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

use super::Vec2;

// {s,c} represents the rotation matrix:
//
// | c -s |
// | s  c |
//
// `vec2(c,s)` represents where the X axis will end up after rotation.
//
/// Represents a rotation in the 2D plane.
//
/// A rotation of 𝞃/4 = 90° rotates the X axis to the Y axis.
//
/// Normally a `Rot2` is normalized (unit-length).
/// If not, it will also scale vectors.
#[repr(C)]
#[derive(Clone, Copy, PartialEq)]
#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
#[cfg_attr(feature = "bytemuck", derive(bytemuck::Pod, bytemuck::Zeroable))]
pub struct Rot2 {
    /// angle.sin()
    s: f32,
    /// angle.cos()
    c: f32,
}

/// Identity rotation
impl Default for Rot2 {
    /// Identity rotation
    fn default() -> Self {
        Self { s: 0.0, c: 1.0 }
    }
}

impl Rot2 {
    /// The identity rotation: nothing rotates
    pub const IDENTITY: Self = Self { s: 0.0, c: 1.0 };

    /// Angle is clockwise in radians.
    /// A 𝞃/4 = 90° rotation means rotating the X axis to the Y axis.
    pub fn from_angle(angle: f32) -> Self {
        let (s, c) = angle.sin_cos();
        Self { s, c }
    }

    pub fn angle(self) -> f32 {
        self.s.atan2(self.c)
    }

    /// The factor by which vectors will be scaled.
    pub fn length(self) -> f32 {
        self.c.hypot(self.s)
    }

    pub fn length_squared(self) -> f32 {
        self.c.powi(2) + self.s.powi(2)
    }

    pub fn is_finite(self) -> bool {
        self.c.is_finite() && self.s.is_finite()
    }

    #[must_use]
    pub fn inverse(self) -> Rot2 {
        Self {
            s: -self.s,
            c: self.c,
        } / self.length_squared()
    }

    #[must_use]
    pub fn normalized(self) -> Self {
        let l = self.length();
        let ret = Self {
            c: self.c / l,
            s: self.s / l,
        };
        crate::emath_assert!(ret.is_finite());
        ret
    }
}

impl std::fmt::Debug for Rot2 {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(
            f,
            "Rot2 {{ angle: {:.1}°, length: {} }}",
            self.angle().to_degrees(),
            self.length()
        )
    }
}

impl std::ops::Mul<Rot2> for Rot2 {
    type Output = Rot2;
    fn mul(self, r: Rot2) -> Rot2 {
        /*
        |lc -ls| * |rc -rs|
        |ls  lc|   |rs  rc|
        */
        Rot2 {
            c: self.c * r.c - self.s * r.s,
            s: self.s * r.c + self.c * r.s,
        }
    }
}

/// Rotates (and maybe scales) the vector.
impl std::ops::Mul<Vec2> for Rot2 {
    type Output = Vec2;
    fn mul(self, v: Vec2) -> Vec2 {
        Vec2 {
            x: self.c * v.x - self.s * v.y,
            y: self.s * v.x + self.c * v.y,
        }
    }
}

/// Scales the rotor.
impl std::ops::Mul<Rot2> for f32 {
    type Output = Rot2;
    fn mul(self, r: Rot2) -> Rot2 {
        Rot2 {
            c: self * r.c,
            s: self * r.s,
        }
    }
}

/// Scales the rotor.
impl std::ops::Mul<f32> for Rot2 {
    type Output = Rot2;
    fn mul(self, r: f32) -> Rot2 {
        Rot2 {
            c: self.c * r,
            s: self.s * r,
        }
    }
}

/// Scales the rotor.
impl std::ops::Div<f32> for Rot2 {
    type Output = Rot2;
    fn div(self, r: f32) -> Rot2 {
        Rot2 {
            c: self.c / r,
            s: self.s / r,
        }
    }
}

#[cfg(test)]
mod test {
    use super::Rot2;
    use crate::vec2;

    #[test]
    fn test_rotation2() {
        {
            let angle = std::f32::consts::TAU / 6.0;
            let rot = Rot2::from_angle(angle);
            assert!((rot.angle() - angle).abs() < 1e-5);
            assert!((rot * rot.inverse()).angle().abs() < 1e-5);
            assert!((rot.inverse() * rot).angle().abs() < 1e-5);
        }

        {
            let angle = std::f32::consts::TAU / 4.0;
            let rot = Rot2::from_angle(angle);
            assert!(((rot * vec2(1.0, 0.0)) - vec2(0.0, 1.0)).length() < 1e-5);
        }

        {
            // Test rotation and scaling
            let angle = std::f32::consts::TAU / 4.0;
            let rot = 3.0 * Rot2::from_angle(angle);
            let rotated = rot * vec2(1.0, 0.0);
            let expected = vec2(0.0, 3.0);
            assert!(
                (rotated - expected).length() < 1e-5,
                "Expected {:?} to equal {:?}. rot: {:?}",
                rotated,
                expected,
                rot,
            );

            let undone = rot.inverse() * rot;
            assert!(undone.angle().abs() < 1e-5);
            assert!((undone.length() - 1.0).abs() < 1e-5,);
        }
    }
}