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eps fix for iou3d
Summary: Fix EPS issue that causes numerical instabilities when boxes are very close Reviewed By: kjchalup Differential Revision: D38661465 fbshipit-source-id: d2b6753cba9dc2f0072ace5289c9aa815a1a29f6
This commit is contained in:
Georgia Gkioxari
Facebook GitHub Bot
parent
06cbba2628
commit
1bfe6bf20a
@ -88,9 +88,9 @@ __global__ void IoUBox3DKernel(
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for (int b1 = 0; b1 < box1_count; ++b1) {
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for (int b2 = 0; b2 < box2_count; ++b2) {
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const bool is_coplanar =
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IsCoplanarFace(box1_intersect[b1], box2_intersect[b2]);
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IsCoplanarTriTri(box1_intersect[b1], box2_intersect[b2]);
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const float area = FaceArea(box1_intersect[b1]);
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if ((is_coplanar) && (area > kEpsilon)) {
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if ((is_coplanar) && (area > aEpsilon)) {
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tri2_keep[b2].keep = false;
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}
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}
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@ -80,9 +80,9 @@ std::tuple<at::Tensor, at::Tensor> IoUBox3DCpu(
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for (int b1 = 0; b1 < box1_intersect.size(); ++b1) {
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for (int b2 = 0; b2 < box2_intersect.size(); ++b2) {
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const bool is_coplanar =
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IsCoplanarFace(box1_intersect[b1], box2_intersect[b2]);
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IsCoplanarTriTri(box1_intersect[b1], box2_intersect[b2]);
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const float area = FaceArea(box1_intersect[b1]);
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if ((is_coplanar) && (area > kEpsilon)) {
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if ((is_coplanar) && (area > aEpsilon)) {
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tri2_keep[b2] = 0;
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}
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}
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@ -12,7 +12,15 @@
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#include <cstdio>
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#include "utils/float_math.cuh"
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__constant__ const float kEpsilon = 1e-5;
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// dEpsilon: Used in dot products and is used to assess whether two unit vectors
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// are orthogonal (or coplanar). It's an epsilon on cos(θ).
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// With dEpsilon = 0.001, two unit vectors are considered co-planar
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// if their θ = 2.5 deg.
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__constant__ const float dEpsilon = 1e-3;
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// aEpsilon: Used once in main function to check for small face areas
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__constant__ const float aEpsilon = 1e-4;
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// kEpsilon: Used only for norm(u) = u/max(||u||, kEpsilon)
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__constant__ const float kEpsilon = 1e-8;
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/*
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_PLANES and _TRIS define the 4- and 3-connectivity
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@ -120,10 +128,37 @@ __device__ inline void GetBoxPlanes(
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}
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}
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// The normal of the face defined by vertices (v0, v1, v2)
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// Define e0 to be the edge connecting (v1, v0)
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// Define e1 to be the edge connecting (v2, v0)
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// normal is the cross product of e0, e1
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// The normal of a plane spanned by vectors e0 and e1
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//
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// Args
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// e0, e1: float3 vectors defining a plane
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//
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// Returns
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// float3: normal of the plane
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//
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__device__ inline float3 GetNormal(const float3 e0, const float3 e1) {
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float3 n = cross(e0, e1);
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n = n / std::fmaxf(norm(n), kEpsilon);
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return n;
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}
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// The center of a triangle defined by vertices (v0, v1, v2)
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//
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// Args
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// v0, v1, v2: float3 coordinates of the vertices of the triangle
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//
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// Returns
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// float3: center of the triangle
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//
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__device__ inline float3
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TriCenter(const float3 v0, const float3 v1, const float3 v2) {
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float3 ctr = (v0 + v1 + v2) / 3.0f;
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return ctr;
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}
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// The normal of the triangle defined by vertices (v0, v1, v2)
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// We find the "best" edges connecting the face center to the vertices,
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// such that the cross product between the edges is maximized.
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//
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// Args
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// v0, v1, v2: float3 coordinates of the vertices of the face
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@ -132,9 +167,24 @@ __device__ inline void GetBoxPlanes(
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// float3: normal for the face
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//
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__device__ inline float3
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FaceNormal(const float3 v0, const float3 v1, const float3 v2) {
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float3 n = cross(v1 - v0, v2 - v0);
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n = n / fmaxf(norm(n), kEpsilon);
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TriNormal(const float3 v0, const float3 v1, const float3 v2) {
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const float3 ctr = TriCenter(v0, v1, v2);
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const float d01 = norm(cross(v0 - ctr, v1 - ctr));
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const float d02 = norm(cross(v0 - ctr, v2 - ctr));
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const float d12 = norm(cross(v1 - ctr, v2 - ctr));
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float3 n = GetNormal(v0 - ctr, v1 - ctr);
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float max_dist = d01;
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if (d02 > max_dist) {
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max_dist = d02;
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n = GetNormal(v0 - ctr, v2 - ctr);
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}
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if (d12 > max_dist) {
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n = GetNormal(v1 - ctr, v2 - ctr);
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}
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return n;
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}
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@ -158,8 +208,75 @@ __device__ inline float FaceArea(const FaceVerts& tri) {
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return norm(n) / 2.0;
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}
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// The normal of a box plane defined by the verts in `plane` with
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// the centroid of the box given by `center`.
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// The center of a plane defined by vertices (v0, v1, v2, v3)
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//
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// Args
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// v0, v1, v2, v3: float3 coordinates of the vertices of the plane
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//
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// Returns
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// float3: center of the plane
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//
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__device__ inline float3 PlaneCenter(
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const float3 v0,
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const float3 v1,
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const float3 v2,
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const float3 v3) {
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float3 ctr = (v0 + v1 + v2 + v3) / 4.0f;
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return ctr;
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}
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// The normal of a planar face with vertices (v0, v1, v2, v3)
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// We find the "best" edges connecting the face center to the vertices,
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// such that the cross product between the edges is maximized.
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//
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// Args
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// e0, e1: float3 coordinates of the vertices of the plane
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//
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// Returns
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// float3: center of the plane
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//
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__device__ inline float3 PlaneNormal(
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const float3 v0,
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const float3 v1,
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const float3 v2,
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const float3 v3) {
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const float3 ctr = PlaneCenter(v0, v1, v2, v3);
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const float d01 = norm(cross(v0 - ctr, v1 - ctr));
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const float d02 = norm(cross(v0 - ctr, v2 - ctr));
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const float d03 = norm(cross(v0 - ctr, v3 - ctr));
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const float d12 = norm(cross(v1 - ctr, v2 - ctr));
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const float d13 = norm(cross(v1 - ctr, v3 - ctr));
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const float d23 = norm(cross(v2 - ctr, v3 - ctr));
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float max_dist = d01;
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float3 n = GetNormal(v0 - ctr, v1 - ctr);
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if (d02 > max_dist) {
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max_dist = d02;
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n = GetNormal(v0 - ctr, v2 - ctr);
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}
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if (d03 > max_dist) {
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max_dist = d03;
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n = GetNormal(v0 - ctr, v3 - ctr);
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}
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if (d12 > max_dist) {
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max_dist = d12;
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n = GetNormal(v1 - ctr, v2 - ctr);
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}
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if (d13 > max_dist) {
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max_dist = d13;
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n = GetNormal(v1 - ctr, v3 - ctr);
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}
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if (d23 > max_dist) {
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n = GetNormal(v2 - ctr, v3 - ctr);
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}
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return n;
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}
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// The normal of a box plane defined by the verts in `plane` such that it
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// points toward the centroid of the box given by `center`.
