fix small face issue for ptmeshdist

Summary:
Fix small face issue for point_mesh distance computation.

The issue lies in the computation of `IsInsideTriangle` which is unstable and non-symmetrical when faces with small areas are given as input. This diff fixes the issue by returning `False` for `IsInsideTriangle` when small faces are given as input.

Reviewed By: bottler

Differential Revision: D29163052

fbshipit-source-id: be297002f26b5e6eded9394fde00553a37406bee
This commit is contained in:
Georgia Gkioxari 2021-06-18 09:29:01 -07:00 committed by Facebook GitHub Bot
parent a343cf534c
commit 88f5d79088
3 changed files with 93 additions and 11 deletions

View File

@ -461,6 +461,27 @@ PointTriangleDistanceBackward(
// vec3 utils //
// ************************************************************* //
// Computes the area of a triangle (v0, v1, v2).
//
// Args:
// v0, v1, v2: vec3 coordinates of the triangle vertices
//
// Returns
// area: float: The area of the triangle
//
__device__ inline float
AreaOfTriangle(const float3& v0, const float3& v1, const float3& v2) {
float3 p0 = v1 - v0;
float3 p1 = v2 - v0;
// compute the hypotenus of the scross product (p0 x p1)
float dd = hypot(
p0.y * p1.z - p0.z * p1.y,
hypot(p0.z * p1.x - p0.x * p1.z, p0.x * p1.y - p0.y * p1.x));
return dd / 2.0;
}
// Computes the barycentric coordinates of a point p relative
// to a triangle (v0, v1, v2), i.e. p = w0 * v0 + w1 * v1 + w2 * v2
// s.t. w0 + w1 + w2 = 1.0
@ -503,6 +524,7 @@ __device__ inline float3 BarycentricCoords3Forward(
// Checks whether the point p is inside the triangle (v0, v1, v2).
// A point is inside the triangle, if all barycentric coordinates
// wrt the triangle are >= 0 & <= 1.
// If the triangle is degenerate, aka line or point, then return False.
//
// NOTE that this function assumes that p lives on the space spanned
// by (v0, v1, v2).
@ -521,11 +543,16 @@ __device__ inline bool IsInsideTriangle(
const float3& v0,
const float3& v1,
const float3& v2) {
float3 bary = BarycentricCoords3Forward(p, v0, v1, v2);
bool x_in = 0.0f <= bary.x && bary.x <= 1.0f;
bool y_in = 0.0f <= bary.y && bary.y <= 1.0f;
bool z_in = 0.0f <= bary.z && bary.z <= 1.0f;
bool inside = x_in && y_in && z_in;
bool inside;
if (AreaOfTriangle(v0, v1, v2) < 1e-5) {
inside = 0;
} else {
float3 bary = BarycentricCoords3Forward(p, v0, v1, v2);
bool x_in = 0.0f <= bary.x && bary.x <= 1.0f;
bool y_in = 0.0f <= bary.y && bary.y <= 1.0f;
bool z_in = 0.0f <= bary.z && bary.z <= 1.0f;
inside = x_in && y_in && z_in;
}
return inside;
}

