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//! Interpolation on types for which it makes sense. use crate::*; /// Pure linear interpolation, i.e. `(1.0 - t) * self + (t) * end`. /// /// For interpolating `Rotor`s with linear interpolation, you almost certainly /// want to normalize the returned `Rotor`. For example, /// ```rs /// let interpolated_rotor = rotor1.lerp(rotor2, 0.5).normalized(); /// ``` /// For most cases (especially where perfomrance is the primary concern, like in /// animation interpolation for games, this 'normalized lerp' or 'nlerp' is probably /// what you want to use. However, there are situations in which you really want /// the interpolation between two `Rotor`s to be of constant angular velocity. In this /// case, check out `Slerp`. pub trait Lerp<T> { fn lerp(&self, end: Self, t: T) -> Self; } macro_rules! impl_lerp { ($($tt:ident => ($($vt:ident),+)),+) => { $($(impl Lerp<$tt> for $vt { /// Linearly interpolate between `self` and `end` by `t` between 0.0 and 1.0. /// i.e. `(1.0 - t) * self + (t) * end`. /// /// For interpolating `Rotor`s with linear interpolation, you almost certainly /// want to normalize the returned `Rotor`. For example, /// ```rs /// let interpolated_rotor = rotor1.lerp(rotor2, 0.5).normalized(); /// ``` /// For most cases (especially where perfomrance is the primary concern, like in /// animation interpolation for games, this 'normalized lerp' or 'nlerp' is probably /// what you want to use. However, there are situations in which you really want /// the interpolation between two `Rotor`s to be of constant angular velocity. In this /// case, check out `Slerp`. #[inline] fn lerp(&self, end: Self, t: $tt) -> Self { *self * ($tt::splat(1.0) - t) + end * t } })+)+ }; } impl_lerp!( f32 => (f32, Vec2, Vec3, Vec4, Bivec2, Bivec3, Rotor2, Rotor3), f32x4 => (f32x4, Vec2x4, Vec3x4, Vec4x4, Bivec2x4, Bivec3x4, Rotor2x4, Rotor3x4), f32x8 => (f32x8, Vec2x8, Vec3x8, Vec4x8, Bivec2x8, Bivec3x8, Rotor2x8, Rotor3x8) ); #[cfg(feature = "f64")] impl_lerp!( f64 => (f64, DVec2, DVec3, DVec4, DBivec2, DBivec3, DRotor2, DRotor3), f64x2 => (f64x2, DVec2x2, DVec3x2, DVec4x2, DBivec2x2, DBivec3x2, DRotor2x2, DRotor3x2), f64x4 => (f64x4, DVec2x4, DVec3x4, DVec4x4, DBivec2x4, DBivec3x4, DRotor2x4, DRotor3x4) ); /// Spherical-linear interpolation. /// /// Basically, interpolation that maintains a constant angular velocity /// from one orientation on a unit hypersphere to another. This is sorta the "high quality" interpolation /// for `Rotor`s, and it can also be used to interpolate other things, one example being interpolation of /// 3d normal vectors. /// /// Note that you should often normalize the result returned by this operation, when working with `Rotor`s, etc! pub trait Slerp<T> { fn slerp(&self, end: Self, t: T) -> Self; } macro_rules! impl_slerp_rotor3 { ($($tt:ident => ($($vt:ident),+)),+) => { $($(impl Slerp<$tt> for $vt { /// Spherical-linear interpolation between `self` and `end` based on `t` from 0.0 to 1.0. /// /// `self` and `end` should both be normalized or something bad will happen! /// /// Basically, interpolation that maintains a constant angular velocity /// from one orientation on a unit hypersphere to another. This is sorta the "high quality" interpolation /// for `Rotor`s, and it can also be used to interpolate other things, one example being interpolation of /// 3d normal vectors. /// /// Note that you should often normalize the result returned by this operation, when working with `Rotor`s, etc! #[inline] fn slerp(&self, end: Self, t: $tt) -> Self { let dot = self.dot(end); if dot > 0.9995 { return self.lerp(end, t); } let dot = dot.min(1.0).max(-1.0); let theta_0 = dot.acos(); // angle between inputs let theta = theta_0 * t; // amount of said angle to travel let v2 = (end - (*self * dot)).normalized(); // create orthonormal basis between self and `v2` let (s, c) = theta.sin_cos(); let mut n = *self; n.s = (c * self.s) + (s * v2.s); n.bv.xy = (c * self.bv.xy) + (s * v2.bv.xy); n.bv.xz = (c * self.bv.xz) + (s * v2.bv.xz); n.bv.yz = (c * self.bv.yz) + (s * v2.bv.yz); n } })+)+ }; } impl_slerp_rotor3!