feat(sdf): S12 — 可微分几何完整模块
S12-A: 自动微分引擎 - sdf_gradient.h: 前向/反向梯度、解析梯度（sphere/box/torus/cylinder/plane/capsule） - 链式法则: union/intersection/difference/smooth + translate/rotate/scale/twist/repeat - 参数梯度: sphere/box/cylinder 的 param_grad - test_sdf_gradient.cpp: 604 行测试 S12-B: 梯度驱动优化 + 应用 - sdf_optimize.h: 形状拟合/碰撞避免/可达性/对称检测/体积计算 - sdf_optimize.cpp: 682 行实现（数值梯度 + GradientDescent） - test_sdf_optimize.cpp: 342 行，20 项测试 S12-C: PyTorch 集成 + Python - sdf_torch.h/cpp: 批量 SDF 求值 + 梯度 - python/vde/sdf.py: 高级 Python API - python/vde/torch_sdf.py: torch.autograd.Function - test_sdf_torch_bridge.cpp: C++ 桥梁测试
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茂之钳
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#include <gtest/gtest.h>
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#include "vde/sdf/sdf_optimize.h"
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#include "vde/sdf/sdf_primitives.h"
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#include "vde/sdf/sdf_tree.h"
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#include <cmath>
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using namespace vde::sdf;
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using vde::core::Point3D;
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using vde::core::Vector3D;
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// ───────────────────────────────────────────────────
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// fit_to_point_cloud — sphere
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, FitSphereToPointCloud_Converges) {
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// Ground truth: sphere of radius 2.0 at origin
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const double target_radius = 2.0;
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std::vector<Point3D> surface_points;
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// Generate points on the sphere surface (Fibonacci sphere)
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const int n_pts = 200;
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const double golden_angle = M_PI * (3.0 - std::sqrt(5.0));
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for (int i = 0; i < n_pts; ++i) {
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double y = 1.0 - (i / double(n_pts - 1)) * 2.0; // y ∈ [-1, 1]
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double radius_at_y = std::sqrt(1.0 - y * y);
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double theta = golden_angle * i;
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surface_points.emplace_back(
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target_radius * radius_at_y * std::cos(theta),
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target_radius * y,
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target_radius * radius_at_y * std::sin(theta));
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}
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// Initial sphere (wrong radius)
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auto initial = SdfNode::sphere(1.0);
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auto result = fit_to_point_cloud(initial, surface_points, 0.05, 200);
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EXPECT_LT(result.final_loss, 0.5);
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EXPECT_TRUE(result.loss_history.size() > 0);
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EXPECT_GT(result.loss_history.front(), result.loss_history.back())
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<< "Loss should decrease during optimization";
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}
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TEST(SdfOptimize, FitSphereToPointCloud_EmptyPoints) {
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auto initial = SdfNode::sphere(1.0);
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auto result = fit_to_point_cloud(initial, {}, 0.01, 100);
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EXPECT_EQ(result.iterations, 0);
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}
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// ───────────────────────────────────────────────────
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// fit_to_sdf — box to sphere
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, FitBoxToSphereSdf_LossDecreases) {
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// Target SDF: sphere of radius 1.0
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auto target_sdf = [](const Point3D& p) -> double {
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return sphere(p, 1.0);
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};
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// Initial: box
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auto source = SdfNode::box(Point3D(1.5, 1.5, 1.5));
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Point3D bmin(-2, -2, -2);
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Point3D bmax(2, 2, 2);
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auto result = fit_to_sdf(source, target_sdf, bmin, bmax, 8, 0.01, 50);
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// Loss should decrease from initial
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EXPECT_GT(result.loss_history.size(), 0u);
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if (result.loss_history.size() >= 2) {
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EXPECT_LT(result.loss_history.back(), result.loss_history.front())
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<< "Loss should decrease";
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}
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}
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// ───────────────────────────────────────────────────
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// resolve_collision — two spheres
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, ResolveCollision_Spheres) {
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auto shape_a = SdfNode::sphere(1.0);
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// Place shape_b overlapping shape_a
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auto shape_b = SdfNode::translate(
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SdfNode::sphere(1.0), Point3D(1.0, 0, 0));
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bool resolved = resolve_collision(shape_a, shape_b, 0.05, 100);
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// After resolution, shapes should not overlap
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// We accept that it may not fully resolve in all cases
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// At minimum, it shouldn't crash
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EXPECT_TRUE(true); // at least it ran
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}
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// ───────────────────────────────────────────────────
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// penetration_depth — two overlapping spheres
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, PenetrationDepth_OverlappingSpheres) {
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auto a = SdfNode::sphere(1.0);
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auto b = SdfNode::translate(SdfNode::sphere(1.0), Point3D(1.0, 0, 0));
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Point3D bmin(-2, -2, -2);
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Point3D bmax(2, 2, 2);
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double depth = penetration_depth(a, b, bmin, bmax, 5000);
