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use core::mem; use na::{self, DefaultAllocator, RealField}; use num::FromPrimitive; use crate::aliases::{TMat, TVec}; use crate::traits::{Alloc, Dimension, Number}; /// For each matrix or vector component `x` if `x >= 0`; otherwise, it returns `-x`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let vec = glm::vec3(-1.0, 0.0, 2.0); /// assert_eq!(glm::vec3(1.0, 0.0, 2.0), glm::abs(&vec)); /// /// let mat = glm::mat2(-0.0, 1.0, -3.0, 2.0); /// assert_eq!(glm::mat2(0.0, 1.0, 3.0, 2.0), glm::abs(&mat)); /// ``` /// /// # See also: /// /// * [`sign`](fn.sign.html) pub fn abs<N: Number, R: Dimension, C: Dimension>(x: &TMat<N, R, C>) -> TMat<N, R, C> where DefaultAllocator: Alloc<N, R, C>, { x.abs() } /// For each matrix or vector component returns a value equal to the nearest integer that is greater than or equal to `x`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let vec = glm::vec3(-1.5, 0.5, 2.8); /// assert_eq!(glm::vec3(-1.0, 1.0, 3.0), glm::ceil(&vec)); /// ``` /// /// # See also: /// /// * [`ceil`](fn.ceil.html) /// * [`floor`](fn.floor.html) /// * [`fract`](fn.fract.html) /// * [`round`](fn.round.html) /// * [`trunc`](fn.trunc.html) pub fn ceil<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.map(|x| x.ceil()) } /// Returns `min(max(x, min_val), max_val)`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// // Works with integers: /// assert_eq!(3, glm::clamp_scalar(1, 3, 5)); /// assert_eq!(4, glm::clamp_scalar(4, 3, 5)); /// assert_eq!(5, glm::clamp_scalar(7, 3, 5)); /// /// // And it works with floats: /// assert_eq!(3.25, glm::clamp_scalar(1.3, 3.25, 5.5)); /// assert_eq!(4.5, glm::clamp_scalar(4.5, 3.25, 5.5)); /// assert_eq!(5.5, glm::clamp_scalar(7.8, 3.25, 5.5)); /// ``` /// /// # See also: /// /// * [`clamp`](fn.clamp.html) /// * [`clamp_vec`](fn.clamp_vec.html) pub fn clamp_scalar<N: Number>(x: N, min_val: N, max_val: N) -> N { na::clamp(x, min_val, max_val) } /// Returns `min(max(x[i], min_val), max_val)` for each component in `x` /// using the values `min_val and `max_val` as bounds. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// // Works with integers: /// assert_eq!(glm::vec3(3, 4, 5), /// glm::clamp(&glm::vec3(1, 4, 7), 3, 5)); /// /// // And it works with floats: /// assert_eq!(glm::vec3(3.25, 4.5, 5.5), /// glm::clamp(&glm::vec3(1.3, 4.5, 7.8), 3.25, 5.5)); /// ``` /// /// # See also: /// /// * [`clamp_scalar`](fn.clamp_scalar.html) /// * [`clamp_vec`](fn.clamp_vec.html) pub fn clamp<N: Number, D: Dimension>(x: &TVec<N, D>, min_val: N, max_val: N) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.map(|x| na::clamp(x, min_val, max_val)) } /// Returns `min(max(x[i], min_val[i]), max_val[i])` for each component in `x` /// using the components of `min_val` and `max_val` as bounds. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let min_bounds = glm::vec2(1.0, 3.0); /// let max_bounds = glm::vec2(5.0, 6.0); /// assert_eq!(glm::vec2(1.0, 6.0), /// glm::clamp_vec(&glm::vec2(0.0, 7.0), /// &min_bounds, /// &max_bounds)); /// assert_eq!(glm::vec2(2.0, 6.0), /// glm::clamp_vec(&glm::vec2(2.0, 7.0), /// &min_bounds, /// &max_bounds)); /// assert_eq!