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//
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// Args
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// plane: float3 coordinates of the vertices of the plane
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// center: float3 coordinates of the center of the box from
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@ -173,23 +290,30 @@ template <typename FaceVertsPlane>
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__device__ inline float3 PlaneNormalDirection(
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const FaceVertsPlane& plane,
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const float3& center) {
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// Only need the first 3 verts of the plane
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// The plane's vertices
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const float3 v0 = plane.v0;
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const float3 v1 = plane.v1;
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const float3 v2 = plane.v2;
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const float3 v3 = plane.v3;
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// We project the center on the plane defined by (v0, v1, v2)
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// We can write center = v0 + a * e0 + b * e1 + c * n
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// The plane's center
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const float3 plane_center = PlaneCenter(v0, v1, v2, v3);
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// The plane's normal
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float3 n = PlaneNormal(v0, v1, v2, v3);
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// We project the center on the plane defined by (v0, v1, v2, v3)
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// We can write center = plane_center + a * e0 + b * e1 + c * n
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// We know that <e0, n> = 0 and <e1, n> = 0 and
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// <a, b> is the dot product between a and b.
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// This means we can solve for c as:
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// c = <center - v0 - a * e0 - b * e1, n> = <center - v0, n>
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float3 n = FaceNormal(v0, v1, v2);
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const float c = dot((center - v0), n);
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// c = <center - plane_center - a * e0 - b * e1, n>
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// = <center - plane_center, n>
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const float c = dot((center - plane_center), n);
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// If c is negative, then we revert the direction of n such that n
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// points "inside"
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if (c < kEpsilon) {
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if (c < 0.0f) {
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n = -1.0f * n;
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}
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@ -318,16 +442,22 @@ __device__ inline float3 PolyhedronCenter(
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//
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__device__ inline bool
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IsInside(const FaceVerts& plane, const float3& normal, const float3& point) {
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// Get one vert of the plane
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// Vertices of the plane
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const float3 v0 = plane.v0;
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const float3 v1 = plane.v1;
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const float3 v2 = plane.v2;
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const float3 v3 = plane.v3;
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// Every point p can be written as p = v0 + a e0 + b e1 + c n
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// The center of the plane
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const float3 plane_ctr = PlaneCenter(v0, v1, v2, v3);
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// Every point p can be written as p = plane_ctr + a e0 + b e1 + c n
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// Solving for c:
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// c = (point - v0 - a * e0 - b * e1).dot(n)
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// c = (point - plane_ctr - a * e0 - b * e1).dot(n)
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// We know that <e0, n> = 0 and <e1, n> = 0
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// So the calculation can be simplified as:
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const float c = dot((point - v0), normal);
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const bool inside = c > -1.0f * kEpsilon;
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const float c = dot((point - plane_ctr), normal);
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const bool inside = c >= 0.0f;
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return inside;
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}
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@ -348,20 +478,150 @@ __device__ inline float3 PlaneEdgeIntersection(
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const float3& normal,
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const float3& p0,
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const float3& p1) {
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// Get one vert of the plane
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// Vertices of the plane
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const float3 v0 = plane.v0;
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const float3 v1 = plane.v1;
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const float3 v2 = plane.v2;
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const float3 v3 = plane.v3;
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// The center of the plane
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const float3 plane_ctr = PlaneCenter(v0, v1, v2, v3);
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// The point of intersection can be parametrized
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// p = p0 + a (p1 - p0) where a in [0, 1]
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// We want to find a such that p is on plane
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// <p - v0, n> = 0
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const float top = dot(-1.0f * (p0 - v0), normal);
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const float bot = dot(p1 - p0, normal);
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const float a = top / bot;
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const float3 p = p0 + a * (p1 - p0);
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// <p - plane_ctr, n> = 0
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float3 direc = p1 - p0;
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direc = direc / fmaxf(norm(direc), kEpsilon);
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float3 p = (p1 + p0) / 2.0f;
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if (abs(dot(direc, normal)) >= dEpsilon) {
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const float top = -1.0f * dot(p0 - plane_ctr, normal);
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const float bot = dot(p1 - p0, normal);
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const float a = top / bot;
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p = p0 + a * (p1 - p0);
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}
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return p;
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}
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// Compute the most distant points between two sets of vertices
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//
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// Args
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// verts1, verts2: list of float3 defining the list of vertices
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//
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// Returns
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// v1m, v2m: float3 vectors of the most distant points
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// in verts1 and verts2 respectively
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//
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__device__ inline std::tuple<float3, float3> ArgMaxVerts(
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std::initializer_list<float3> verts1,
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std::initializer_list<float3> verts2) {
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auto v1m = float3();
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auto v2m = float3();
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float maxdist = -1.0f;
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for (const auto& v1 : verts1) {
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for (const auto& v2 : verts2) {
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if (norm(v1 - v2) > maxdist) {
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v1m = v1;
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v2m = v2;
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maxdist = norm(v1 - v2);
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}
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}
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}
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return std::make_tuple(v1m, v2m);
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}
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// Compute a boolean indicator for whether or not two faces
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// are coplanar
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//
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// Args
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// tri1, tri2: FaceVerts struct of the vertex coordinates of
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// the triangle face
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//
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// Returns
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// bool: whether or not the two faces are coplanar
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//
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__device__ inline bool IsCoplanarTriTri(
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const FaceVerts& tri1,
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const FaceVerts& tri2) {
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// Get verts for face 1
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const float3 v0_1 = tri1.v0;
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const float3 v1_1 = tri1.v1;
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const float3 v2_1 = tri1.v2;
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const float3 tri1_ctr = TriCenter(v0_1, v1_1, v2_1);
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const float3 tri1_n = TriNormal(v0_1, v1_1, v2_1);
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// Get verts for face 2
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const float3 v0_2 = tri2.v0;
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const float3 v1_2 = tri2.v1;
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const float3 v2_2 = tri2.v2;
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const float3 tri2_ctr = TriCenter(v0_2, v1_2, v2_2);
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const float3 tri2_n = TriNormal(v0_2, v1_2, v2_2);
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// Check if parallel
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const bool check1 = abs(dot(tri1_n, tri2_n)) > 1 - dEpsilon;
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// Compute most distant points
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auto argvs =
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ArgMaxVerts({tri1.v0, tri1.v1, tri1.v2}, {tri2.v0, tri2.v1, tri2.v2});
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const float3 v1m = std::get<0>(argvs);
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const float3 v2m = std::get<1>(argvs);
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float3 n12m = v1m - v2m;
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n12m = n12m / fmaxf(norm(n12m), kEpsilon);
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const bool check2 = (abs(dot(n12m, tri1_n)) < dEpsilon) ||
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(abs(dot(n12m, tri2_n)) < dEpsilon);
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return (check1 && check2);
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}
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// Compute a boolean indicator for whether or not a triangular and a planar
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// face are coplanar
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//
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// Args
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// tri, plane: FaceVerts struct of the vertex coordinates of
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// the triangle and planar face
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// normal: the normal direction of the plane pointing "inside"
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//
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// Returns
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// bool: whether or not the two faces are coplanar
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//
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__device__ inline bool IsCoplanarTriPlane(
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const FaceVerts& tri,
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const FaceVerts& plane,
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const float3& normal) {
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// Get verts for tri
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const float3 v0t = tri.v0;
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const float3 v1t = tri.v1;
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const float3 v2t = tri.v2;
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const float3 tri_ctr = TriCenter(v0t, v1t, v2t);
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const float3 nt = TriNormal(v0t, v1t, v2t);
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// check if parallel
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const bool check1 = abs(dot(nt, normal)) > 1 - dEpsilon;
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// Compute most distant points
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auto argvs = ArgMaxVerts(
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{tri.v0, tri.v1, tri.v2}, {plane.v0, plane.v1, plane.v2, plane.v3});
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const float3 v1m = std::get<0>(argvs);
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const float3 v2m = std::get<1>(argvs);
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float3 n12m = v1m - v2m;
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n12m = n12m / fmaxf(norm(n12m), kEpsilon);
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const bool check2 = abs(dot(n12m, normal)) < dEpsilon;
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return (check1 && check2);
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}
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// Triangle is clipped into a quadrilateral
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// based on the intersection points with the plane.
