trait, /// `Zero`. Adding this to another vector should have no effect: /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Vector2; /// /// let v = Vector2::new(1, 2); /// assert_eq!(v + Vector2::zero(), v); /// ``` /// /// ## Scalar multiplication /// /// Vectors can be multiplied or divided by their associated scalars via the /// following traits: /// /// - `Mul<Self::Scalar, Output = Self>` /// - `Div<Self::Scalar, Output = Self>` /// - `Rem<Self::Scalar, Output = Self>` /// /// ```rust /// use cgmath::Vector2; /// /// let translation = Vector2::new(3.0, 4.0); /// let scale_factor = 2.0; /// /// let upscaled_translation = translation * scale_factor; /// let downscaled_translation = translation / scale_factor; /// ``` pub trait VectorSpace: Copy + Clone where Self: Zero, Self: Add<Self, Output = Self>, Self: Sub<Self, Output = Self>, Self: iter::Sum<Self>, // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092 Self: Mul<<Self as VectorSpace>::Scalar, Output = Self>, Self: Div<<Self as VectorSpace>::Scalar, Output = Self>, Self: Rem<<Self as VectorSpace>::Scalar, Output = Self>, { /// The associated scalar. type Scalar: BaseNum; /// Returns the result of linearly interpolating the vector /// towards `other` by the specified amount. #[inline] fn lerp(self, other: Self, amount: Self::Scalar) -> Self { self + ((other - self) * amount) } } /// A type with a distance function between values. /// /// Examples are vectors, points, and quaternions. pub trait MetricSpace: Sized { /// The metric to be returned by the `distance` function. type Metric: BaseFloat; /// Returns the squared distance. /// /// This does not perform an expensive square root operation like in /// `MetricSpace::distance` method, and so can be used to compare distances /// more efficiently. fn distance2(self, other: Self) -> Self::Metric; /// The distance between two values. fn distance(self, other: Self) -> Self::Metric { Float::sqrt(Self::distance2(self, other)) } } /// Vectors that also have a [dot](https://en.wikipedia.org/wiki/Dot_product) /// (or [inner](https://en.wikipedia.org/wiki/Inner_product_space)) product. /// /// The dot product allows for the definition of other useful operations, like /// finding the magnitude of a vector or normalizing it. /// /// Examples include vectors and quaternions. pub trait InnerSpace: VectorSpace where // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092 <Self as VectorSpace>::Scalar: BaseFloat, Self: MetricSpace<Metric = <Self as VectorSpace>::Scalar>, // Self: approx::AbsDiffEq<Epsilon = <Self as VectorSpace>::Scalar>, // Self: approx::RelativeEq<Epsilon = <Self as VectorSpace>::Scalar>, Self: approx::UlpsEq<Epsilon = <Self as VectorSpace>::Scalar>, { /// Vector dot (or inner) product. fn dot(self, other: Self) -> Self::Scalar; /// Returns `true` if the vector is perpendicular (at right angles) to the /// other vector. fn is_perpendicular(self, other: Self) -> bool { ulps_eq!(Self::dot(self, other), &Self::Scalar::zero()) } /// Returns the squared magnitude. /// /// This does not perform an expensive square root operation like in /// `InnerSpace::magnitude` method, and so can be used to compare magnitudes /// more efficiently. #[inline] fn magnitude2(self) -> Self::Scalar { Self::dot(self, self) } /// The distance from the tail to the tip of the vector. #[inline] fn magnitude(self) -> Self::Scalar { Float::sqrt(self.magnitude2()) } /// Returns the angle between two vectors in radians. fn angle(self, other: Self) -> Rad<Self::Scalar> { Rad::acos(Self::dot(self, other) / (self.magnitude() * other.magnitude())) } /// Returns a vector with the same direction, but with a magnitude of `1`. #[inline] fn normalize(self) -> Self { self.normalize_to(Self::Scalar::one()) } /// Returns a vector with the same direction and a given magnitude. #[inline] fn normalize_to(self, magnitude: Self::Scalar) -> Self { self * (magnitude / self.magnitude()) } /// Returns the /// [vector projection](https://en.wikipedia.org/wiki/Vector_projection) /// of the current inner space projected onto the supplied argument. #[inline] fn project_on(self, other: Self) -> Self { other * (self.dot(other) / other.magnitude2()) } } /// Points in a [Euclidean space](https://en.wikipedia.org/wiki/Euclidean_space) /// with an associated space of displacement vectors. /// /// # Point-Vector distinction /// /// `cgmath` distinguishes between points and vectors in the following way: /// /// - Points are _locations_ relative to an origin /// - Vectors are _displacements_ between those points /// /// For example, to find the midpoint between two points, you can write the /// following: /// /// ```rust /// use cgmath::Point3; /// /// let p0 = Point3::new(1.0, 2.0, 3.0); /// let p1 = Point3::new(-3.0, 1.0, 2.0); /// let midpoint: Point3<f32> = p0 + (p1 - p0) * 0.5; /// ``` /// /// Breaking the expression up, and adding explicit types makes it clearer /// to see what is going on: /// /// ```rust /// # use cgmath::{Point3, Vector3}; /// # /// # let p0 = Point3::new(1.0, 2.0, 3.0); /// # let p1 = Point3::new(-3.0, 1.0, 2.0); /// # /// let dv: Vector3<f32> = p1 - p0; /// let half_dv: Vector3<f32> = dv * 0.5; /// let midpoint: Point3<f32> = p0 + half_dv; /// ``` /// /// ## Converting between points and vectors /// /// Points can be converted to and from displacement vectors using the /// `EuclideanSpace::{from_vec, to_vec}` methods. Note that under the hood these /// are implemented as inlined a type conversion, so should not have any /// performance implications. /// /// ## References /// /// - [CGAL 4.7 - 2D and 3D Linear Geometry Kernel: 3.1 Points and Vectors](http://doc.cgal.org/latest/Kernel_23/index.html#Kernel_23PointsandVectors) /// - [What is the difference between a point and a vector](http://math.stackexchange.com/q/645827) /// pub trait EuclideanSpace: Copy + Clone where // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092 Self: Array<Element = <Self as EuclideanSpace>::Scalar>, Self: Add<<Self as EuclideanSpace>::Diff, Output = Self>, Self: Sub<<Self as EuclideanSpace>::Diff, Output = Self>, Self: Sub<Self, Output = <Self as EuclideanSpace>::Diff>, Self: Mul<<Self as EuclideanSpace>::Scalar, Output = Self>, Self: Div<<Self as EuclideanSpace>::Scalar, Output = Self>, Self: Rem<<Self as EuclideanSpace>::Scalar, Output = Self>, { /// The associated scalar over which the space is defined. /// /// Due to the equality constraints demanded by `Self::Diff`, this is effectively just an /// alias to `Self::Diff::Scalar`. type Scalar: BaseNum; /// The associated space of displacement vectors. type Diff: VectorSpace<Scalar = Self::Scalar>; /// The point at the origin of the Euclidean space. fn origin() -> Self; /// Convert a displacement vector to a point. /// /// This can be considered equivalent to the addition of the displacement /// vector `v` to to `Self::origin()`. fn from_vec(v: Self::Diff) -> Self; /// Convert a point to a displacement vector. /// /// This can be seen as equivalent to the displacement vector from /// `Self::origin()` to `self`. fn to_vec(self) -> Self::Diff; /// Returns the middle point between two other points. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Point3; /// /// let p = Point3::midpoint( /// Point3::new(1.0, 2.0, 3.0), /// Point3::new(3.0, 1.0, 2.0), /// ); /// ``` #[inline] fn midpoint(self, other: Self) -> Self { self + (other - self) / cast(2).unwrap() } /// Returns the average position of all points in the slice. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Point2; /// /// let triangle = [ /// Point2::new(1.0, 1.0), /// Point2::new(2.0, 3.0), /// Point2::new(3.0, 1.0), /// ]; /// /// let centroid = Point2::centroid(&triangle); /// ``` #[inline] fn centroid(points: &[Self]) -> Self { let total_displacement = points .iter() .fold(Self::Diff::zero(), |acc, p| acc + p.to_vec()); Self::from_vec(total_displacement / cast(points.len()).unwrap()) } /// This is a weird one, but its useful for plane calculations. fn dot(self, v: Self::Diff) -> Self::Scalar; } /// A column-major matrix of arbitrary dimensions. /// /// Because this is constrained to the `VectorSpace` trait, this means that /// following operators are required to be implemented: /// /// Matrix addition: /// /// - `Add<Output = Self>` /// - `Sub<Output = Self>` /// - `Neg<Output = Self>` /// /// Scalar multiplication: /// /// - `Mul<Self::Scalar, Output = Self>` /// - `Div<Self::Scalar, Output = Self>` /// - `Rem<Self::Scalar, Output = Self>` /// /// Note that matrix multiplication is not required for implementors of this /// trait. This is due to the complexities of implementing these operators with /// Rust's current type system. For the multiplication of square matrices, /// see `SquareMatrix`. pub trait Matrix: VectorSpace where Self::Scalar: BaseFloat, // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092 Self: Index<usize, Output = <Self as Matrix>::Column>, Self: IndexMut<usize, Output = <Self as Matrix>::Column>, Self: approx::AbsDiffEq<Epsilon = <Self as VectorSpace>::Scalar>, Self: approx::RelativeEq<Epsilon = <Self as VectorSpace>::Scalar>, Self: approx::UlpsEq<Epsilon = <Self as VectorSpace>::Scalar>, { /// The row vector of the matrix. type Row: VectorSpace<Scalar = Self::Scalar> + Array<Element = Self::Scalar>; /// The column vector of the matrix. type Column: VectorSpace<Scalar = Self::Scalar> + Array<Element = Self::Scalar>; /// The result of transposing the matrix type Transpose: Matrix<Scalar = Self::Scalar, Row = Self::Column, Column = Self::Row>; /// Get the pointer to the first element of the array. #[inline] fn as_ptr(&self) -> *const Self::Scalar { &self[0][0] } /// Get a mutable pointer to the first element of the array. #[inline] fn as_mut_ptr(&mut self) -> *mut Self::Scalar { &mut self[0][0] } /// Replace a column in the array. #[inline] fn replace_col(&mut self, c: usize, src: Self::Column) -> Self::Column { use std::mem; mem::replace(&mut self[c], src) } /// Get a row from this matrix by-value. fn row(&self, r: usize) -> Self::Row; /// Swap two rows of this array. fn swap_rows(&mut self, a: usize, b: usize); /// Swap two columns of this array. fn swap_columns(&mut self, a: usize, b: usize); /// Swap the values at index `a` and `b` fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize)); /// Transpose this matrix, returning a new matrix. fn transpose(&self) -> Self::Transpose; } /// A column-major major matrix where the rows and column vectors are of the same dimensions. pub trait SquareMatrix where Self::Scalar: BaseFloat, Self: One, Self: iter::Product<Self>, Self: Matrix< // FIXME: Can be cleaned up once equality constraints in where clauses are implemented Column = <Self as SquareMatrix>::ColumnRow, Row = <Self as SquareMatrix>::ColumnRow, Transpose = Self, >, Self: Mul<<Self as SquareMatrix>::ColumnRow, Output = <Self as SquareMatrix>::ColumnRow>, Self: Mul<Self, Output = Self>, { // FIXME: Will not be needed once equality constraints in where clauses are implemented /// The row/column vector of the matrix. /// /// This is used to constrain the column and rows to be of the same type in lieu of equality /// constraints being implemented for `where` clauses. Once those are added, this type will /// likely go away. type ColumnRow: VectorSpace<Scalar = Self::Scalar> + Array<Element = Self::Scalar>; /// Create a new diagonal matrix using the supplied value. fn from_value(value: Self::Scalar) -> Self; /// Create a matrix from a non-uniform scale fn from_diagonal(diagonal: Self::ColumnRow) -> Self; /// The [identity matrix]. Multiplying this matrix with another should have /// no effect. /// /// Note that this is exactly the same as `One::one`. The term 'identity /// matrix' is more common though, so we provide this method as an /// alternative. /// /// [identity matrix]: https://en.wikipedia.org/wiki/Identity_matrix #[inline] fn identity() -> Self { Self::one() } /// Transpose this matrix in-place. fn transpose_self(&mut self); /// Take the determinant of this matrix. fn determinant(&self) -> Self::Scalar; /// Return a vector containing the diagonal of this matrix. fn diagonal(&self) -> Self::ColumnRow; /// Return the trace of this matrix. That is, the sum of the diagonal. #[inline] fn trace(&self) -> Self::Scalar { self.diagonal().sum() } /// Invert this matrix, returning a new matrix. `m.mul_m(m.invert())` is /// the identity matrix. Returns `None` if this matrix is not invertible /// (has a determinant of zero). fn invert(&self) -> Option<Self>; /// Test if this matrix is invertible. #[inline] fn is_invertible(&self) -> bool { ulps_ne!(self.determinant(), &Self::Scalar::zero()) } /// Test if this matrix is the identity matrix. That is, it is diagonal /// and every element in the diagonal is one. #[inline] fn is_identity(&self) -> bool { ulps_eq!(self, &Self::identity()) } /// Test if this is a diagonal matrix. That is, every element outside of /// the diagonal is 0. fn is_diagonal(&self) -> bool; /// Test if this matrix is symmetric. That is, it is equal to its /// transpose. fn is_symmetric(&self) -> bool; } /// Angles and their associated trigonometric functions. /// /// Typed angles allow for the writing of self-documenting code that makes it /// clear when semantic violations have occured - for example, adding degrees to /// radians, or adding a number to an angle. /// pub trait Angle where Self: Copy + Clone, Self: PartialEq + cmp::PartialOrd, // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092 Self: approx::AbsDiffEq<Epsilon = <Self as Angle>::Unitless>, Self: approx::RelativeEq<Epsilon = <Self as