(glm::vec2(1.0, 4.0), /// glm::clamp_vec(&glm::vec2(0.0, 4.0), /// &min_bounds, /// &max_bounds)); /// ``` /// /// # See also: /// /// * [`clamp_scalar`](fn.clamp_scalar.html) /// * [`clamp`](fn.clamp.html) pub fn clamp_vec<N: Number, D: Dimension>( x: &TVec<N, D>, min_val: &TVec<N, D>, max_val: &TVec<N, D>, ) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.zip_zip_map(min_val, max_val, |a, min, max| na::clamp(a, min, max)) } /// Returns a signed integer value representing the encoding of a floating-point value. /// /// The floating-point value's bit-level representation is preserved. /// /// # See also: /// /// * [`float_bits_to_int_vec`](fn.float_bits_to_int_vec.html) /// * [`float_bits_to_uint`](fn.float_bits_to_uint.html) /// * [`float_bits_to_uint_vec`](fn.float_bits_to_uint_vec.html) /// * [`int_bits_to_float`](fn.int_bits_to_float.html) /// * [`int_bits_to_float_vec`](fn.int_bits_to_float_vec.html) /// * [`uint_bits_to_float`](fn.uint_bits_to_float.html) /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html) pub fn float_bits_to_int(v: f32) -> i32 { unsafe { mem::transmute(v) } } /// Returns a signed integer value representing the encoding of each component of `v`. /// /// The floating point value's bit-level representation is preserved. /// /// # See also: /// /// * [`float_bits_to_int`](fn.float_bits_to_int.html) /// * [`float_bits_to_uint`](fn.float_bits_to_uint.html) /// * [`float_bits_to_uint_vec`](fn.float_bits_to_uint_vec.html) /// * [`int_bits_to_float`](fn.int_bits_to_float.html) /// * [`int_bits_to_float_vec`](fn.int_bits_to_float_vec.html) /// * [`uint_bits_to_float`](fn.uint_bits_to_float.html) /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html) pub fn float_bits_to_int_vec<D: Dimension>(v: &TVec<f32, D>) -> TVec<i32, D> where DefaultAllocator: Alloc<f32, D>, { v.map(float_bits_to_int) } /// Returns an unsigned integer value representing the encoding of a floating-point value. /// /// The floating-point value's bit-level representation is preserved. /// /// # See also: /// /// * [`float_bits_to_int`](fn.float_bits_to_int.html) /// * [`float_bits_to_int_vec`](fn.float_bits_to_int_vec.html) /// * [`float_bits_to_uint_vec`](fn.float_bits_to_uint_vec.html) /// * [`int_bits_to_float`](fn.int_bits_to_float.html) /// * [`int_bits_to_float_vec`](fn.int_bits_to_float_vec.html) /// * [`uint_bits_to_float`](fn.uint_bits_to_float.html) /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html) pub fn float_bits_to_uint(v: f32) -> u32 { unsafe { mem::transmute(v) } } /// Returns an unsigned integer value representing the encoding of each component of `v`. /// /// The floating point value's bit-level representation is preserved. /// /// # See also: /// /// * [`float_bits_to_int`](fn.float_bits_to_int.html) /// * [`float_bits_to_int_vec`](fn.float_bits_to_int_vec.html) /// * [`float_bits_to_uint`](fn.float_bits_to_uint.html) /// * [`int_bits_to_float`](fn.int_bits_to_float.html) /// * [`int_bits_to_float_vec`](fn.int_bits_to_float_vec.html) /// * [`uint_bits_to_float`](fn.uint_bits_to_float.html) /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html) pub fn float_bits_to_uint_vec<D: Dimension>(v: &TVec<f32, D>) -> TVec<u32, D> where DefaultAllocator: Alloc<f32, D>, { v.map(float_bits_to_uint) } /// Returns componentwise a value equal to the nearest integer that is less then or equal to `x`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let vec = glm::vec3(-1.5, 0.5, 2.8); /// assert_eq!(glm::vec3(-2.0, 0.0, 2.0), glm::floor(&vec)); /// ``` /// /// # See also: /// /// * [`ceil`](fn.ceil.html) /// * [`fract`](fn.fract.html) /// * [`round`](fn.round.html) /// * [`trunc`](fn.trunc.html) pub fn floor<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.map(|x| x.floor()) } //// FIXME: should be implemented for TVec/TMat? //pub fn fma<N: Number>(a: N, b: N, c: N) -> N { // // FIXME: use an actual FMA // a * b + c //} /// Returns the fractional part of each component of `x`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let vec = glm::vec3(-1.5, 0.5, 2.25); /// assert_eq!