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// Then the quadrilateral is divided into two triangles.
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@ -477,6 +737,14 @@ __device__ inline int ClipTriByPlane(
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const bool isin1 = IsInside(plane, normal, v1);
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const bool isin2 = IsInside(plane, normal, v2);
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// Check coplanar
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const bool iscoplanar = IsCoplanarTriPlane(tri, plane, normal);
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if (iscoplanar) {
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// Return input vertices
|
||||
face_verts_out[0] = {v0, v1, v2};
|
||||
return 1;
|
||||
}
|
||||
|
||||
// All in
|
||||
if (isin0 && isin1 && isin2) {
|
||||
// Return input vertices
|
||||
@ -515,40 +783,6 @@ __device__ inline int ClipTriByPlane(
|
||||
return 0;
|
||||
}
|
||||
|
||||
// Compute a boolean indicator for whether or not two faces
|
||||
// are coplanar
|
||||
//
|
||||
// Args
|
||||
// tri1, tri2: FaceVerts struct of the vertex coordinates of
|
||||
// the triangle face
|
||||
//
|
||||
// Returns
|
||||
// bool: whether or not the two faces are coplanar
|
||||
//
|
||||
__device__ inline bool IsCoplanarFace(
|
||||
const FaceVerts& tri1,
|
||||
const FaceVerts& tri2) {
|
||||
// Get verts for face 1
|
||||
const float3 v0 = tri1.v0;
|
||||
const float3 v1 = tri1.v1;
|
||||
const float3 v2 = tri1.v2;
|
||||
|
||||
const float3 n1 = FaceNormal(v0, v1, v2);
|
||||
int coplanar_count = 0;
|
||||
|
||||
// Check v0, v1, v2
|
||||
if (abs(dot(tri2.v0 - v0, n1)) < kEpsilon) {
|
||||
coplanar_count++;
|
||||
}
|
||||
if (abs(dot(tri2.v1 - v0, n1)) < kEpsilon) {
|
||||
coplanar_count++;
|
||||
}
|
||||
if (abs(dot(tri2.v2 - v0, n1)) < kEpsilon) {
|
||||
coplanar_count++;
|
||||
}
|
||||
return (coplanar_count == 3);
|
||||
}
|
||||
|
||||
// Get the triangles from each box which are part of the
|
||||
// intersecting polyhedron by computing the intersection
|
||||
// points with each of the planes.
|
||||
|
||||
@ -18,7 +18,15 @@
|
||||
#include <type_traits>
|
||||
#include "utils/vec3.h"
|
||||
|
||||
const auto kEpsilon = 1e-5;
|
||||
// dEpsilon: Used in dot products and is used to assess whether two unit vectors
|
||||
// are orthogonal (or coplanar). It's an epsilon on cos(θ).
|
||||
// With dEpsilon = 0.001, two unit vectors are considered co-planar
|
||||
// if their θ = 2.5 deg.
|
||||
const auto dEpsilon = 1e-3;
|
||||
// aEpsilon: Used once in main function to check for small face areas
|
||||
const auto aEpsilon = 1e-4;
|
||||
// kEpsilon: Used only for norm(u) = u/max(||u||, kEpsilon)
|
||||
const auto kEpsilon = 1e-8;
|
||||
|
||||
/*
|
||||
_PLANES and _TRIS define the 4- and 3-connectivity
|
||||
@ -129,20 +137,108 @@ inline face_verts GetBoxPlanes(const Box& box) {
|
||||
return box_planes;
|
||||
}
|
||||
|
||||
// The normal of the face defined by vertices (v0, v1, v2)
|
||||
// Define e0 to be the edge connecting (v1, v0)
|
||||
// Define e1 to be the edge connecting (v2, v0)
|
||||
// normal is the cross product of e0, e1
|
||||
// The normal of a plane spanned by vectors e0 and e1
|
||||
//
|
||||
// Args
|
||||
// v0, v1, v2: vec3 coordinates of the vertices of the face
|
||||
// e0, e1: vec3 vectors defining a plane
|
||||
//
|
||||
// Returns
|
||||
// vec3: normal of the plane
|
||||
//
|
||||
inline vec3<float> GetNormal(const vec3<float> e0, const vec3<float> e1) {
|
||||
vec3<float> n = cross(e0, e1);
|
||||
n = n / std::fmaxf(norm(n), kEpsilon);
|
||||
return n;
|
||||
}
|
||||
|
||||
// The center of a triangle tri
|
||||
//
|
||||
// Args
|
||||
// tri: vec3 coordinates of the vertices of the triangle
|
||||
//
|
||||
// Returns
|
||||
// vec3: center of the triangle
|
||||
//
|
||||
inline vec3<float> TriCenter(const std::vector<vec3<float>>& tri) {
|
||||
// Vertices of the triangle
|
||||
const vec3<float> v0 = tri[0];
|
||||
const vec3<float> v1 = tri[1];
|
||||
const vec3<float> v2 = tri[2];
|
||||
|
||||
return (v0 + v1 + v2) / 3.0f;
|
||||
}
|
||||
|
||||
// The normal of the triangle defined by vertices (v0, v1, v2)
|
||||
// We find the "best" edges connecting the face center to the vertices,
|
||||
// such that the cross product between the edges is maximized.