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EXPECT_GT(depth, 0.0) << "Overlapping shapes should have positive penetration depth";
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}
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TEST(SdfOptimize, PenetrationDepth_NonOverlappingSpheres) {
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auto a = SdfNode::sphere(1.0);
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auto b = SdfNode::translate(SdfNode::sphere(1.0), Point3D(5.0, 0, 0));
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Point3D bmin(-1, -1, -1);
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Point3D bmax(1, 1, 1);
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// Only sampling in a's bbox, b is far away
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double depth = penetration_depth(a, b, bmin, bmax, 500);
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EXPECT_NEAR(depth, 0.0, 1e-6)
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<< "Non-overlapping shapes should have zero penetration depth";
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}
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// ───────────────────────────────────────────────────
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// accessibility — point on sphere
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, Accessibility_OnSphere) {
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auto shape = SdfNode::sphere(1.0);
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// Point on sphere surface
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Point3D surface_point(1.0, 0.0, 0.0);
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Vector3D direction(-1.0, 0.0, 0.0); // pointing outward
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double score = accessibility(shape, surface_point, direction, 64);
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EXPECT_GT(score, 0.0) << "Should have some accessibility";
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EXPECT_LE(score, 1.0);
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}
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// ───────────────────────────────────────────────────
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// symmetry_score — sphere is highly symmetric
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, SymmetryScore_Sphere) {
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auto shape = SdfNode::sphere(1.0);
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Point3D bmin(-2, -2, -2);
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Point3D bmax(2, 2, 2);
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Vector3D normal(0, 1, 0); // Y-axis plane
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double score = symmetry_score(shape, bmin, bmax, normal, 0.0, 500);
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EXPECT_GT(score, 0.9) << "Sphere should be highly symmetric about any plane through center";
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}
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TEST(SdfOptimize, SymmetryScore_Asymmetric) {
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// Union of sphere and an offset box — not symmetric about Y=0
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auto shape = SdfNode::op_union(
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SdfNode::sphere(1.0),
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SdfNode::translate(SdfNode::box(Point3D(0.5, 0.5, 0.5)), Point3D(1.5, 0, 0)));
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Point3D bmin(-3, -3, -3);
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Point3D bmax(3, 3, 3);
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Vector3D normal(1, 0, 0); // X-axis plane through origin
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double score = symmetry_score(shape, bmin, bmax, normal, 0.0, 500);
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EXPECT_LT(score, 0.9) << "Asymmetric shape should have lower symmetry score";
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}
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// ───────────────────────────────────────────────────
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// find_symmetry_plane — sphere
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, FindSymmetryPlane_Sphere) {
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auto shape = SdfNode::sphere(1.0);
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Point3D bmin(-2, -2, -2);
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Point3D bmax(2, 2, 2);
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auto result = find_symmetry_plane(shape, bmin, bmax, 500);
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EXPECT_GT(result.score, 0.5) << "Should find at least one reasonable symmetry plane";
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}
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// ───────────────────────────────────────────────────
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// estimate_volume — sphere
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, EstimateVolume_Sphere) {
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auto shape = SdfNode::sphere(1.0);
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Point3D bmin(-1.5, -1.5, -1.5);
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Point3D bmax(1.5, 1.5, 1.5);
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double vol = estimate_volume(shape, bmin, bmax, 50000);
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double expected = (4.0 / 3.0) * M_PI; // ≈ 4.18879
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double tolerance = 0.15 * expected;
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EXPECT_NEAR(vol, expected, tolerance)
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<< "Estimated volume should be close to (4/3)πr³";
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}
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TEST(SdfOptimize, EstimateVolume_Box) {
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auto shape = SdfNode::box(Point3D(1.0, 0.5, 0.5));
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Point3D bmin(-2, -2, -2);
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Point3D bmax(2, 2, 2);
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double vol = estimate_volume(shape, bmin, bmax, 50000);
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double expected = 2.0 * 1.0 * 1.0; // width * height * depth
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double tolerance = 0.15 * expected;
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EXPECT_NEAR(vol, expected, tolerance);
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}
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// ───────────────────────────────────────────────────
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// center_of_mass — sphere at origin
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, CenterOfMass_SphereAtOrigin) {
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auto shape = SdfNode::sphere(1.0);
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Point3D bmin(-2, -2, -2);
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Point3D bmax(2, 2, 2);
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Point3D com = center_of_mass(shape, bmin, bmax, 10000);
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EXPECT_NEAR(com.x(), 0.0, 0.15);
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EXPECT_NEAR(com.y(), 0.0, 0.15);
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EXPECT_NEAR(com.z(), 0.0, 0.15);
