[WIP] Fix SDF behavior of ppsci.geometry.Mesh and SDFMesh

[Copilot]

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Create a comprehensive, regression-tested fix for the SDF behavior of ppsci.geometry.Mesh / SDFMesh, taking PR #1263 as the starting point but addressing hidden correctness problems rather than copying it blindly.

Context

PR #1263 ([BUG]fix bugs in make_sdf function) correctly identifies that make_sdf(vectors) currently derives its normalization origin and scale from the query batch. This makes the result dependent on which points are evaluated together. SDFMesh.random_points() calls is_inside() repeatedly on individual batches, then sample_interior() evaluates SDF again over the assembled sample; near the surface, numerical differences can therefore make accepted interior points yield positive signed distance / negative sdf weights after the framework negates SDF.

The current problematic implementation is in ppsci/geometry/mesh.py, make_sdf near the bottom of the file. Relevant consumers include:

• SDFMesh.from_stl, translate, and scale, which construct an SDF closure with make_sdf.
• SDFMesh.is_inside, which relies on self.sdf_func(x) < 0.
• SDFMesh.sample_interior, which negates SDF to create positive weights and optionally returns derivatives.
• Boolean operations (union, difference, intersection), which compose SDF closures and gradients.

Required implementation goals

1. Make SDF normalization invariant to query batching:

   • Calculate and capture mesh-derived normalization values once when make_sdf(vectors) is created.
   • Apply exactly the same fixed affine transform to every query point.
   • Preserve physical distance units by rescaling returned SDF values to the original coordinate scale.
   • Handle degenerate geometry safely: do not divide by zero if the mesh has zero extent. Prefer a clear ValueError at construction time, unless the repository’s established behavior/tests justify another approach.

2. Preserve the actual signed-distance/gradient contract:

   • Confirm the expected input and return types of ppsci.geometry.sdf.signed_distance_field; do not introduce list conversions unless they are required by the checked-in implementation/API.
   • With compute_sdf_derivatives=True, calculate a finite, correctly oriented unit gradient in original/world coordinate space from query point and closest/hit point.
   • Avoid NaN/Inf on points exactly on the surface. Define and test the chosen behavior (for example zero gradient for zero distance), and ensure it is consistent with the existing sample_interior negation convention.
   • Do not mix normalized flattened point coordinates with hit points when computing gradients.

3. Ensure behavior is compatible with transforms and CSG:

   • Validate SDF sign/distance and batch invariance for a simple watertight mesh (e.g. cube/tetrahedron) constructed in tests without external STL files where feasible.
   • Validate that translated and uniformly scaled SDFMesh instances still have correct SDF signs and distance scaling.
   • Validate at least one composed SDF operation if it can be tested without fragile third-party dependencies.

4. Add focused regression tests:

   • A point evaluated alone, in one batch, and as part of a larger/differently distributed batch must return equal SDF (within numerical tolerance).
   • Points accepted by SDFMesh.random_points / returned by sample_interior must not produce materially negative final "sdf" weights. Use an appropriate small numerical tolerance near the boundary, rather than asserting exact non-negativity if the SDF backend has floating-point noise.
   • Test gradient finiteness and orientation if SDF backend functionality supports hit points in the test environment.
   • Tests should be deterministic and avoid adding heavyweight optional dependencies where possible. Follow the project’s existing test layout/conventions; if SDF dependencies are optional, use existing skip patterns or isolate pure helper logic suitably.

5. Maintain project style and public API compatibility. Update docstrings/comments only where necessary to clarify the fixed-coordinate normalization and derivative convention.

Review notes / likely hidden issues to specifically investigate

• PR [BUG]fix bugs in make_sdf function #1263 changes the gradient calculation from an opaque expression to pts - hit_points. Verify orientation rather than assuming it: SDFMesh.sample_interior separately negates derivatives, and the sign must agree with that contract.
• The PR’s conversion of mesh vertices / points to list[tuple] may be unnecessary or may degrade performance/API compatibility; use the type expected by the local SDF wrapper.
• The PR’s norms[norms < 1e-6] = 1.0 avoids division by zero but leaves the original nonzero vector divided by 1 for near-surface values; choose behavior intentionally and test it.
• Mesh vertex arrays may contain repeated vertices; this must not affect normalization or SDF triangle indexing.

Validation

Run the narrow added/affected tests and any relevant formatting/lint checks available in the repository. In the PR description, clearly state the original batch-dependent normalization defect, the additional edge cases fixed, and tests executed.

