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
// #![doc(html_logo_url = "https://rin.rs/logo.svg")]
// #![doc(html_favicon_url = "https://rin.rs/favicon.ico")]
/*!
 * This module mostly re-exports na (a graphics oriented wrapper for nalgebra)
 * angle (a type safe wrapper for angle measseures) and adds a few simple functions
 * useful for graphics math
 */
pub use na::*;
pub use angle::{Angle, Deg, Rad, cast as angle_cast};
// pub use num_traits;
pub use num_traits::{NumCast, Float, One, Zero, cast, ToPrimitive};
use std::f64;
use std::mem;
use std::ops::{Add,Sub,Mul,Div,ShlAssign};

pub use self::rectangle::{Rect, InsideRect};
pub type DualQuat<T = f32> = dual_quat::DualQuaternion<T>;
pub use dual_quat::DualQuaternion;
pub use approx::*;

mod rectangle;

/// Adds a 3d translation to a Mat4
pub fn add_translation<T: RealField + BaseNum>(mat: &Mat4<T>, t: &Vec3<T>) -> Mat4<T>{
    let trans_mat = Isometry3::from_parts(Translation::from(t.clone()), one()).to_homogeneous();
    *mat * trans_mat
}


// TODO: this should be an angle method in vec2 and pnt2
pub fn atan2<T: Float + BaseNum>(v1: &Vec2<T>, v2: &Vec2<T>) -> Rad<T>{
    Rad((v1.x * v2.y - v1.y * v2.x).atan2( v1.x * v2.x + v1.y * v2.y ))
}

/// Linear interpolation
#[inline]
pub fn lerp<U: RealField, T: Add<T, Output = T> + Mul<U, Output = T>>(p0: T, p1: T, pct: U) -> T{
    p0 * (one::<U>() - pct) + p1 * pct
}

/// Bezier interpolation from `from` to `to` using the control points
/// `cp1` and `cp2` at the normalized distance `pct`
pub fn bezier_interpolate<T, U>(from: U, cp1: U, cp2: U, to: U, pct: T) -> U
where
    T: RealField + NumCast,
    U: Sub<U, Output=U> + Mul<T, Output=U> + Add<U, Output=U> + Copy
{
    let c:U = (cp1 - from) * num_traits::cast::<f64,T>(3.0).unwrap();
    let b:U = (cp2 - cp1) * num_traits::cast::<f64,T>(3.0).unwrap() - c;
    let a:U = to - from - c - b;

    let t = pct;
    let t2 = t*t;
    let t3 = t2*t;
    a*t3 + b*t2 + c*t + from
}

pub fn smoothstep<T>(edge0: T, edge1: T, x: T) -> T
where
    T: Float + NumCast,
{
    let x = clamp((x - edge0) / (edge1 - edge0), zero(), one());
    x * x * (num_traits::cast::<f64,T>(3.).unwrap() - num_traits::cast::<f64,T>(2.).unwrap() * x)
}

/// Map a value from an input range `inmin..inmax`
/// to an output range `outmin..outmax`
#[inline]
pub fn map<T: Copy>(value: T, inmin: T, inmax: T, outmin: T, outmax: T) -> T
    where T: Add<T, Output = T> + Mul<T, Output = T> + Sub<T, Output = T> + Div<T, Output = T> + Clone + Zero + PartialEq{
    if inmin == inmax {
		outmin
	} else {
		(value - inmin) / (inmax - inmin) * (outmax - outmin) + outmin
	}
}

/// Map a value from an input range `inmin..inmax`
/// to an output range `outmin..outmax` and clamp the
/// result to be inside the output range
#[inline]
pub fn map_clamp<T: Copy>(value: T, inmin: T, inmax: T, outmin: T, outmax: T) -> T
    where T: Add<T, Output = T> + Mul<T, Output = T> + Sub<T, Output = T> + Div<T, Output = T> + Clone + Zero + PartialEq + PartialOrd{
    let out = map(value, inmin, inmax, outmin, outmax);
    if outmax > outmin {
        clamp(out, outmin, outmax)
    }else if outmax < outmin {
        clamp(out, outmax, outmin)
    }else{
        outmin
    }
}

/// Wrap a value in the range `from..to`
#[inline]
pub fn wrap<T: RealField>(value:T, from:T, to:T) -> T{
    let mut from = from;
    let mut to = to;

    if from > to{
        mem::swap(&mut from,&mut to);
    }

    let cycle = to - from;

    if cycle == zero(){
        return zero();
    }

    value - cycle * ((value - from) / cycle).floor()
}

/// Wrap an integer value in the range `from..to`
#[inline]
pub fn iwrap<T: num_traits::PrimInt + ::std::fmt::Display>(mut value:T, from:T, to:T) -> T{
    let mut from = from;
    let mut to = to;

    if from > to{
        mem::swap(&mut from,&mut to);
    }

    let cycle = to - from;

    if cycle == num_traits::zero(){
        return num_traits::zero();
    }

    if value < from {
        value = value + cycle * ((from - value) / cycle + num_traits::one());
    }

    from + (value - from) % cycle
}


/// Intersection of line segments p0 - p1 and p2 - p3
#[inline]
pub fn line_segment_intersection(p0: Pnt2, p1: Pnt2, p2: Pnt2, p3: Pnt2) -> Option<Pnt2>
{
    let s1_x = p1.x - p0.x;
    let s1_y = p1.y - p0.y;
    let s2_x = p3.x - p2.x;
    let s2_y = p3.y - p2.y;

    let s = (-s1_y * (p0.x - p2.x) + s1_x * (p0.y - p2.y)) / (-s2_x * s1_y + s1_x * s2_y);
    let t = ( s2_x * (p0.y - p2.y) - s2_y * (p0.x - p2.x)) / (-s2_x * s1_y + s1_x * s2_y);

    if s >= 0.0 && s <= 1.0 && t >= 0.0 && t <= 1.0{
        Some(Pnt2::new(p0.x + (t * s1_x), p0.y + (t * s1_y)))
    }else{
        None
    }
}