|
||||
//
|
||||
// Args
|
||||
// tri: vec3 coordinates of the vertices of the face
|
||||
//
|
||||
// Returns
|
||||
// vec3: normal for the face
|
||||
//
|
||||
inline vec3<float> FaceNormal(vec3<float> v0, vec3<float> v1, vec3<float> v2) {
|
||||
vec3<float> n = cross(v1 - v0, v2 - v0);
|
||||
n = n / std::fmaxf(norm(n), kEpsilon);
|
||||
inline vec3<float> TriNormal(const std::vector<vec3<float>>& tri) {
|
||||
// Get center of triangle
|
||||
const vec3<float> ctr = TriCenter(tri);
|
||||
|
||||
// find the "best" normal as cross product of edges from center
|
||||
float max_dist = -1.0f;
|
||||
vec3<float> n = {0.0f, 0.0f, 0.0f};
|
||||
for (int i = 0; i < 2; ++i) {
|
||||
for (int j = i + 1; j < 3; ++j) {
|
||||
const float dist = norm(cross(tri[i] - ctr, tri[j] - ctr));
|
||||
if (dist > max_dist) {
|
||||
n = GetNormal(tri[i] - ctr, tri[j] - ctr);
|
||||
}
|
||||
}
|
||||
}
|
||||
return n;
|
||||
}
|
||||
|
||||
// The center of a plane
|
||||
//
|
||||
// Args
|
||||
// plane: vec3 coordinates of the vertices of the plane
|
||||
//
|
||||
// Returns
|
||||
// vec3: center of the plane
|
||||
//
|
||||
inline vec3<float> PlaneCenter(const std::vector<vec3<float>>& plane) {
|
||||
// Vertices of the plane
|
||||
const vec3<float> v0 = plane[0];
|
||||
const vec3<float> v1 = plane[1];
|
||||
const vec3<float> v2 = plane[2];
|
||||
const vec3<float> v3 = plane[3];
|
||||
|
||||
return (v0 + v1 + v2 + v3) / 4.0f;
|
||||
}
|
||||
|
||||
// The normal of a planar face with vertices (v0, v1, v2, v3)
|
||||
// We find the "best" edges connecting the face center to the vertices,
|
||||
// such that the cross product between the edges is maximized.
|
||||
//
|
||||
// Args
|
||||
// plane: vec3 coordinates of the vertices of the planar face
|
||||
//
|
||||
// Returns
|
||||
// vec3: normal of the planar face
|
||||
//
|
||||
inline vec3<float> PlaneNormal(const std::vector<vec3<float>>& plane) {
|
||||
// Get center of planar face
|
||||
vec3<float> ctr = PlaneCenter(plane);
|
||||
|
||||
// find the "best" normal as cross product of edges from center
|
||||
float max_dist = -1.0f;
|
||||
vec3<float> n = {0.0f, 0.0f, 0.0f};
|
||||
for (int i = 0; i < 3; ++i) {
|
||||
for (int j = i + 1; j < 4; ++j) {
|
||||
const float dist = norm(cross(plane[i] - ctr, plane[j] - ctr));
|
||||
if (dist > max_dist) {
|
||||
n = GetNormal(plane[i] - ctr, plane[j] - ctr);
|
||||
}
|
||||
}
|
||||
}
|
||||
return n;
|
||||
}
|
||||
|
||||
@ -166,8 +262,9 @@ inline float FaceArea(const std::vector<vec3<float>>& tri) {
|
||||
return norm(n) / 2.0;
|
||||
}
|
||||
|
||||
// The normal of a box plane defined by the verts in `plane` with
|
||||
// the centroid of the box given by `center`.
|
||||
// The normal of a box plane defined by the verts in `plane` such that it
|
||||
// points toward the centroid of the box given by `center`.
|
||||
//
|
||||
// Args
|
||||
// plane: vec3 coordinates of the vertices of the plane
|
||||
// center: vec3 coordinates of the center of the box from
|
||||
@ -180,23 +277,22 @@ inline float FaceArea(const std::vector<vec3<float>>& tri) {
|
||||
inline vec3<float> PlaneNormalDirection(
|
||||
const std::vector<vec3<float>>& plane,
|
||||
const vec3<float>& center) {
|
||||
// Only need the first 3 verts of the plane
|
||||
const vec3<float> v0 = plane[0];
|
||||
const vec3<float> v1 = plane[1];
|
||||
const vec3<float> v2 = plane[2];
|
||||
// The plane's center & normal
|
||||
const vec3<float> plane_center = PlaneCenter(plane);
|
||||
vec3<float> n = PlaneNormal(plane);
|
||||
|
||||
// We project the center on the plane defined by (v0, v1, v2)
|
||||
// We can write center = v0 + a * e0 + b * e1 + c * n
|
||||
// We project the center on the plane defined by (v0, v1, v2, v3)
|
||||
// We can write center = plane_center + a * e0 + b * e1 + c * n
|
||||
// We know that <e0, n> = 0 and <e1, n> = 0 and
|
||||
// <a, b> is the dot product between a and b.
|
||||
// This means we can solve for c as:
|
||||
// c = <center - v0 - a * e0 - b * e1, n> = <center - v0, n>
|
||||
vec3<float> n = FaceNormal(v0, v1, v2);
|
||||
const float c = dot((center - v0), n);
|
||||
// c = <center - plane_center - a * e0 - b * e1, n>
|
||||
// = <center - plane_center, n>
|
||||
const float c = dot((center - plane_center), n);
|
||||
|
||||
// If c is negative, then we revert the direction of n such that n
|
||||
// points "inside"
|
||||
if (c < kEpsilon) {
|
||||
if (c < 0.0f) {
|
||||
n = -1.0f * n;
|
||||
}
|
||||
|
||||
@ -308,16 +404,16 @@ inline bool IsInside(
|
||||
const std::vector<vec3<float>>& plane,
|
||||
const vec3<float>& normal,
|
||||
const vec3<float>& point) {
|
||||
// Get one vert of the plane
|
||||
const vec3<float> v0 = plane[0];
|
||||
// The center of the plane
|
||||
const vec3<float> plane_ctr = PlaneCenter(plane);
|
||||
|
||||
// Every point p can be written as p = v0 + a e0 + b e1 + c n
|
||||
// Every point p can be written as p = plane_ctr + a e0 + b e1 + c n
|
||||
// Solving for c:
|
||||
// c = (point - v0 - a * e0 - b * e1).dot(n)
|
||||
// c = (point - plane_ctr - a * e0 - b * e1).dot(n)
|
||||
// We know that <e0, n> = 0 and <e1, n> = 0
|
||||
// So the calculation can be simplified as:
|
||||
const float c = dot((point - v0), normal);
|
||||
const bool inside = c > -1.0f * kEpsilon;
|
||||
const float c = dot((point - plane_ctr), normal);
|
||||
const bool inside = c >= 0.0f;
|
||||
return inside;
|
||||
}
|
||||
|
||||
@ -338,20 +434,124 @@ inline vec3<float> PlaneEdgeIntersection(
|
||||
const vec3<float>& normal,
|
||||
const vec3<float>& p0,
|
||||
const vec3<float>& p1) {
|
||||
// Get one vert of the plane
|
||||
const vec3<float> v0 = plane[0];
|
||||
// The center of the plane
|
||||
const vec3<float> plane_ctr = PlaneCenter(plane);
|
||||
|
||||