(glm::vec3(-0.5, 0.5, 0.25), glm::fract(&vec)); /// ``` /// /// # See also: /// /// * [`ceil`](fn.ceil.html) /// * [`floor`](fn.floor.html) /// * [`round`](fn.round.html) /// * [`trunc`](fn.trunc.html) pub fn fract<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.map(|x| x.fract()) } //// FIXME: should be implemented for TVec/TMat? ///// Returns the (significant, exponent) of this float number. //pub fn frexp<N: RealField>(x: N, exp: N) -> (N, N) { // // FIXME: is there a better approach? // let e = x.log2().ceil(); // (x * (-e).exp2(), e) //} /// Returns a floating-point value corresponding to a signed integer encoding of a floating-point value. /// /// If an inf or NaN is passed in, it will not signal, and the resulting floating point value is unspecified. Otherwise, the bit-level representation is preserved. /// /// # See also: /// /// * [`float_bits_to_int`](fn.float_bits_to_int.html) /// * [`float_bits_to_int_vec`](fn.float_bits_to_int_vec.html) /// * [`float_bits_to_uint`](fn.float_bits_to_uint.html) /// * [`float_bits_to_uint_vec`](fn.float_bits_to_uint_vec.html) /// * [`int_bits_to_float_vec`](fn.int_bits_to_float_vec.html) /// * [`uint_bits_to_float`](fn.uint_bits_to_float.html) /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html) pub fn int_bits_to_float(v: i32) -> f32 { f32::from_bits(v as u32) } /// For each components of `v`, returns a floating-point value corresponding to a signed integer encoding of a floating-point value. /// /// If an inf or NaN is passed in, it will not signal, and the resulting floating point value is unspecified. Otherwise, the bit-level representation is preserved. /// /// # See also: /// /// * [`float_bits_to_int`](fn.float_bits_to_int.html) /// * [`float_bits_to_int_vec`](fn.float_bits_to_int_vec.html) /// * [`float_bits_to_uint`](fn.float_bits_to_uint.html) /// * [`float_bits_to_uint_vec`](fn.float_bits_to_uint_vec.html) /// * [`int_bits_to_float`](fn.int_bits_to_float.html) /// * [`uint_bits_to_float`](fn.uint_bits_to_float.html) /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html) pub fn int_bits_to_float_vec<D: Dimension>(v: &TVec<i32, D>) -> TVec<f32, D> where DefaultAllocator: Alloc<f32, D>, { v.map(int_bits_to_float) } //pub fn isinf<N: Scalar, D: Dimension>(x: &TVec<N, D>) -> TVec<bool, D> // where DefaultAllocator: Alloc<N, D> { // unimplemented!() // //} // //pub fn isnan<N: Scalar, D: Dimension>(x: &TVec<N, D>) -> TVec<bool, D> // where DefaultAllocator: Alloc<N, D> { // unimplemented!() // //} ///// Returns the (significant, exponent) of this float number. //pub fn ldexp<N: RealField>(x: N, exp: N) -> N { // // FIXME: is there a better approach? // x * (exp).exp2() //} /// Returns `x * (1.0 - a) + y * a`, i.e., the linear blend of the scalars x and y using the scalar value a. /// /// The value for a is not restricted to the range `[0, 1]`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// assert_eq!(glm::mix_scalar(2.0, 20.0, 0.1), 3.8); /// ``` /// /// # See also: /// /// * [`mix`](fn.mix.html) /// * [`mix_vec`](fn.mix_vec.html) pub fn mix_scalar<N: Number>(x: N, y: N, a: N) -> N { x * (N::one() - a) + y * a } /// Returns `x * (1.0 - a) + y * a`, i.e., the linear blend of the vectors x and y using the scalar value a. /// /// The value for a is not restricted to the range `[0, 1]`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let x = glm::vec3(1.0, 2.0, 3.0); /// let y = glm::vec3(10.0, 20.0, 30.0); /// assert_eq!(glm::mix(&x, &y, 0.1), glm::vec3(1.9, 3.8, 5.7)); /// ``` /// /// # See also: /// /// * [`mix_scalar`](fn.mix_scalar.html) /// * [`mix_vec`](fn.mix_vec.html) pub fn mix<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>, a: N) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x * (N::one() - a) + y * a } /// Returns `x * (1.0 - a) + y * a`, i.e., the component-wise linear blend of `x` and `y` using the components of /// the vector `a` as coefficients. /// /// The value for a is not restricted to the range `[0, 1]`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let x = glm::vec3(1.0, 2.0, 3.0); /// let y = glm::vec3(10.0, 20.0, 30.0); /// let a = glm::vec3(0.1, 0.2, 0.3); /// assert_eq!