/// Convert a quaternion to euler angles
#[inline]
//TODO: Generics are gone cause both Real and Float provide asin, atan...
pub fn to_euler(q: &UnitQuat) -> (Rad<f32>, Rad<f32>, Rad<f32>){
    let q = q.quaternion();
	let test = q.i*q.j + q.k*q.w;
    let two = 2.0;
    let one = 1.0;
	if test > num_traits::cast(0.499).unwrap() { // singularity at north pole
		( Rad(two * q.i.atan2(q.w)),  // heading
		 Rad::half_pi(),              // attitude
		 num_traits::zero() )                     // bank
	} else if test < num_traits::cast(-0.499).unwrap() { // singularity at south pole
		( Rad(-two * q.i.atan2(q.w)), // heading
		  - Rad::half_pi(),           // attitude
		  num_traits::zero() )                    // bank
	} else {
		let sqx = q.i * q.i;
		let sqy = q.j * q.j;
		let sqz = q.k * q.k;
		(
            Rad((two * q.j * q.w - two * q.i * q.k).atan2(one - two*sqy - two*sqz)), // heading
		    Rad((two*test).asin()),                                                  // attitude
		    Rad((two*q.i * q.w - two* q.j * q.k).atan2(one - two*sqx - two*sqz)),    // bank
        )
	}
}

/// Convert a quaternion to tait bryan angles
#[inline]
//TODO: Generics are gone cause both Real and Float provide asin, atan...
pub fn to_tait_bryan(q: &UnitQuat) -> (Rad<f32>, Rad<f32>, Rad<f32>){
    let q = q.quaternion();
	let sq0 = q.w*q.w;
	let sq1 = q.i*q.i;
	let sq2 = q.j*q.j;
	let sq3 = q.k*q.k;
    let _2 = 2.0;

	// we can now use the same terms as in the textbook.
	let roll  =	Rad((_2 * q.j * q.k + _2 * q.w * q.i).atan2(sq3 - sq2 - sq1 + sq0));
	let pitch =	Rad(-(_2 * q.i * q.k - _2 * q.w * q.j).asin());
	let yaw	  =	Rad((_2 * q.i * q.j + _2 * q.w * q.k).atan2(sq1 + sq0 - sq3 - sq2));

	(roll,pitch,yaw)
}

pub enum RotOrder{
    XYZ,
    XZY,
    YXZ,
    YZX,
    ZXY,
    ZYX,
}

struct AxisParity{
    axis: Vec3<usize>,
    parity: bool,
}

impl RotOrder{
    fn to_axis_parity(self) -> AxisParity{
        let axis_parity = match self{
            RotOrder::XYZ => ([0usize, 1, 2], false),
            RotOrder::XZY => ([0, 2, 1], false),
            RotOrder::YXZ => ([1, 0, 2], true),
            RotOrder::YZX => ([1, 2, 0], true),
            RotOrder::ZXY => ([2, 0, 1], false),
            RotOrder::ZYX => ([2, 1, 0], true),
        };
        unsafe{ mem::transmute(axis_parity) }
    }
}

/// Convert euler angles with a certain rotation order
/// into a quaternion
pub fn euler_to_quaternion(rot: &Vec3, rot_order: RotOrder) -> UnitQuat{
    let r = rot_order.to_axis_parity();
    let i = r.axis.x;
    let j = r.axis.y;
    let k = r.axis.z;

    let ti = rot[i] * 0.5;
    let tj = rot[j] * if r.parity { -0.5 } else { 0.5 };
    let th = rot[k] * 0.5;

    let ci = ti.cos();
    let cj = tj.cos();
    let ch = th.cos();
    let si = ti.sin();
    let sj = tj.sin();
    let sh = th.sin();

    let cc = ci * ch;
    let cs = ci * sh;
    let sc = si * ch;
    let ss = si * sh;

    let mut a: [f32;3] = unsafe{ mem::MaybeUninit::uninit().assume_init() };
    a[i] = cj * sc - sj * cs;
    a[j] = cj * ss + sj * cc;
    a[k] = cj * cs - sj * sc;

    let w = cj * cc + sj * ss;
    let x = a[0];
    let y = a[1];
    let z = a[2];

    let mut q = Quaternion::new(w,x,y,z);

    if r.parity { q[j + 1] = -q[j + 1] };

    UnitQuat::from_quaternion(q)
}

/// Next power of two
///
/// 63 -> 64
/// 200 -> 256
/// ...
pub fn next_pow2<T: BaseNum + PartialOrd + ShlAssign<T>>(v: T) -> T{
    let mut rval= one();
	while rval<v{
        rval<<=one();
    }
	rval
}

pub fn next_multiple<T: BaseNum>(value: T, multiple: T) -> T{
    let rem = value.inlined_clone() % multiple.inlined_clone();
    if rem != zero() {
        let add = multiple - rem;
        value + add
    }else{
        value
    }
}

pub trait IsParallel {
    fn is_parallel(&self, other: &Self) -> bool;
}

impl<T: PartialEq + Scalar + RealField + Float> IsParallel for Vec3<T> {
    fn is_parallel(&self, other: &Vec3<T>) -> bool {
        Float::abs(Float::abs(self.dot(&other)) - self.norm() * other.norm()) < T::epsilon()
    }
}