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

use number_traits::{Num, Signed, Sqrt, Trig};
use create::{clone, create};


#[inline]
pub fn rotation_x<'a, 'b, T: Copy + Num + Trig>(out: &'b [T; 4]) -> T {
    (T::from_usize(2) * out[0] * out[3] + T::from_usize(2) * out[1] * out[2])
        .atan2(&(T::one() - T::from_usize(2) * (out[2] * out[2] + out[3] * out[3])))
}

#[inline]
pub fn rotation_y<'a, 'b, T: Copy + Signed + Trig>(out: &'b [T; 4]) -> T {
    let theta = T::from_usize(2) * (out[0] * out[2] + out[3] * out[1]);
    (if theta < -T::one() {-T::one()} else if theta > T::one() {T::one()} else {theta}).asin()
}

#[inline]
pub fn rotation_z<'a, 'b, T: Copy + Num + Trig>(out: &'b [T; 4]) -> T {
    (T::from_usize(2) * out[0] * out[1] + T::from_usize(2) * out[2] * out[3])
        .atan2(&(T::one() - T::from_usize(2) * (out[1] * out[1] + out[2] * out[2])))
}

#[inline]
pub fn rotate_x<'a, 'b, T: Copy + Num + Trig>(out: &'a mut [T; 4], a: &'b [T; 4], angle: T) -> &'a mut [T; 4] {
    let ax = a[0];
    let ay = a[1];
    let az = a[2];
    let aw = a[3];
    let half_angle = angle / T::from_usize(2);
    let bx = half_angle.sin();
    let bw = half_angle.cos();

    out[0] = ax * bw + aw * bx;
    out[1] = ay * bw + az * bx;
    out[2] = az * bw - ay * bx;
    out[3] = aw * bw - ax * bx;
    out
}

#[inline]
pub fn rotate_y<'a, 'b, T: Copy + Num + Trig>(out: &'a mut [T; 4], a: &'b [T; 4], angle: T) -> &'a mut [T; 4] {
    let ax = a[0];
    let ay = a[1];
    let az = a[2];
    let aw = a[3];
    let half_angle = angle / T::from_usize(2);
    let by = half_angle.sin();
    let bw = half_angle.cos();

    out[0] = ax * bw - az * by;
    out[1] = ay * bw + aw * by;
    out[2] = az * bw + ax * by;
    out[3] = aw * bw - ay * by;
    out
}

#[inline]
pub fn rotate_z<'a, 'b, T: Copy + Num + Trig>(out: &'a mut [T; 4], a: &'b [T; 4], angle: T) -> &'a mut [T; 4] {
    let ax = a[0];
    let ay = a[1];
    let az = a[2];
    let aw = a[3];
    let half_angle = angle / T::from_usize(2);
    let bz = half_angle.sin();
    let bw = half_angle.cos();

    out[0] = ax * bw + ay * bz;
    out[1] = ay * bw - ax * bz;
    out[2] = az * bw + aw * bz;
    out[3] = aw * bw - az * bz;
    out
}

#[inline]
pub fn rotate<'a, 'b, T: Copy + Num + Trig>(out: &'a mut [T; 4], a: &'b [T; 4], x: T, y: T, z: T) -> &'a mut [T; 4] {
    let mut tmp_a = clone(a);
    let mut tmp_b = create(T::zero(), T::zero(), T::zero(), T::one());
    rotate_z(&mut tmp_a, &a, z);
    rotate_x(&mut tmp_b, &tmp_a, x);
    rotate_y(out, &tmp_b, y);
    out
}

#[inline]
pub fn look_rotation<'a, 'b, T: Copy + Num>(out: &'a mut [T; 4], forward: &'b [T; 3], up: &'b [T; 3]) -> &'a mut [T; 4] {
    let fx = forward[0];
    let fy = forward[1];
    let fz = forward[2];
    let ux = up[0];
    let uy = up[1];
    let uz = up[2];

    let ax = uy * fz - uz * fy;
    let ay = uz * fx - ux * fz;
    let az = ux * fy - uy * fx;

    let d = (T::one() + ux * fx + uy * fy + uz * fz) * T::from_usize(2);
    let dsq = d * d;
    let s = if dsq != T::zero() {T::one() / dsq} else {dsq};

    out[0] = ax * s;
    out[1] = ay * s;
    out[2] = az * s;
    out[3] = dsq / T::from_usize(2);
    out
}

