isomesh 0.0.9

Engine-agnostic isosurface extraction: signed distance field in, triangles out. no_std, f32 and f64, no math library in the public API.
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

//! Tests for Hermite extraction.
//!
//! The load-bearing one is `normals_agree_on_a_face_and_disagree_across_an_edge`
//! — that is the ticket's acceptance criterion and the property the whole of
//! dual contouring rests on. If normals were constant across a cell, there would
//! be nothing for a vertex solve to solve.

use super::{HermiteCell, HermiteCrossing};
use crate::cube::{EDGE_CORNERS, corner_offset, is_inside};
use crate::fields::{BoxExact, Sphere};
use crate::{Sdf, vec3};

/// Sample the eight corners of a cell, as an extractor would before calling in.
fn corners<S: Sdf<Scalar = f64>>(sdf: &S, origin: [f64; 3], size: f64) -> [f64; 8] {
    let mut values = [0.0; 8];
    for (corner, slot) in values.iter_mut().enumerate() {
        let offset = corner_offset(corner as u8);
        *slot = sdf.sample([
            origin[0] + size * f64::from(offset[0]),
            origin[1] + size * f64::from(offset[1]),
            origin[2] + size * f64::from(offset[2]),
        ]);
    }
    values
}

fn cell<S: Sdf<Scalar = f64>>(sdf: &S, origin: [f64; 3], size: f64) -> HermiteCell<f64> {
    HermiteCell::from_corners(sdf, &corners(sdf, origin, size), origin, size)
}

/// **The acceptance criterion.**
///
/// On a cell straddling one flat face of a box, every crossing normal is the
/// same face normal. On a cell straddling an edge where two faces meet, they are
/// not — and the disagreement is what a vertex solve reads to find the edge.
#[test]
fn normals_agree_on_a_face_and_disagree_across_an_edge() {
    let field = BoxExact::<f64>::canonical(); // [-1, 1]^3
    let size = 0.25;

    // A cell straddling the +x face, well away from any edge of the box.
    let face = cell(&field, [0.9, -0.1, -0.1], size);
    assert!(
        face.len() >= 4,
        "expected a face crossing, got {}",
        face.len()
    );
    let first = face.iter().next().expect("a crossing").normal;
    for crossing in face.iter() {
        let agreement = vec3::dot(crossing.normal, first);
        assert!(
            (agreement - 1.0).abs() < 1e-9,
            "a flat face must give one normal, got {:?} vs {first:?}",
            crossing.normal
        );
    }
    // And that normal is the face's own.
    assert!((first[0] - 1.0).abs() < 1e-9, "{first:?}");

    // A cell straddling the +x/+y edge of the box.
    let edge = cell(&field, [0.9, 0.9, -0.1], size);
    assert!(
        edge.len() >= 4,
        "expected an edge crossing, got {}",
        edge.len()
    );
    let mut minimum_agreement = 1.0f64;
    for a in edge.iter() {
        for b in edge.iter() {
            minimum_agreement = minimum_agreement.min(vec3::dot(a.normal, b.normal));
        }
    }
    // Two perpendicular faces meet here, so some pair of normals is at 90°.
    assert!(
        minimum_agreement < 1e-9,
        "an edge cell must carry disagreeing normals, min dot was {minimum_agreement}"
    );
}

/// Normals are unit length, because the QEF is written in terms of `nᵢ · (x − pᵢ)`
/// and a non-unit normal silently reweights that plane against the others.
#[test]
fn normals_are_unit_length() {
    for field_origin in [[0.9, -0.1, -0.1], [0.9, 0.9, -0.1], [-1.1, -0.1, 0.3]] {
        let cell = cell(&BoxExact::<f64>::canonical(), field_origin, 0.25);
        for crossing in cell.iter() {
            let length = vec3::length(crossing.normal);
            assert!(
                (length - 1.0).abs() < 1e-12,
                "normal {:?} has length {length}",
                crossing.normal
            );
        }
    }
}

/// Every crossing sits on its own edge, between that edge's two corners.
#[test]
fn crossings_lie_on_the_edges_they_belong_to() {
    let field = Sphere::<f64>::canonical();
    let origin = [0.8, -0.2, -0.2];
    let size = 0.4;
    let cell = cell(&field, origin, size);
    assert!(!cell.is_empty());

    for edge in 0..12u8 {
        let Some(crossing) = cell.get(edge) else {
            continue;
        };
        let [lo, hi] = EDGE_CORNERS[edge as usize];
        let (lo_offset, hi_offset) = (corner_offset(lo), corner_offset(hi));
        for axis in 0..3 {
            let a = origin[axis] + size * f64::from(lo_offset[axis]);
            let b = origin[axis] + size * f64::from(hi_offset[axis]);
            let (low, high) = if a < b { (a, b) } else { (b, a) };
            assert!(
                crossing.position[axis] >= low - 1e-12 && crossing.position[axis] <= high + 1e-12,
                "edge {edge} axis {axis}: {} outside [{low}, {high}]",
                crossing.position[axis]
            );
        }
    }
}

