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
|
// This file is part of the 64k demo project.
// It implements a lightweight SDF-based physics engine.
#include "3d/physics.h"
#include "3d/bvh.h"
#include "3d/sdf_cpu.h"
#include <algorithm>
namespace {
// Helper to get world AABB (copied from bvh.cc or shared)
AABB get_world_aabb(const Object3D& obj) {
BoundingVolume local = obj.get_local_bounds();
mat4 model = obj.get_model_matrix();
vec3 corners[8] = {
{local.min.x, local.min.y, local.min.z},
{local.max.x, local.min.y, local.min.z},
{local.min.x, local.max.y, local.min.z},
{local.max.x, local.max.y, local.min.z},
{local.min.x, local.min.y, local.max.z},
{local.max.x, local.min.y, local.max.z},
{local.min.x, local.max.y, local.max.z},
{local.max.x, local.max.y, local.max.z},
};
AABB world;
for (int i = 0; i < 8; ++i) {
vec4 p = model * vec4(corners[i].x, corners[i].y, corners[i].z, 1.0f);
world.expand(p.xyz());
}
return world;
}
} // namespace
float PhysicsSystem::sample_sdf(const Object3D& obj, vec3 world_p) {
mat4 inv_model = obj.get_model_matrix().inverse();
vec4 local_p4 = inv_model * vec4(world_p.x, world_p.y, world_p.z, 1.0f);
vec3 q = local_p4.xyz();
float d = 1000.0f;
if (obj.type == ObjectType::SPHERE) {
d = q.len() - 1.0f;
} else if (obj.type == ObjectType::BOX || obj.type == ObjectType::CUBE) {
d = sdf::sdBox(q, vec3(1.0f, 1.0f, 1.0f));
} else if (obj.type == ObjectType::TORUS) {
d = sdf::sdTorus(q, vec2(1.0f, 0.4f));
} else if (obj.type == ObjectType::PLANE) {
d = sdf::sdPlane(q, vec3(0.0f, 1.0f, 0.0f), 0.0f);
}
// Extract scale from model matrix (assuming orthogonal with uniform or
// non-uniform scale)
mat4 model = obj.get_model_matrix();
float sx = vec3(model.m[0], model.m[1], model.m[2]).len();
float sy = vec3(model.m[4], model.m[5], model.m[6]).len();
float sz = vec3(model.m[8], model.m[9], model.m[10]).len();
float s = std::min(sx, std::min(sy, sz));
return d * s;
}
void PhysicsSystem::resolve_collision(Object3D& a, Object3D& b) {
if (a.is_static && b.is_static)
return;
// Probe points for 'a' (center and corners)
BoundingVolume local = a.get_local_bounds();
mat4 model_a = a.get_model_matrix();
vec3 probes[9] = {
{0, 0, 0}, // Center
{local.min.x, local.min.y, local.min.z},
{local.max.x, local.min.y, local.min.z},
{local.min.x, local.max.y, local.min.z},
{local.max.x, local.max.y, local.min.z},
{local.min.x, local.min.y, local.max.z},
{local.max.x, local.min.y, local.max.z},
{local.min.x, local.max.y, local.max.z},
{local.max.x, local.max.y, local.max.z},
};
for (int i = 0; i < 9; ++i) {
vec3 world_probe =
(model_a * vec4(probes[i].x, probes[i].y, probes[i].z, 1.0f)).xyz();
float d = sample_sdf(b, world_probe);
if (d < 0.0f) {
// Collision detected!
float penetration = -d;
// Calculate normal via gradient of b's SDF
auto b_sdf = [this, &b](vec3 p) { return sample_sdf(b, p); };
vec3 normal = sdf::calc_normal(world_probe, b_sdf);
// Resolution
if (!a.is_static) {
// Positional correction
a.position += normal * penetration;
// Velocity response
float v_dot_n = vec3::dot(a.velocity, normal);
if (v_dot_n < 0) {
a.velocity -= normal * (1.0f + a.restitution) * v_dot_n;
}
}
}
}
}
void PhysicsSystem::update(Scene& scene, float dt) {
if (dt <= 0)
return;
// 1. Integration
for (auto& obj : scene.objects) {
if (obj.is_static)
continue;
obj.velocity += gravity * dt;
obj.position += obj.velocity * dt;
}
// 2. Broad Phase
BVH bvh;
BVHBuilder::build(bvh, scene.objects);
// 3. Narrow Phase & Resolution
// We do multiple iterations for better stability? Just 1 for now.
for (int iter = 0; iter < 2; ++iter) {
for (int i = 0; i < (int)scene.objects.size(); ++i) {
Object3D& a = scene.objects[i];
if (a.is_static)
continue;
AABB query_box = get_world_aabb(a);
std::vector<int> candidates;
bvh.query(query_box, candidates);
for (int cand_idx : candidates) {
if (cand_idx == i)
continue;
resolve_collision(a, scene.objects[cand_idx]);
}
}
}
}
|