Angle>::Unitless>, Self: approx::UlpsEq<Epsilon = <Self as Angle>::Unitless>, Self: Zero, Self: Neg<Output = Self>, Self: Add<Self, Output = Self>, Self: Sub<Self, Output = Self>, Self: Rem<Self, Output = Self>, Self: Mul<<Self as Angle>::Unitless, Output = Self>, Self: Div<Self, Output = <Self as Angle>::Unitless>, Self: Div<<Self as Angle>::Unitless, Output = Self>, Self: iter::Sum, { type Unitless: BaseFloat; /// Return the angle, normalized to the range `[0, full_turn)`. #[inline] fn normalize(self) -> Self { let rem = self % Self::full_turn(); if rem < Self::zero() { rem + Self::full_turn() } else { rem } } /// Return the angle, normalized to the range `[-turn_div_2, turn_div_2)`. #[inline] fn normalize_signed(self) -> Self { let rem = self.normalize(); if Self::turn_div_2() < rem { rem - Self::full_turn() } else { rem } } /// Return the angle rotated by half a turn. #[inline] fn opposite(self) -> Self { Self::normalize(self + Self::turn_div_2()) } /// Returns the interior bisector of the two angles. #[inline] fn bisect(self, other: Self) -> Self { let half = cast(0.5f64).unwrap(); Self::normalize((self - other) * half + self) } /// A full rotation. fn full_turn() -> Self; /// Half of a full rotation. #[inline] fn turn_div_2() -> Self { let factor: Self::Unitless = cast(2).unwrap(); Self::full_turn() / factor } /// A third of a full rotation. #[inline] fn turn_div_3() -> Self { let factor: Self::Unitless = cast(3).unwrap(); Self::full_turn() / factor } /// A quarter of a full rotation. #[inline] fn turn_div_4() -> Self { let factor: Self::Unitless = cast(4).unwrap(); Self::full_turn() / factor } /// A sixth of a full rotation. #[inline] fn turn_div_6() -> Self { let factor: Self::Unitless = cast(6).unwrap(); Self::full_turn() / factor } /// Compute the sine of the angle, returning a unitless ratio. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Rad; /// /// let angle = Rad(35.0); /// let ratio: f32 = Rad::sin(angle); /// ``` fn sin(self) -> Self::Unitless; /// Compute the cosine of the angle, returning a unitless ratio. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Rad; /// /// let angle = Rad(35.0); /// let ratio: f32 = Rad::cos(angle); /// ``` fn cos(self) -> Self::Unitless; /// Compute the tangent of the angle, returning a unitless ratio. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Rad; /// /// let angle = Rad(35.0); /// let ratio: f32 = Rad::tan(angle); /// ``` fn tan(self) -> Self::Unitless; /// Compute the sine and cosine of the angle, returning the result as a /// pair. /// /// This does not have any performance benefits, but calculating both the /// sine and cosine of a single angle is a common operation. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Rad; /// /// let angle = Rad(35.0); /// let (s, c) = Rad::sin_cos(angle); /// ``` fn sin_cos(self) -> (Self::Unitless, Self::Unitless); /// Compute the cosecant of the angle. /// /// This is the same as computing the reciprocal of `Self::sin`. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Rad; /// /// let angle = Rad(35.0); /// let ratio: f32 = Rad::csc(angle); /// ``` #[inline] fn csc(self) -> Self::Unitless { Self::sin(self).recip() } /// Compute the cotangent of the angle. /// /// This is the same as computing the reciprocal of `Self::tan`. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Rad; /// /// let angle = Rad(35.0); /// let ratio: f32 = Rad::cot(angle); /// ``` #[inline] fn cot(self) -> Self::Unitless { Self::tan(self).recip() } /// Compute the secant of the angle. /// /// This is the same as computing the reciprocal of `Self::cos`. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Rad; /// /// let angle = Rad(35.0); /// let ratio: f32 = Rad::sec(angle); /// ``` #[inline] fn sec(self) -> Self::Unitless { Self::cos(self).recip() } /// Compute the arcsine of the ratio, returning the resulting angle. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Rad; /// /// let angle: Rad<f32> = Rad::asin(0.5); /// ``` fn asin(ratio: Self::Unitless) -> Self; /// Compute the arccosine of the ratio, returning the resulting angle. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Rad; /// /// let angle: Rad<f32> = Rad::acos(0.5); /// ``` fn acos(ratio: Self::Unitless) -> Self; /// Compute the arctangent of the ratio, returning the resulting angle. /// /// ```rust /// use cgmath::prelude::*; /// use cgmath::Rad; /// /// let angle: Rad<f32> = Rad::atan(0.5); /// ``` fn atan(ratio: Self::Unitless) -> Self; fn atan2(a: Self::Unitless, b: Self::Unitless) -> Self; }