// The point of intersection can be parametrized
|
||||
// p = p0 + a (p1 - p0) where a in [0, 1]
|
||||
// We want to find a such that p is on plane
|
||||
// <p - v0, n> = 0
|
||||
const float top = dot(-1.0f * (p0 - v0), normal);
|
||||
const float bot = dot(p1 - p0, normal);
|
||||
const float a = top / bot;
|
||||
const vec3<float> p = p0 + a * (p1 - p0);
|
||||
// <p - ctr, n> = 0
|
||||
|
||||
vec3<float> direc = p1 - p0;
|
||||
direc = direc / std::fmaxf(norm(direc), kEpsilon);
|
||||
|
||||
vec3<float> p = (p1 + p0) / 2.0f;
|
||||
|
||||
if (std::abs(dot(direc, normal)) >= dEpsilon) {
|
||||
const float top = -1.0f * dot(p0 - plane_ctr, normal);
|
||||
const float bot = dot(p1 - p0, normal);
|
||||
const float a = top / bot;
|
||||
p = p0 + a * (p1 - p0);
|
||||
}
|
||||
return p;
|
||||
}
|
||||
|
||||
// Compute the most distant points between two sets of vertices
|
||||
//
|
||||
// Args
|
||||
// verts1, verts2: vec3 defining the list of vertices
|
||||
//
|
||||
// Returns
|
||||
// v1m, v2m: vec3 vectors of the most distant points
|
||||
// in verts1 and verts2 respectively
|
||||
//
|
||||
inline std::tuple<vec3<float>, vec3<float>> ArgMaxVerts(
|
||||
const std::vector<vec3<float>>& verts1,
|
||||
const std::vector<vec3<float>>& verts2) {
|
||||
vec3<float> v1m = {0.0f, 0.0f, 0.0f};
|
||||
vec3<float> v2m = {0.0f, 0.0f, 0.0f};
|
||||
float maxdist = -1.0f;
|
||||
|
||||
for (const auto& v1 : verts1) {
|
||||
for (const auto& v2 : verts2) {
|
||||
if (norm(v1 - v2) > maxdist) {
|
||||
v1m = v1;
|
||||
v2m = v2;
|
||||
maxdist = norm(v1 - v2);
|
||||
}
|
||||
}
|
||||
}
|
||||
return std::make_tuple(v1m, v2m);
|
||||
}
|
||||
|
||||
// Compute a boolean indicator for whether or not two faces
|
||||
// are coplanar
|
||||
//
|
||||
// Args
|
||||
// tri1, tri2: std:vector<vec3> of the vertex coordinates of
|
||||
// triangle faces
|
||||
//
|
||||
// Returns
|
||||
// bool: whether or not the two faces are coplanar
|
||||
//
|
||||
inline bool IsCoplanarTriTri(
|
||||
const std::vector<vec3<float>>& tri1,
|
||||
const std::vector<vec3<float>>& tri2) {
|
||||
// Get normal for tri 1
|
||||
const vec3<float> n1 = TriNormal(tri1);
|
||||
|
||||
// Get normal for tri 2
|
||||
const vec3<float> n2 = TriNormal(tri2);
|
||||
|
||||
// Check if parallel
|
||||
const bool check1 = std::abs(dot(n1, n2)) > 1 - dEpsilon;
|
||||
|
||||
// Compute most distant points
|
||||
auto argvs = ArgMaxVerts(tri1, tri2);
|
||||
const auto [v1m, v2m] = argvs;
|
||||
|
||||
vec3<float> n12m = v1m - v2m;
|
||||
n12m = n12m / std::fmaxf(norm(n12m), kEpsilon);
|
||||
|
||||
const bool check2 = (std::abs(dot(n12m, n1)) < dEpsilon) ||
|
||||
(std::abs(dot(n12m, n2)) < dEpsilon);
|
||||
|
||||
return (check1 && check2);
|
||||
}
|
||||
|
||||
// Compute a boolean indicator for whether or not a triangular and a planar
|
||||
// face are coplanar
|
||||
//
|
||||
// Args
|
||||
// tri, plane: std:vector<vec3> of the vertex coordinates of
|
||||
// triangular face and planar face
|
||||
// normal: the normal direction of the plane pointing "inside"
|
||||
//
|
||||
// Returns
|
||||
// bool: whether or not the two faces are coplanar
|
||||
//
|
||||
inline bool IsCoplanarTriPlane(
|
||||
const std::vector<vec3<float>>& tri,
|
||||
const std::vector<vec3<float>>& plane,
|
||||
const vec3<float>& normal) {
|
||||
// Get normal for tri
|
||||
const vec3<float> nt = TriNormal(tri);
|
||||
|
||||
// check if parallel
|
||||
const bool check1 = std::abs(dot(nt, normal)) > 1 - dEpsilon;
|
||||
|
||||
// Compute most distant points
|
||||
auto argvs = ArgMaxVerts(tri, plane);
|
||||
const auto [v1m, v2m] = argvs;
|
||||
|
||||
vec3<float> n12m = v1m - v2m;
|
||||
n12m = n12m / std::fmaxf(norm(n12m), kEpsilon);
|
||||
|
||||
const bool check2 = std::abs(dot(n12m, normal)) < dEpsilon;
|
||||
|
||||
return (check1 && check2);
|
||||
}
|
||||
|
||||
// Triangle is clipped into a quadrilateral
|
||||
// based on the intersection points with the plane.
|
||||
// Then the quadrilateral is divided into two triangles.
|
||||
@ -436,6 +636,14 @@ inline face_verts ClipTriByPlane(
|
||||
const vec3<float> v1 = tri[1];
|
||||
const vec3<float> v2 = tri[2];
|
||||
|
||||
// Check coplanar
|
||||
const bool iscoplanar = IsCoplanarTriPlane(tri, plane, normal);
|
||||
if (iscoplanar) {
|
||||
// Return input vertices
|
||||
face_verts tris = {{v0, v1, v2}};
|
||||
return tris;
|
||||
}
|
||||
|
||||
// Check each of the triangle vertices to see if it is inside the plane
|
||||
const bool isin0 = IsInside(plane, normal, v0);
|
||||
const bool isin1 = IsInside(plane, normal, v1);
|
||||
@ -480,35 +688,6 @@ inline face_verts ClipTriByPlane(
|
||||
return empty_tris;
|
||||
}
|
||||
|
||||
// Compute a boolean indicator for whether or not two faces
|
||||
// are coplanar
|
||||
//
|
||||
// Args
|
||||
// tri1, tri2: std:vector<vec3> of the vertex coordinates of
|
||||
// triangle faces
|
||||
//
|
||||
// Returns
|
||||
// bool: whether or not the two faces are coplanar
|
||||
//
|
||||
inline bool IsCoplanarFace(
|
||||
const std::vector<vec3<float>>& tri1,
|
||||
const std::vector<vec3<float>>& tri2) {
|
||||
// Get verts for face 1
|
||||
const vec3<float> v0 = tri1[0];
|
||||
const vec3<float> v1 = tri1[1];
|
||||
const vec3<float> v2 = tri1[2];
|
||||
|
||||
const vec3<float> n1 = FaceNormal(v0, v1, v2);
|
||||
int coplanar_count = 0;
|
||||
for (int i = 0; i < 3; ++i) {
|
||||
float d = std::abs(dot(tri2[i] - v0, n1));
|
||||
if (d < kEpsilon) {
|
||||
coplanar_count = coplanar_count + 1;
|
||||
}
|
||||
}
|
||||
return (coplanar_count == 3);
|
||||
}
|
||||
|
||||
// Get the triangles from each box which are part of the
|
||||
// intersecting polyhedron by computing the intersection
|
||||
// points with each of the planes.
