glam 0.33.2

A simple and fast 3D math library for games and graphics
Documentation 
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

// Generated from camera_impl.rs.tera template. Edit the template, not the generated file.

//! Internal primitives for building view and projection matrices.
//!
//! Each function is parameterized over const generics that select the
//! coordinate system convention:
//!
//! * `RH` - right-handed (`true`) vs left-handed (`false`) view space
//! * `ZO` - NDC Z maps to `[0, 1]` (`true`) vs `[-1, 1]` (`false`)
//! * `YFLIP` - NDC Y points down (`true`) vs up (`false`)
//!
//! These are called by the public wrappers in `lh::proj`, `rh::proj`,
//! `lh::view`, and `rh::view` and should not be used directly.

use crate::{f64::math, DAffine3, DMat3, DMat4, DQuat, DVec3, DVec4};

/// Computes an orthonormal view basis from eye, direction, and up.
#[inline(always)]
#[must_use]
fn look_to_axes4<const RH: bool>(eye: DVec3, dir: DVec3, up: DVec3) -> [DVec3; 4] {
    glam_assert!(dir.is_normalized());
    glam_assert!(up.is_normalized());
    let f = if RH { dir } else { -dir };
    let s = f.cross(up).normalize();
    let u = s.cross(f);
    [
        DVec3::new(s.x, u.x, -f.x),
        DVec3::new(s.y, u.y, -f.y),
        DVec3::new(s.z, u.z, -f.z),
        DVec3::new(-eye.dot(s), -eye.dot(u), eye.dot(f)),
    ]
}

/// Same as [`look_to_axes4`] but without the translation row.
#[inline(always)]
#[must_use]
fn look_to_axes3<const RH: bool>(dir: DVec3, up: DVec3) -> [DVec3; 3] {
    glam_assert!(dir.is_normalized());
    glam_assert!(up.is_normalized());
    let f = if RH { dir } else { -dir };
    let s = f.cross(up).normalize();
    let u = s.cross(f);
    [
        DVec3::new(s.x, u.x, -f.x),
        DVec3::new(s.y, u.y, -f.y),
        DVec3::new(s.z, u.z, -f.z),
    ]
}

/// Assembles a `DMat4` view matrix from eye, direction, and up.
#[inline]
#[must_use]
pub(crate) fn look_to_mat4<const RH: bool>(eye: DVec3, dir: DVec3, up: DVec3) -> DMat4 {
    let axes = look_to_axes4::<RH>(eye, dir, up);
    DMat4::from_cols(
        axes[0].extend(0.0),
        axes[1].extend(0.0),
        axes[2].extend(0.0),
        axes[3].extend(1.0),
    )
}

/// Assembles an `DAffine3` view transform from eye, direction, and up.
#[inline]
#[must_use]
pub(crate) fn look_to_affine3<const RH: bool>(eye: DVec3, dir: DVec3, up: DVec3) -> DAffine3 {
    let axes = look_to_axes4::<RH>(eye, dir, up);
    DAffine3 {
        matrix3: DMat3::from_cols(axes[0], axes[1], axes[2]),
        translation: axes[3],
    }
}

/// Returns a `DMat3` view rotation (no translation) from direction and up.
#[inline]
#[must_use]
pub(crate) fn look_to_mat3<const RH: bool>(dir: DVec3, up: DVec3) -> DMat3 {
    let axes = look_to_axes3::<RH>(dir, up);
    DMat3::from_cols(axes[0], axes[1], axes[2])
}

/// Returns a `DQuat` representing a view rotation from direction and up.
#[inline]
#[must_use]
pub(crate) fn look_to_quat<const RH: bool>(dir: DVec3, up: DVec3) -> DQuat {
    let axes = look_to_axes3::<RH>(dir, up);
    DQuat::from_rotation_axes(axes[0], axes[1], axes[2])
}

/// Builds a perspective projection matrix from FOV, aspect, and near/far planes.
///
/// # Panics
///
/// Will panic if `near` or `far` are <= 0 when `glam_assert` is enabled.
#[inline]
#[must_use]
pub(crate) fn perspective<const RH: bool, const ZO: bool, const YFLIP: bool>(
    vertical_fov: f64,
    aspect_ratio: f64,
    near: f64,
    far: f64,
) -> DMat4 {
    glam_assert!(near > 0.0 && far > 0.0);
    let (sin_fov, cos_fov) = math::sin_cos(0.5 * vertical_fov);
    let h = cos_fov / sin_fov;
    let xx = h / aspect_ratio;
    let yy = if YFLIP { -h } else { h };
    let z_range_inv = 1.0 / (far - near);

    let (zz, tz, zw) = match (ZO, RH) {
        (true, false) => (far * z_range_inv, -near * far * z_range_inv, 1.0),
        (false, false) => (
            (far + near) * z_range_inv,
            -2.0 * far * near * z_range_inv,
            1.0,
        ),
        (true, true) => (-far * z_range_inv, -near * far * z_range_inv, -1.0),
        (false, true) => (
            -(far + near) * z_range_inv,
            -2.0 * far * near * z_range_inv,
            -1.0,
        ),
    };

    DMat4::from_cols(
        DVec4::new(xx, 0.0, 0.0, 0.0),
        DVec4::new(0.0, yy, 0.0, 0.0),
        DVec4::new(0.0, 0.0, zz, zw),
        DVec4::new(0.0, 0.0, tz, 0.0),
    )
}