#[inline]
pub fn from_axis_angle<'a, 'b, T: Copy + Num + Trig>(out: &'a mut [T; 4], axis: &'b [T; 3], angle: T) -> &'a mut [T; 4] {
    let half_angle = angle / T::from_usize(2);
    let s = half_angle.sin();

    out[0] = axis[0] * s;
    out[1] = axis[1] * s;
    out[2] = axis[2] * s;
    out[3] = half_angle.cos();
    out
}

#[inline]
pub fn get_axis_angle<'a, 'b, T: Copy + Num + Trig>(out: &'a mut [T; 3], q: &'b [T; 4]) -> T {
    let angle = q[3].acos() * T::from_usize(2);
    let s = angle.sin() / T::from_usize(2);

    if s != T::zero() {
        out[0] = q[0] / s;
        out[1] = q[1] / s;
        out[2] = q[2] / s;
    } else {
        out[0] = T::zero();
        out[1] = T::zero();
        out[2] = T::one();
    }

    return angle;
}

#[inline]
pub fn from_mat<'a, 'b, T: Copy + Num + Sqrt>(
    out: &'a mut [T; 4],
    m11: T, m12: T, m13: T,
    m21: T, m22: T, m23: T,
    m31: T, m32: T, m33: T
) -> &'a mut [T; 4] {
    let trace = m11 + m22 + m33;

    if trace > T::zero() {
        let s = T::from_f32(0.5f32) / (trace + T::one()).sqrt();

        out[3] = T::from_f32(0.25f32) / s;
        out[0] = (m32 - m23) * s;
        out[1] = (m13 - m31) * s;
        out[2] = (m21 - m12) * s;
    } else if m11 > m22 && m11 > m33 {
        let s = T::from_usize(2) * (T::one() + m11 - m22 - m33).sqrt();
        let inv_s = T::one() / s;

        out[3] = (m32 - m23) * inv_s;
        out[0] = s / T::from_isize(4isize);
        out[1] = (m12 + m21) * inv_s;
        out[2] = (m13 + m31) * inv_s;
    } else if m22 > m33 {
        let s = T::from_usize(2) * (T::one() + m22 - m11 - m33).sqrt();
        let inv_s = T::one() / s;

        out[3] = (m13 - m31) * inv_s;
        out[0] = (m12 + m21) * inv_s;
        out[1] = s / T::from_isize(4isize);
        out[2] = (m23 + m32) * inv_s;
    } else {
        let s = T::from_usize(2) * (T::one() + m33 - m11 - m22).sqrt();
        let inv_s = T::one() / s;

        out[3] = (m21 - m12) * inv_s;
        out[0] = (m13 + m31) * inv_s;
        out[1] = (m23 + m32) * inv_s;
        out[2] = s / T::from_isize(4isize);
    }
    out
}

#[inline]
pub fn from_mat2<'a, 'b, T: Copy + Num + Sqrt>(out: &'a mut [T; 4], m: &'b [T; 4]) -> &'a mut [T; 4] {
    from_mat(
        out,
        m[0], m[2], T::zero(),
        m[1], m[3], T::zero(),
        T::zero(), T::zero(), T::one()
    )
}

#[inline]
pub fn from_mat32<'a, 'b, T: Copy + Num + Sqrt>(out: &'a mut [T; 4], m: &'b [T; 6]) -> &'a mut [T; 4] {
    from_mat(
        out,
        m[0], m[2], T::zero(),
        m[1], m[3], T::zero(),
        T::zero(), T::zero(), T::one()
    )
}

#[inline]
pub fn from_mat3<'a, 'b, T: Copy + Num + Sqrt>(out: &'a mut [T; 4], m: &'b [T; 9]) -> &'a mut [T; 4] {
    from_mat(
        out,
        m[0], m[3], m[6],
        m[1], m[4], m[7],
        m[2], m[5], m[8]
    )
}

#[inline]
pub fn from_mat4<'a, 'b, T: Copy + Num + Sqrt>(out: &'a mut [T; 4], m: &'b [T; 16]) -> &'a mut [T; 4] {
    from_mat(
        out,
        m[0], m[4], m[8],
        m[1], m[5], m[9],
        m[2], m[6], m[10]
    )
}