|
||||
|
||||
@ -21,7 +21,8 @@ from .common_testing import get_random_cuda_device, get_tests_dir, TestCaseMixin
|
||||
OBJECTRON_TO_PYTORCH3D_FACE_IDX = [0, 4, 6, 2, 1, 5, 7, 3]
|
||||
DATA_DIR = get_tests_dir() / "data"
|
||||
DEBUG = False
|
||||
EPS = 1e-5
|
||||
DOT_EPS = 1e-3
|
||||
AREA_EPS = 1e-4
|
||||
|
||||
UNIT_BOX = [
|
||||
[0, 0, 0],
|
||||
@ -457,6 +458,207 @@ class TestIoU3D(TestCaseMixin, unittest.TestCase):
|
||||
self.assertClose(
|
||||
iou, torch.tensor([[0.91]], device=vol.device, dtype=vol.dtype), atol=1e-2
|
||||
)
|
||||
# symmetry
|
||||
vol, iou = overlap_fn(box15b[None], box15a[None])
|
||||
self.assertClose(
|
||||
iou, torch.tensor([[0.91]], device=vol.device, dtype=vol.dtype), atol=1e-2
|
||||
)
|
||||
|
||||
# 16th test: From GH issue 1287
|
||||
box16a = torch.tensor(
|
||||
[
|
||||
[-167.5847, -70.6167, -2.7927],
|
||||
[-166.7333, -72.4264, -2.7927],
|
||||
[-166.7333, -72.4264, -4.5927],
|
||||
[-167.5847, -70.6167, -4.5927],
|
||||
[-163.0605, -68.4880, -2.7927],
|
||||
[-162.2090, -70.2977, -2.7927],
|
||||
[-162.2090, -70.2977, -4.5927],
|
||||
[-163.0605, -68.4880, -4.5927],
|
||||
],
|
||||
device=device,
|
||||
dtype=torch.float32,
|
||||
)
|
||||
|
||||
box16b = torch.tensor(
|
||||
[
|
||||
[-167.5847, -70.6167, -2.7927],
|
||||
[-166.7333, -72.4264, -2.7927],
|
||||
[-166.7333, -72.4264, -4.5927],
|
||||
[-167.5847, -70.6167, -4.5927],
|
||||
[-163.0605, -68.4880, -2.7927],
|
||||
[-162.2090, -70.2977, -2.7927],
|
||||
[-162.2090, -70.2977, -4.5927],
|
||||
[-163.0605, -68.4880, -4.5927],
|
||||
],
|
||||
device=device,
|
||||
dtype=torch.float32,
|
||||
)
|
||||
vol, iou = overlap_fn(box16a[None], box16b[None])
|
||||
self.assertClose(
|
||||
iou, torch.tensor([[1.0]], device=vol.device, dtype=vol.dtype), atol=1e-2
|
||||
)
|
||||
# symmetry
|
||||
vol, iou = overlap_fn(box16b[None], box16a[None])
|
||||
self.assertClose(
|
||||
iou, torch.tensor([[1.0]], device=vol.device, dtype=vol.dtype), atol=1e-2
|
||||
)
|
||||
|
||||
# 17th test: From GH issue 1287
|
||||
box17a = torch.tensor(
|
||||
[
|
||||
[-33.94158, -4.51639, 0.96941],
|
||||
[-34.67156, -2.65437, 0.96941],
|
||||
[-34.67156, -2.65437, -0.95367],
|
||||
[-33.94158, -4.51639, -0.95367],
|
||||
[-38.75954, -6.40521, 0.96941],
|
||||
[-39.48952, -4.54319, 0.96941],
|
||||
[-39.48952, -4.54319, -0.95367],
|
||||
[-38.75954, -6.40521, -0.95367],
|
||||
],
|
||||
device=device,
|
||||
dtype=torch.float32,
|
||||
)
|
||||
|
||||
box17b = torch.tensor(
|
||||
[
|
||||
[-33.94159, -4.51638, 0.96939],
|
||||
[-34.67158, -2.65437, 0.96939],
|
||||
[-34.67158, -2.65437, -0.95368],
|
||||
[-33.94159, -4.51638, -0.95368],
|
||||
[-38.75954, -6.40523, 0.96939],
|
||||
[-39.48953, -4.54321, 0.96939],
|
||||
[-39.48953, -4.54321, -0.95368],
|
||||
[-38.75954, -6.40523, -0.95368],
|
||||
],
|
||||
device=device,
|
||||
dtype=torch.float32,
|
||||
)
|
||||
vol, iou = overlap_fn(box17a[None], box17b[None])
|
||||
self.assertClose(
|
||||
iou, torch.tensor([[1.0]], device=vol.device, dtype=vol.dtype), atol=1e-2
|
||||
)
|
||||
# symmetry
|
||||
vol, iou = overlap_fn(box17b[None], box17a[None])
|
||||
self.assertClose(
|
||||
iou, torch.tensor([[1.0]], device=vol.device, dtype=vol.dtype), atol=1e-2
|
||||
)
|
||||
|
||||
# 18th test: From GH issue 1287
|
||||
box18a = torch.tensor(
|
||||
[
|
||||
[-105.6248, -32.7026, -1.2279],
|
||||
[-106.4690, -30.8895, -1.2279],
|
||||
[-106.4690, -30.8895, -3.0279],
|
||||
[-105.6248, -32.7026, -3.0279],
|
||||
[-110.1575, -34.8132, -1.2279],
|
||||
[-111.0017, -33.0001, -1.2279],
|
||||
[-111.0017, -33.0001, -3.0279],
|
||||
[-110.1575, -34.8132, -3.0279],
|
||||
],
|
||||
device=device,
|
||||
dtype=torch.float32,
|
||||
)
|
||||
box18b = torch.tensor(
|
||||
[
|
||||
[-105.5094, -32.9504, -1.0641],
|
||||
[-106.4272, -30.9793, -1.0641],
|
||||
[-106.4272, -30.9793, -3.1916],
|
||||
[-105.5094, -32.9504, -3.1916],
|
||||
[-110.0421, -35.0609, -1.0641],
|
||||
[-110.9599, -33.0899, -1.0641],
|
||||
[-110.9599, -33.0899, -3.1916],
|
||||
[-110.0421, -35.0609, -3.1916],
|
||||
],
|
||||
device=device,
|
||||
dtype=torch.float32,
|
||||
)
|
||||
# from Meshlab
|
||||
vol_inters = 17.108501
|
||||
vol_box1 = 18.000067
|
||||
vol_box2 = 23.128527
|
||||
iou_mesh = vol_inters / (vol_box1 + vol_box2 - vol_inters)
|
||||
vol, iou = overlap_fn(box18a[None], box18b[None])
|
||||
self.assertClose(
|
||||
iou,
|
||||
torch.tensor([[iou_mesh]], device=vol.device, dtype=vol.dtype),
|
||||
atol=1e-2,
|
||||
)
|
||||
self.assertClose(
|
||||
vol,
|
||||
torch.tensor([[vol_inters]], device=vol.device, dtype=vol.dtype),
|
||||
atol=1e-2,
|
||||
)
|
||||
# symmetry
|
||||
vol, iou = overlap_fn(box18b[None], box18a[None])
|
||||
self.assertClose(
|
||||
iou,
|
||||
torch.tensor([[iou_mesh]], device=vol.device, dtype=vol.dtype),
|
||||
atol=1e-2,
|
||||
)
|
||||