The following is the prior conversation context from the user's chat exploration (may be truncated):

User: 请帮忙判断下这个修复是否是合理的

Assistant: 我来帮你审查这个PR的合理性。首先让我查看一下PR的具体改动内容。

Assistant: Let me fetch the actual changes from the PR:

Assistant: 现在让我查看 sample_interior 函数的实现，以及 SDF 的使用方式：

User: 请你继续

Assistant: 现在我已经理解了这个修复的核心问题。让我详细分析：

问题分析

修复是合理的 ✅

这个修复针对的是 make_sdf 函数中的一个精度一致性问题，修复思路正确。

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问题根源

旧代码的缺陷（第 1362-1404 行，main 分支）

def make_sdf(vectors: np.ndarray):
    def sdf_func(points: np.ndarray, compute_sdf_derivatives=False):
        # ❌ 问题：根据每批采样点动态调整边界
        points = points.copy()
        x_min, y_min, z_min = np.min(points, axis=0)  # 基于输入点
        x_max, y_max, z_max = np.max(points, axis=0)
        max_dis = max(max((x_max - x_min), (y_max - y_min)), (z_max - z_min))
        
        # 同时调整三角形和点
        store_triangles = vectors.copy()
        store_triangles[:, :, 0] -= x_min
        # ... 其他调整

核心问题：

1. 每次调用 sdf_func(points) 时，归一化的参考坐标系都可能不同
2. 某个内部点在一批数据中被判定为内部（sdf < 0）
3. 但在另一批数据中可能被判定为外部（sdf > 0），因为归一化边界不同
4. 这导致同一点的 SDF 值符号可能反转，内部约束损失出现负数

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新代码的修复（PR 改动）

def make_sdf(vectors: np.ndarray):
    # ✅ 在创建 sdf_func 闭包时，就固定好几何的边界
    verts = vectors.reshape(-1, 3)
    v_min = verts.min(axis=0)
    v_max = verts.max(axis=0)
    max_dis = np.max(v_max - v_min)
    norm_mesh = (verts - v_min) / max_dis
    
    def sdf_func(points: np.ndarray, compute_sdf_derivatives=False):
        # ✅ 使用固定的网格和归一化参数
        pts = (points - v_min) / max_dis  # 使用原始几何的边界
        # ...

优势：

• 所有采样点都基于原始几何的边界进行归一化
• 保证一致性：同一点的 SDF 值永远不变
• 解决内部点判定不一致的问题

---

代码质量评估

优点 ✅

1. 逻辑清晰：将归一化从动态计算改为静态预计算
2. 修复准确：直击问题根源
3. 代码简化：移除了冗余的 copy 和动态计算，性能更优

需要注意的地方 ⚠️

在 PR 的梯度计算部分有改动：

旧代码（第 1393-1399 行）：

sdf_derives = sdf_derives.numpy().reshape(-1)
sdf_derives = -(sdf_derives - points)  # ← 这里的逻辑有问题
sdf_derives = np.reshape(sdf_derives, (sdf_derives.shape[0] // 3, 3))
sdf_derives = sdf_derives / np.linalg.norm(sdf_derives, axis=1, keepdims=True)

新代码（PR 改动）：

hit_points = hit_points.numpy().reshape(-1, 3)
grad_vec = pts - hit_points  # ✅ 更清晰：点到最近表面点的向量
norms = np.linalg.norm(grad_vec, axis=1, keepdims=True)
norms[norms < 1e-6] = 1.0  # ✅ 处理数值稳定性
grad = grad_vec / norms

这部分改动：

• 更正确：使用 hit_points 而不是复杂的减法
• 更稳定：处理了零向量的情况（norms < 1e-6）
• 更清晰：梯度的几何意义更明显

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建议

✅ 这个修复应该被合并

但建议检查以下几点：

1. 测试覆盖：确保有单元测试验证

   • 相同点多次计算 SDF 结果一致
   • 内部点的 SDF 值始终为负
   • 外部点的 SDF 值始终为正

2. 梯度计算验证：确认数值梯度与 SDF 梯度的对应关系

3. 向后兼容：检查是否有其他代码依赖旧的动态边界行为

这是一个有必要的 bug 修复，核心思想是用一致的参考坐标系替代动态变化的参考坐标系。

User: 这个PR本身是否有其他隐蔽的问题

User: 请你基于这个PR和上述判断，帮我重新提交一个PR，彻底修复下Mesh类存在的问题

Assistant: 我已经准备好创建一个新的 PR（基于 develop），包含对 SDFMesh 批处理无关 SDF、零尺度网格、梯度方向/零距离稳定性，以及回归测试的完整修复；目前正在等待你确认启动该代码修改任务。

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