View File

@ -560,6 +560,26 @@ PointTriangleDistanceBackward(
return std::make_tuple(grad_p, grad_v0, grad_v1, grad_v2);
}
// Computes the area of a triangle (v0, v1, v2).
// Args:
// v0, v1, v2: vec3 coordinates of the triangle vertices
//
// Returns:
// area: float: the area of the triangle
//
template <typename T>
T AreaOfTriangle(const vec3<T>& v0, const vec3<T>& v1, const vec3<T>& v2) {
vec3<T> p0 = v1 - v0;
vec3<T> p1 = v2 - v0;
// compute the hypotenus of the scross product (p0 x p1)
float dd = std::hypot(
p0.y * p1.z - p0.z * p1.y,
std::hypot(p0.z * p1.x - p0.x * p1.z, p0.x * p1.y - p0.y * p1.x));
return dd / 2.0;
}
// Computes the squared distance of a point p relative to a triangle (v0, v1,
// v2). If the point's projection p0 on the plane spanned by (v0, v1, v2) is
// inside the triangle with vertices (v0, v1, v2), then the returned value is
@ -604,6 +624,7 @@ vec3<T> BarycentricCoords3Forward(
// Checks whether the point p is inside the triangle (v0, v1, v2).
// A point is inside the triangle, if all barycentric coordinates
// wrt the triangle are >= 0 & <= 1.
// If the triangle is degenerate, aka line or point, then return False.
//
// NOTE that this function assumes that p lives on the space spanned
// by (v0, v1, v2).
@ -623,11 +644,16 @@ static bool IsInsideTriangle(
const vec3<T>& v0,
const vec3<T>& v1,
const vec3<T>& v2) {
vec3<T> bary = BarycentricCoords3Forward(p, v0, v1, v2);
bool x_in = 0.0f <= bary.x && bary.x <= 1.0f;
bool y_in = 0.0f <= bary.y && bary.y <= 1.0f;
bool z_in = 0.0f <= bary.z && bary.z <= 1.0f;
bool inside = x_in && y_in && z_in;
bool inside;
if (AreaOfTriangle(v0, v1, v2) < 1e-5) {
inside = 0;
} else {
vec3<T> bary = BarycentricCoords3Forward(p, v0, v1, v2);
bool x_in = 0.0f <= bary.x && bary.x <= 1.0f;
bool y_in = 0.0f <= bary.y && bary.y <= 1.0f;
bool z_in = 0.0f <= bary.z && bary.z <= 1.0f;
inside = x_in && y_in && z_in;
}
return inside;
}

View File

@ -96,7 +96,7 @@ class TestPointMeshDistance(TestCaseMixin, unittest.TestCase):
d20 = v2.dot(v0)
d21 = v2.dot(v1)
denom = d00 * d11 - d01 * d01
denom = d00 * d11 - d01 * d01 + TestPointMeshDistance.eps()
s2 = (d11 * d20 - d01 * d21) / denom
s3 = (d00 * d21 - d01 * d20) / denom
s1 = 1.0 - s2 - s3
@ -117,6 +117,13 @@ class TestPointMeshDistance(TestCaseMixin, unittest.TestCase):
Returns:
inside: BoolTensor of shape (1)
"""
v0 = tri[1] - tri[0]
v1 = tri[2] - tri[0]
area = torch.cross(v0, v1).norm() / 2.0
# check if triangle is a line or a point. In that case, return False
if area < 1e-5:
return False
bary = TestPointMeshDistance._point_to_bary(point, tri)
inside = ((bary >= 0.0) * (bary <= 1.0)).all()
return inside
@ -836,6 +843,28 @@ class TestPointMeshDistance(TestCaseMixin, unittest.TestCase):
)
self.assertClose(pcls.points_list()[i].grad, pcls_op.points_list()[i].grad)
def test_small_faces_case(self):
for device in [torch.device("cpu"), torch.device("cuda:0")]:
mesh_vertices = torch.tensor(
[
[-0.0021, -0.3769, 0.7146],
[-0.0161, -0.3771, 0.7146],
[-0.0021, -0.3771, 0.7147],
],
dtype=torch.float32,
device=device,
)
mesh1_faces = torch.tensor([[0, 2, 1]], device=device)
mesh2_faces = torch.tensor([[2, 0, 1]], device=device)
pcd_points = torch.tensor([[-0.3623, -0.5340, 0.7727]], device=device)
mesh1 = Meshes(verts=[mesh_vertices], faces=[mesh1_faces])
mesh2 = Meshes(verts=[mesh_vertices], faces=[mesh2_faces])
pcd = Pointclouds(points=[pcd_points])
loss1 = point_mesh_face_distance(mesh1, pcd)
loss2 = point_mesh_face_distance(mesh2, pcd)
self.assertClose(loss1, loss2)
@staticmethod
def point_mesh_edge(N: int, V: int, F: int, P: int, device: str):
device = torch.device(device)