self.assertClose(
|
||||
vol,
|
||||
torch.tensor([[vol_inters]], device=vol.device, dtype=vol.dtype),
|
||||
atol=1e-2,
|
||||
)
|
||||
|
||||
# 19th example: From GH issue 1287
|
||||
box19a = torch.tensor(
|
||||
[
|
||||
[-59.4785, -15.6003, 0.4398],
|
||||
[-60.2263, -13.6928, 0.4398],
|
||||
[-60.2263, -13.6928, -1.3909],
|
||||
[-59.4785, -15.6003, -1.3909],
|
||||
[-64.1743, -17.4412, 0.4398],
|
||||
[-64.9221, -15.5337, 0.4398],
|
||||
[-64.9221, -15.5337, -1.3909],
|
||||
[-64.1743, -17.4412, -1.3909],
|
||||
],
|
||||
device=device,
|
||||
dtype=torch.float32,
|
||||
)
|
||||
box19b = torch.tensor(
|
||||
[
|
||||
[-59.4874, -15.5775, -0.1512],
|
||||
[-60.2174, -13.7155, -0.1512],
|
||||
[-60.2174, -13.7155, -1.9820],
|
||||
[-59.4874, -15.5775, -1.9820],
|
||||
[-64.1832, -17.4185, -0.1512],
|
||||
[-64.9132, -15.5564, -0.1512],
|
||||
[-64.9132, -15.5564, -1.9820],
|
||||
[-64.1832, -17.4185, -1.9820],
|
||||
],
|
||||
device=device,
|
||||
dtype=torch.float32,
|
||||
)
|
||||
# from Meshlab
|
||||
vol_inters = 12.505723
|
||||
vol_box1 = 18.918238
|
||||
vol_box2 = 18.468531
|
||||
iou_mesh = vol_inters / (vol_box1 + vol_box2 - vol_inters)
|
||||
vol, iou = overlap_fn(box19a[None], box19b[None])
|
||||
self.assertClose(
|
||||
iou,
|
||||
torch.tensor([[iou_mesh]], device=vol.device, dtype=vol.dtype),
|
||||
atol=1e-2,
|
||||
)
|
||||
self.assertClose(
|
||||
vol,
|
||||
torch.tensor([[vol_inters]], device=vol.device, dtype=vol.dtype),
|
||||
atol=1e-2,
|
||||
)
|
||||
# symmetry
|
||||
vol, iou = overlap_fn(box19b[None], box19a[None])
|
||||
self.assertClose(
|
||||
iou,
|
||||
torch.tensor([[iou_mesh]], device=vol.device, dtype=vol.dtype),
|
||||
atol=1e-2,
|
||||
)
|
||||
self.assertClose(
|
||||
vol,
|
||||
torch.tensor([[vol_inters]], device=vol.device, dtype=vol.dtype),
|
||||
atol=1e-2,
|
||||
)
|
||||
|
||||
def _test_real_boxes(self, overlap_fn, device):
|
||||
data_filename = "./real_boxes.pkl"
|
||||
@ -715,7 +917,86 @@ def get_plane_verts(box: torch.Tensor) -> torch.Tensor:
|
||||
return plane_verts
|
||||
|
||||
|
||||
def box_planar_dir(box: torch.Tensor, eps: float = 1e-4) -> torch.Tensor:
|
||||
def get_tri_center_normal(tris: torch.Tensor) -> torch.Tensor:
|
||||
"""
|
||||
Returns the center and normal of triangles
|
||||
Args:
|
||||
tris: tensor of shape (T, 3, 3)
|
||||
Returns:
|
||||
center: tensor of shape (T, 3)
|
||||
normal: tensor of shape (T, 3)
|
||||
"""
|
||||
add_dim0 = False
|
||||
if tris.ndim == 2:
|
||||
tris = tris.unsqueeze(0)
|
||||
add_dim0 = True
|
||||
|
||||
ctr = tris.mean(1) # (T, 3)
|
||||
normals = torch.zeros_like(ctr)
|
||||
|
||||
v0, v1, v2 = tris.unbind(1) # 3 x (T, 3)
|
||||
|
||||
# unvectorized solution
|
||||
T = tris.shape[0]
|
||||
for t in range(T):
|
||||
ns = torch.zeros((3, 3), device=tris.device)
|
||||
ns[0] = torch.cross(v0[t] - ctr[t], v1[t] - ctr[t], dim=-1)
|
||||
ns[1] = torch.cross(v0[t] - ctr[t], v2[t] - ctr[t], dim=-1)
|
||||
ns[2] = torch.cross(v1[t] - ctr[t], v2[t] - ctr[t], dim=-1)
|
||||
|
||||
i = torch.norm(ns, dim=-1).argmax()
|
||||
normals[t] = ns[i]
|
||||
|
||||
if add_dim0:
|
||||
ctr = ctr[0]
|
||||
normals = normals[0]
|
||||
normals = F.normalize(normals, dim=-1)
|
||||
return ctr, normals
|
||||
|
||||
|
||||
def get_plane_center_normal(planes: torch.Tensor) -> torch.Tensor:
|
||||
"""
|
||||
Returns the center and normal of planes
|
||||
Args:
|
||||
planes: tensor of shape (P, 4, 3)
|
||||
Returns:
|
||||
center: tensor of shape (P, 3)
|
||||
normal: tensor of shape (P, 3)
|
||||
"""
|
||||
add_dim0 = False
|
||||
if planes.ndim == 2:
|
||||
planes = planes.unsqueeze(0)
|
||||
add_dim0 = True
|
||||
|
||||
ctr = planes.mean(1) # (P, 3)
|
||||
normals = torch.zeros_like(ctr)
|
||||
|
||||
v0, v1, v2, v3 = planes.unbind(1) # 4 x (P, 3)
|
||||
|
||||
# unvectorized solution
|
||||
P = planes.shape[0]
|
||||
for t in range(P):
|
||||
ns = torch.zeros((6, 3), device=planes.device)
|
||||
ns[0] = torch.cross(v0[t] - ctr[t], v1[t] - ctr[t], dim=-1)
|
||||
ns[1] = torch.cross(v0[t] - ctr[t], v2[t] - ctr[t], dim=-1)
|
||||
ns[2] = torch.cross(v0[t] - ctr[t], v3[t] - ctr[t], dim=-1)
|
||||
ns[3] = torch.cross(v1[t] - ctr[t], v2[t] - ctr[t], dim=-1)
|
||||
ns[4] = torch.cross(v1[t] - ctr[t], v3[t] - ctr[t], dim=-1)
|
||||
ns[5] = torch.cross(v2[t] - ctr[t], v3[t] - ctr[t], dim=-1)
|
||||
|
||||
i = torch.norm(ns, dim=-1).argmax()
|
||||
normals[t] = ns[i]
|
||||
|
||||
if add_dim0:
|
||||
ctr = ctr[0]
|
||||
normals = normals[0]
|
||||
normals = F.normalize(normals, dim=-1)
|
||||
return ctr, normals
|
||||
|
||||
|
||||
def box_planar_dir(
|
||||
box: torch.Tensor, dot_eps: float = DOT_EPS, area_eps: float = AREA_EPS
|
||||
) -> torch.Tensor:
|
||||
"""
|
||||
Finds the unit vector n which is perpendicular to each plane in the box
|
||||
and points towards the inside of the box.