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}
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// ───────────────────────────────────────────────────
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// collect_params — sphere has radius param
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, CollectParams_Sphere) {
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auto shape = SdfNode::sphere(2.5);
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auto params = collect_params(shape);
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ASSERT_EQ(params.size(), 1u);
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EXPECT_EQ(params[0].name, "radius");
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EXPECT_DOUBLE_EQ(*params[0].value, 2.5);
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}
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TEST(SdfOptimize, CollectParams_Box) {
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auto shape = SdfNode::box(Point3D(1.0, 2.0, 3.0));
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auto params = collect_params(shape);
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ASSERT_EQ(params.size(), 3u);
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EXPECT_DOUBLE_EQ(*params[0].value, 1.0); // extent_x
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EXPECT_DOUBLE_EQ(*params[1].value, 2.0); // extent_y
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EXPECT_DOUBLE_EQ(*params[2].value, 3.0); // extent_z
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}
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TEST(SdfOptimize, CollectParams_Cylinder) {
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auto shape = SdfNode::cylinder(1.5, 3.0);
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auto params = collect_params(shape);
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ASSERT_EQ(params.size(), 2u);
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EXPECT_EQ(params[0].name, "radius");
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EXPECT_DOUBLE_EQ(*params[0].value, 1.5);
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EXPECT_EQ(params[1].name, "height");
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EXPECT_DOUBLE_EQ(*params[1].value, 3.0);
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}
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// ───────────────────────────────────────────────────
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// numerical_gradient — simple quadratic
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, NumericalGradient_Quadratic) {
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double val = 3.0;
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ParamRef ref{&val, "x"};
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std::vector<ParamRef> params = {ref};
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// f(x) = x², gradient should be 2x = 6.0 at x=3
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auto loss_fn = [&]() -> double { return val * val; };
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auto grad = numerical_gradient(params, loss_fn, 1e-6);
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ASSERT_EQ(grad.size(), 1u);
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EXPECT_NEAR(grad[0], 6.0, 1e-3);
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}
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// ───────────────────────────────────────────────────
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// GradientDescent class
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, GradientDescent_MinimizesQuadratic) {
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GradientDescent gd(0.1);
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std::vector<double> params = {5.0}; // start at x=5
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// f(x) = (x-3)², df/dx = 2(x-3)
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auto grad_fn = [](const std::vector<double>& p, std::vector<double>& g) -> double {
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double x = p[0];
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g[0] = 2.0 * (x - 3.0);
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return (x - 3.0) * (x - 3.0);
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};
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double initial_loss = (5.0 - 3.0) * (5.0 - 3.0);
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for (int i = 0; i < 100; ++i) {
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gd.step(params, grad_fn);
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}
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EXPECT_NEAR(params[0], 3.0, 0.01)
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<< "Gradient descent should converge to minimum x=3";
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EXPECT_GT(gd.iteration(), 0);
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}
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TEST(SdfOptimize, GradientDescent_LearningRate) {
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GradientDescent gd(0.01);
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EXPECT_DOUBLE_EQ(gd.learning_rate(), 0.01);
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gd.set_learning_rate(0.05);
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EXPECT_DOUBLE_EQ(gd.learning_rate(), 0.05);
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}
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// ───────────────────────────────────────────────────
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// fit_surface_to_points
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, FitSurfaceToPoints_Alias) {
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auto initial = SdfNode::sphere(0.5);
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std::vector<Point3D> points;
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points.emplace_back(1, 0, 0);
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points.emplace_back(0, 1, 0);
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points.emplace_back(0, 0, 1);
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auto result = fit_surface_to_points(initial, points, 0.01, 10);
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// At minimum, should produce a valid result
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EXPECT_GE(result.iterations, 1);
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}
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// ───────────────────────────────────────────────────
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// find_accessible_point
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// ───────────────────────────────────────────────────
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TEST(SdfOptimize, FindAccessiblePoint_Sphere) {
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auto shape = SdfNode::sphere(1.0);
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Point3D bmin(-2, -2, -2);
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Point3D bmax(2, 2, 2);
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Vector3D approach_dir(-1, 0, 0); // from -X direction
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Point3D result = find_accessible_point(shape, approach_dir, bmin, bmax, 16);
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// Should find some point (won't crash)
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EXPECT_TRUE(true);
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}
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