( f32 => (Rotor3) ); #[cfg(feature = "f64")] impl_slerp_rotor3!( f64 => (DRotor3) ); macro_rules! impl_slerp_rotor3_wide { ($($tt:ident => ($($vt:ident),+)),+) => { $($(impl Slerp<$tt> for $vt { /// Spherical-linear interpolation between `self` and `end` based on `t` from 0.0 to 1.0. /// /// `self` and `end` should both be normalized or something bad will happen! /// /// The implementation for SIMD types also requires that the two things being interpolated between /// are not exactly aligned, or else the result is undefined. /// /// Basically, interpolation that maintains a constant angular velocity /// from one orientation on a unit hypersphere to another. This is sorta the "high quality" interpolation /// for `Rotor`s, and it can also be used to interpolate other things, one example being interpolation of /// 3d normal vectors. /// /// Note that you should often normalize the result returned by this operation, when working with `Rotor`s, etc! #[inline] fn slerp(&self, end: Self, t: $tt) -> Self { let dot = self.dot(end); let dot = dot.min($tt::splat(1.0)).max($tt::splat(-1.0)); let theta_0 = dot.acos(); // angle between inputs let theta = theta_0 * t; // amount of said angle to travel let v2 = (end - (*self * dot)).normalized(); // create orthonormal basis between self and `v2` let (s, c) = theta.sin_cos(); let mut n = *self; n.s = (c * self.s) + (s * v2.s); n.bv.xy = (c * self.bv.xy) + (s * v2.bv.xy); n.bv.xz = (c * self.bv.xz) + (s * v2.bv.xz); n.bv.yz = (c * self.bv.yz) + (s * v2.bv.yz); n } })+)+ }; } impl_slerp_rotor3_wide!( f32x4 => (Rotor3x4), f32x8 => (Rotor3x8) ); #[cfg(feature = "f64")] impl_slerp_rotor3_wide!( f64x2 => (DRotor3x2), f64x4 => (DRotor3x4) ); macro_rules! impl_slerp_gen { ($($tt:ident => ($($vt:ident),+)),+) => { $($(impl Slerp<$tt> for $vt { /// Spherical-linear interpolation between `self` and `end` based on `t` from 0.0 to 1.0. /// /// `self` and `end` should both be normalized or something bad will happen! /// /// The implementation for SIMD types also requires that the two things being interpolated between /// are not exactly aligned, or else the result is undefined. /// /// Basically, interpolation that maintains a constant angular velocity /// from one orientation on a unit hypersphere to another. This is sorta the "high quality" interpolation /// for `Rotor`s, and it can also be used to interpolate other things, one example being interpolation of /// 3d normal vectors. /// /// Note that you should often normalize the result returned by this operation, when working with `Rotor`s, etc! #[inline] fn slerp(&self, end: Self, t: $tt) -> Self { let dot = self.dot(end); let dot = dot.min($tt::splat(1.0)).max($tt::splat(-1.0)); let theta_0 = dot.acos(); // angle between inputs let theta = theta_0 * t; // amount of said angle to travel let v2 = (end - (*self * dot)).normalized(); // create orthonormal basis between self and `v2` let (s, c) = theta.sin_cos(); *self * c + v2 * s } })+)+ }; } impl_slerp_gen!( f32 => (Vec2, Vec3, Vec4, Bivec2, Bivec3, Rotor2), f32x4 => (Vec2x4, Vec3x4, Vec4x4, Bivec2x4, Bivec3x4, Rotor2x4), f32x8 => (Vec2x8, Vec3x8, Vec4x8, Bivec2x8, Bivec3x8, Rotor2x8) ); #[cfg(feature = "f64")] impl_slerp_gen!( f64 => (DVec2, DVec3, DVec4, DBivec2, DBivec3, DRotor2), f64x2 => (DVec2x2, DVec3x2, DVec4x2, DBivec2x2, DBivec3x2, DRotor2x2), f64x4 => (DVec2x4, DVec3x4, DVec4x4, DBivec2x4, DBivec3x4, DRotor2x4) );