/// The mask has to agree with the corner signs, or the solve is fed edges that
/// carry no surface.
#[test]
fn the_mask_matches_the_corner_signs() {
    let field = Sphere::<f64>::canonical();
    let origin = [0.8, -0.2, -0.2];
    let values = corners(&field, origin, 0.4);
    let cell = HermiteCell::from_corners(&field, &values, origin, 0.4);

    let mut expected = 0usize;
    for (edge, [lo, hi]) in EDGE_CORNERS.iter().copied().enumerate() {
        let cut = is_inside(values[lo as usize]) != is_inside(values[hi as usize]);
        assert_eq!(cell.contains(edge as u8), cut, "edge {edge}");
        expected += usize::from(cut);
    }
    assert_eq!(cell.len(), expected);
    assert_eq!(cell.iter().count(), expected);
}

/// A cell the surface misses carries nothing at all.
#[test]
fn a_cell_with_no_crossing_is_empty() {
    let field = Sphere::<f64>::canonical();
    let cell = cell(&field, [1.5, 1.5, 1.5], 0.25);
    assert!(cell.is_empty());
    assert_eq!(cell.len(), 0);
    assert_eq!(cell.iter().count(), 0);
    assert_eq!(cell.centroid(), None);
    assert!(cell.get(0).is_none());
}

/// The centroid is exactly the vertex Surface Nets would place, so dual
/// contouring starts from the same point and the comparison in E-104 isolates
/// the solve.
#[test]
fn the_centroid_is_the_surface_nets_vertex() {
    let field = BoxExact::<f64>::canonical();
    let origin = [0.9, 0.9, -0.1];
    let cell = cell(&field, origin, 0.25);
    let centroid = cell.centroid().expect("a crossing");

    let mut expected = [0.0f64; 3];
    for crossing in cell.iter() {
        for (axis, slot) in expected.iter_mut().enumerate() {
            *slot += crossing.position[axis];
        }
    }
    let inverse = 1.0 / cell.len() as f64;
    for axis in 0..3 {
        assert!((centroid[axis] - expected[axis] * inverse).abs() < 1e-15);
    }
}

/// Extraction reads only the corner values it is handed, so the same cell
/// sampled twice gives the same answer bit for bit.
#[test]
fn extraction_is_deterministic() {
    let field = BoxExact::<f64>::canonical();
    let origin = [0.9, 0.9, -0.1];
    let a = cell(&field, origin, 0.25);
    let b = cell(&field, origin, 0.25);
    assert_eq!(a.len(), b.len());
    for (left, right) in a.iter().zip(b.iter()) {
        assert_eq!(left, right);
    }
}

#[test]
fn f32_extraction_works_too() {
    let field = BoxExact::<f32>::canonical();
    let mut values = [0.0f32; 8];
    for (corner, slot) in values.iter_mut().enumerate() {
        let offset = corner_offset(corner as u8);
        *slot = field.sample([
            0.9 + 0.25 * offset[0] as f32,
            -0.1 + 0.25 * offset[1] as f32,
            -0.1 + 0.25 * offset[2] as f32,
        ]);
    }
    let cell = HermiteCell::from_corners(&field, &values, [0.9, -0.1, -0.1], 0.25);
    assert!(!cell.is_empty());
    for crossing in cell.iter() {
        assert!((vec3::length(crossing.normal) - 1.0).abs() < 1e-5);
    }
}

/// A sphere's normals all point away from its centre, which is the sanity check
/// that the gradient is being read the right way round.
#[test]
fn normals_point_away_from_the_solid() {
    let field = Sphere::<f64>::canonical();
    let cell = cell(&field, [0.8, -0.2, -0.2], 0.4);
    assert!(!cell.is_empty());
    for HermiteCrossing { position, normal } in cell.iter() {
        let outward = vec3::scale(*position, vec3::length(*position).recip());
        assert!(
            vec3::dot(*normal, outward) > 0.999,
            "normal {normal:?} should agree with the radial direction {outward:?}"
        );
    }
}