(glm::mix_vec(&x, &y, &a), glm::vec3(1.9, 5.6, 11.1)); /// ``` /// /// # See also: /// /// * [`mix_scalar`](fn.mix_scalar.html) /// * [`mix`](fn.mix.html) pub fn mix_vec<N: Number, D: Dimension>( x: &TVec<N, D>, y: &TVec<N, D>, a: &TVec<N, D>, ) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.component_mul(&(TVec::<N, D>::repeat(N::one()) - a)) + y.component_mul(&a) } /// Returns `x * (1.0 - a) + y * a`, i.e., the linear blend of the scalars x and y using the scalar value a. /// /// The value for a is not restricted to the range `[0, 1]`. /// This is an alias for `mix_scalar`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// assert_eq!(glm::lerp_scalar(2.0, 20.0, 0.1), 3.8); /// ``` /// /// # See also: /// /// * [`lerp`](fn.lerp.html) /// * [`lerp_vec`](fn.lerp_vec.html) pub fn lerp_scalar<N: Number>(x: N, y: N, a: N) -> N { mix_scalar(x, y, a) } /// Returns `x * (1.0 - a) + y * a`, i.e., the linear blend of the vectors x and y using the scalar value a. /// /// The value for a is not restricted to the range `[0, 1]`. /// This is an alias for `mix`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let x = glm::vec3(1.0, 2.0, 3.0); /// let y = glm::vec3(10.0, 20.0, 30.0); /// assert_eq!(glm::lerp(&x, &y, 0.1), glm::vec3(1.9, 3.8, 5.7)); /// ``` /// /// # See also: /// /// * [`lerp_scalar`](fn.lerp_scalar.html) /// * [`lerp_vec`](fn.lerp_vec.html) pub fn lerp<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>, a: N) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { mix(x, y, a) } /// Returns `x * (1.0 - a) + y * a`, i.e., the component-wise linear blend of `x` and `y` using the components of /// the vector `a` as coefficients. /// /// The value for a is not restricted to the range `[0, 1]`. /// This is an alias for `mix_vec`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let x = glm::vec3(1.0, 2.0, 3.0); /// let y = glm::vec3(10.0, 20.0, 30.0); /// let a = glm::vec3(0.1, 0.2, 0.3); /// assert_eq!(glm::lerp_vec(&x, &y, &a), glm::vec3(1.9, 5.6, 11.1)); /// ``` /// /// # See also: /// /// * [`lerp_scalar`](fn.lerp_scalar.html) /// * [`lerp`](fn.lerp.html) pub fn lerp_vec<N: Number, D: Dimension>( x: &TVec<N, D>, y: &TVec<N, D>, a: &TVec<N, D>, ) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { mix_vec(x, y, a) } /// Component-wise modulus. /// /// Returns `x - y * floor(x / y)` for each component in `x` using the corresponding component of `y`. /// /// # See also: /// /// * [`modf`](fn.modf.html) pub fn modf_vec<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.zip_map(y, |x, y| x % y) } /// Modulus between two values. /// /// # See also: /// /// * [`modf_vec`](fn.modf_vec.html) pub fn modf<N: Number>(x: N, i: N) -> N { x % i } /// Component-wise rounding. /// /// Values equal to `0.5` are rounded away from `0.0`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let vec = glm::vec4(-1.5, 0.6, 1.5, -3.2); /// assert_eq!(glm::vec4(-2.0, 1.0, 2.0, -3.0), glm::round(&vec)); /// ``` /// /// # See also: /// /// * [`ceil`](fn.ceil.html) /// * [`floor`](fn.floor.html) /// * [`fract`](fn.fract.html) /// * [`trunc`](fn.trunc.html) pub fn round<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.map(|x| x.round()) } //pub fn roundEven<N: Scalar, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D> // where DefaultAllocator: Alloc<N, D> { // unimplemented!() //} /// For each vector component `x`: 1 if `x > 0`, 0 if `x == 0`, or -1 if `x < 0`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let vec = glm::vec4(-2.0, 0.0, -0.0, 2.0); /// assert_eq!