/// Like [`perspective`] but with an infinite far plane.
///
/// Depth approaches 1 as distance -> infinity.
///
/// # Panics
///
/// Will panic if `near` <= 0 when `glam_assert` is enabled.
#[inline]
#[must_use]
pub(crate) fn perspective_infinite<const RH: bool, const ZO: bool, const YFLIP: bool>(
    vertical_fov: f64,
    aspect_ratio: f64,
    near: f64,
) -> DMat4 {
    glam_assert!(near > 0.0);
    let (sin_fov, cos_fov) = math::sin_cos(0.5 * vertical_fov);
    let h = cos_fov / sin_fov;
    let xx = h / aspect_ratio;
    let yy = if YFLIP { -h } else { h };
    let zz = if RH { -1.0 } else { 1.0 };
    let zw = zz;
    let tz = if ZO { -near } else { -2.0 * near };
    DMat4::from_cols(
        DVec4::new(xx, 0.0, 0.0, 0.0),
        DVec4::new(0.0, yy, 0.0, 0.0),
        DVec4::new(0.0, 0.0, zz, zw),
        DVec4::new(0.0, 0.0, tz, 0.0),
    )
}

/// Infinite perspective with reversed Z: near maps to depth 1, infinity to 0.
///
/// Improves floating-point depth precision for distant objects.
///
/// # Panics
///
/// Will panic if `near` <= 0 when `glam_assert` is enabled.
#[inline]
#[must_use]
pub(crate) fn perspective_infinite_reverse<const RH: bool, const YFLIP: bool>(
    vertical_fov: f64,
    aspect_ratio: f64,
    near: f64,
) -> DMat4 {
    glam_assert!(near > 0.0);
    let (sin_fov, cos_fov) = math::sin_cos(0.5 * vertical_fov);
    let h = cos_fov / sin_fov;
    let xx = h / aspect_ratio;
    let yy = if YFLIP { -h } else { h };
    let zw = if RH { -1.0 } else { 1.0 };
    let tz = near;
    DMat4::from_cols(
        DVec4::new(xx, 0.0, 0.0, 0.0),
        DVec4::new(0.0, yy, 0.0, 0.0),
        DVec4::new(0.0, 0.0, 0.0, zw),
        DVec4::new(0.0, 0.0, tz, 0.0),
    )
}

/// Builds an orthographic projection from left, right, bottom, top, near, far bounds.
#[inline]
#[must_use]
pub(crate) fn orthographic<const RH: bool, const ZO: bool, const YFLIP: bool>(
    left: f64,
    right: f64,
    bottom: f64,
    top: f64,
    near: f64,
    far: f64,
) -> DMat4 {
    let width_inv = 1.0 / (right - left);
    let height_inv = 1.0 / (top - bottom);
    let depth_inv = 1.0 / (far - near);
    let xx = width_inv + width_inv;
    let yy = if YFLIP {
        -(height_inv + height_inv)
    } else {
        height_inv + height_inv
    };
    let zz = match (RH, ZO) {
        (true, true) => -depth_inv,
        (false, true) => depth_inv,
        (true, false) => -2.0 * depth_inv,
        (false, false) => 2.0 * depth_inv,
    };
    let tx = -(left + right) * width_inv;
    let ty = -(top + bottom) * height_inv;
    let tz = if ZO {
        -near * depth_inv
    } else {
        -(far + near) * depth_inv
    };
    DMat4::from_cols(
        DVec4::new(xx, 0.0, 0.0, 0.0),
        DVec4::new(0.0, yy, 0.0, 0.0),
        DVec4::new(0.0, 0.0, zz, 0.0),
        DVec4::new(tx, ty, tz, 1.0),
    )
}

/// Builds a perspective projection from a general frustum.
///
/// # Panics
///
/// Will panic if `near` or `far` are <= 0 when `glam_assert` is enabled.
#[inline]
#[must_use]
pub(crate) fn frustum<const RH: bool, const ZO: bool, const YFLIP: bool>(
    left: f64,
    right: f64,
    bottom: f64,
    top: f64,
    near: f64,
    far: f64,
) -> DMat4 {
    glam_assert!(near > 0.0 && far > 0.0);
    let inv_width = 1.0 / (right - left);
    let inv_height = 1.0 / (top - bottom);
    let inv_depth = 1.0 / (far - near);
    let two_near = 2.0 * near;
    let xx = two_near * inv_width;
    let yy = if YFLIP {
        -two_near * inv_height
    } else {
        two_near * inv_height
    };
    let zx = (right + left) * inv_width;
    let zy = if YFLIP {
        -(top + bottom) * inv_height
    } else {
        (top + bottom) * inv_height
    };
    let (zz, zw, tz) = match (RH, ZO) {
        (true, true) => (-far * inv_depth, -1.0, -(far * near) * inv_depth),
        (false, true) => (far * inv_depth, 1.0, -(far * near) * inv_depth),
        (true, false) => (
            -(far + near) * inv_depth,
            -1.0,
            -(2.0 * far * near) * inv_depth,
        ),
        (false, false) => (
            (far + near) * inv_depth,
            1.0,
            -(2.0 * far * near) * inv_depth,
        ),
    };
    DMat4::from_cols(
        DVec4::new(xx, 0.0, 0.0, 0.0),
        DVec4::new(0.0, yy, 0.0, 0.0),
        DVec4::new(zx, zy, zz, zw),
        DVec4::new(0.0, 0.0, tz, 0.0),
    )
}