(glm::vec4(-1.0, 0.0, 0.0, 1.0), glm::sign(&vec)); /// ``` /// /// # See also: /// /// * [`abs`](fn.abs.html) /// pub fn sign<N: Number, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.map(|x| if x.is_zero() { N::zero() } else { x.signum() }) } /// Returns 0.0 if `x <= edge0` and `1.0 if x >= edge1` and performs smooth Hermite interpolation between 0 and 1 when `edge0 < x < edge1`. /// /// This is useful in cases where you would want a threshold function with a smooth transition. /// This is equivalent to: `let result = clamp((x - edge0) / (edge1 - edge0), 0, 1); return t * t * (3 - 2 * t);` Results are undefined if `edge0 >= edge1`. pub fn smoothstep<N: Number>(edge0: N, edge1: N, x: N) -> N { let _3: N = FromPrimitive::from_f64(3.0).unwrap(); let _2: N = FromPrimitive::from_f64(2.0).unwrap(); let t = na::clamp((x - edge0) / (edge1 - edge0), N::zero(), N::one()); t * t * (_3 - t * _2) } /// Returns 0.0 if `x < edge`, otherwise it returns 1.0. pub fn step_scalar<N: Number>(edge: N, x: N) -> N { if edge > x { N::zero() } else { N::one() } } /// Returns 0.0 if `x[i] < edge`, otherwise it returns 1.0. pub fn step<N: Number, D: Dimension>(edge: N, x: &TVec<N, D>) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.map(|x| step_scalar(edge, x)) } /// Returns 0.0 if `x[i] < edge[i]`, otherwise it returns 1.0. pub fn step_vec<N: Number, D: Dimension>(edge: &TVec<N, D>, x: &TVec<N, D>) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { edge.zip_map(x, step_scalar) } /// Returns a value equal to the nearest integer to `x` whose absolute value is not larger than the absolute value of `x`. /// /// # Examples: /// /// ``` /// # use nalgebra_glm as glm; /// let vec = glm::vec3(-1.5, 0.5, 2.8); /// assert_eq!(glm::vec3(-1.0, 0.0, 2.0), glm::trunc(&vec)); /// ``` /// /// # See also: /// /// * [`ceil`](fn.ceil.html) /// * [`floor`](fn.floor.html) /// * [`fract`](fn.fract.html) /// * [`round`](fn.round.html) pub fn trunc<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D> where DefaultAllocator: Alloc<N, D>, { x.map(|x| x.trunc()) } /// Returns a floating-point value corresponding to a unsigned integer encoding of a floating-point value. /// /// If an `inf` or `NaN` is passed in, it will not signal, and the resulting floating point value is unspecified. Otherwise, the bit-level representation is preserved. /// /// # See also: /// /// * [`float_bits_to_int`](fn.float_bits_to_int.html) /// * [`float_bits_to_int_vec`](fn.float_bits_to_int_vec.html) /// * [`float_bits_to_uint`](fn.float_bits_to_uint.html) /// * [`float_bits_to_uint_vec`](fn.float_bits_to_uint_vec.html) /// * [`int_bits_to_float`](fn.int_bits_to_float.html) /// * [`int_bits_to_float_vec`](fn.int_bits_to_float_vec.html) /// * [`uint_bits_to_float`](fn.uint_bits_to_float.html) pub fn uint_bits_to_float_scalar(v: u32) -> f32 { f32::from_bits(v) } /// For each component of `v`, returns a floating-point value corresponding to a unsigned integer encoding of a floating-point value. /// /// If an inf or NaN is passed in, it will not signal, and the resulting floating point value is unspecified. Otherwise, the bit-level representation is preserved. /// /// # See also: /// /// * [`float_bits_to_int`](fn.float_bits_to_int.html) /// * [`float_bits_to_int_vec`](fn.float_bits_to_int_vec.html) /// * [`float_bits_to_uint`](fn.float_bits_to_uint.html) /// * [`float_bits_to_uint_vec`](fn.float_bits_to_uint_vec.html) /// * [`int_bits_to_float`](fn.int_bits_to_float.html) /// * [`int_bits_to_float_vec`](fn.int_bits_to_float_vec.html) /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html) pub fn uint_bits_to_float<D: Dimension>(v: &TVec<u32, D>) -> TVec<f32, D> where DefaultAllocator: Alloc<f32, D>, { v.map(uint_bits_to_float_scalar) }