|
||||
@ -731,33 +1012,33 @@ def box_planar_dir(box: torch.Tensor, eps: float = 1e-4) -> torch.Tensor:
|
||||
assert box.shape[0] == 8 and box.shape[1] == 3
|
||||
|
||||
# center point of each box
|
||||
ctr = box.mean(0).view(1, 3)
|
||||
box_ctr = box.mean(0).view(1, 3)
|
||||
|
||||
verts = get_plane_verts(box) # (6, 4, 3)
|
||||
|
||||
v0, v1, v2, v3 = verts.unbind(1) # each v of shape (6, 3)
|
||||
|
||||
# We project the ctr on the plane defined by (v0, v1, v2, v3)
|
||||
# We define e0 to be the edge connecting (v1, v0)
|
||||
# We define e1 to be the edge connecting (v2, v0)
|
||||
# And n is the cross product of e0, e1, either pointing "inside" or not.
|
||||
e0 = F.normalize(v1 - v0, dim=-1)
|
||||
e1 = F.normalize(v2 - v0, dim=-1)
|
||||
n = F.normalize(torch.cross(e0, e1, dim=-1), dim=-1)
|
||||
# box planes
|
||||
plane_verts = get_plane_verts(box) # (6, 4, 3)
|
||||
v0, v1, v2, v3 = plane_verts.unbind(1)
|
||||
plane_ctr, n = get_plane_center_normal(plane_verts)
|
||||
|
||||
# Check all verts are coplanar
|
||||
if not ((v3 - v0).unsqueeze(1).bmm(n.unsqueeze(2)).abs() < eps).all().item():
|
||||
if (
|
||||
not (
|
||||
F.normalize(v3 - v0, dim=-1).unsqueeze(1).bmm(n.unsqueeze(2)).abs()
|
||||
< dot_eps
|
||||
)
|
||||
.all()
|
||||
.item()
|
||||
):
|
||||
msg = "Plane vertices are not coplanar"
|
||||
raise ValueError(msg)
|
||||
|
||||
# Check all faces have non zero area
|
||||
area1 = torch.cross(v1 - v0, v2 - v0, dim=-1).norm(dim=-1) / 2
|
||||
area2 = torch.cross(v3 - v0, v2 - v0, dim=-1).norm(dim=-1) / 2
|
||||
if (area1 < eps).any().item() or (area2 < eps).any().item():
|
||||
if (area1 < area_eps).any().item() or (area2 < area_eps).any().item():
|
||||
msg = "Planes have zero areas"
|
||||
raise ValueError(msg)
|
||||
|
||||
# We can write: `ctr = v0 + a * e0 + b * e1 + c * n`, (1).
|
||||
# We can write: `box_ctr = plane_ctr + a * e0 + b * e1 + c * n`, (1).
|
||||
# With <e0, n> = 0 and <e1, n> = 0, where <.,.> refers to the dot product,
|
||||
# since that e0 is orthogonal to n. Same for e1.
|
||||
"""
|
||||
@ -768,16 +1049,17 @@ def box_planar_dir(box: torch.Tensor, eps: float = 1e-4) -> torch.Tensor:
|
||||
B = torch.ones((numF, 2), dtype=torch.float32, device=device)
|
||||
A[:, 0, 1] = (e0 * e1).sum(-1)
|
||||
A[:, 1, 0] = (e0 * e1).sum(-1)
|
||||
B[:, 0] = ((ctr - v0) * e0).sum(-1)
|
||||
B[:, 1] = ((ctr - v1) * e1).sum(-1)
|
||||
B[:, 0] = ((box_ctr - plane_ctr) * e0).sum(-1)
|
||||
B[:, 1] = ((box_ctr - plane_ctr) * e1).sum(-1)
|
||||
ab = torch.linalg.solve(A, B) # (numF, 2)
|
||||
a, b = ab.unbind(1)
|
||||
# solving for c
|
||||
c = ((ctr - v0 - a.view(numF, 1) * e0 - b.view(numF, 1) * e1) * n).sum(-1)
|
||||
c = ((box_ctr - plane_ctr - a.view(numF, 1) * e0 - b.view(numF, 1) * e1) * n).sum(-1)
|
||||
"""
|
||||
# Since we know that <e0, n> = 0 and <e1, n> = 0 (e0 and e1 are orthogonal to n),
|
||||
# the above solution is equivalent to
|
||||
c = ((ctr - v0) * n).sum(-1)
|
||||
direc = F.normalize(box_ctr - plane_ctr, dim=-1) # (6, 3)
|
||||
c = (direc * n).sum(-1)
|
||||
# If c is negative, then we revert the direction of n such that n points "inside"
|
||||
negc = c < 0.0
|
||||
n[negc] *= -1.0
|
||||
@ -848,7 +1130,7 @@ def box_volume(box: torch.Tensor) -> torch.Tensor:
|
||||
return vols
|
||||
|
||||
|
||||
def coplanar_tri_faces(tri1: torch.Tensor, tri2: torch.Tensor, eps: float = EPS):
|
||||
def coplanar_tri_faces(tri1: torch.Tensor, tri2: torch.Tensor, eps: float = DOT_EPS):
|
||||
"""
|
||||
Determines whether two triangle faces in 3D are coplanar
|
||||
Args:
|
||||
@ -857,17 +1139,49 @@ def coplanar_tri_faces(tri1: torch.Tensor, tri2: torch.Tensor, eps: float = EPS)
|
||||
Returns:
|
||||
is_coplanar: bool
|
||||
"""
|
||||
v0, v1, v2 = tri1.unbind(0)
|
||||
e0 = F.normalize(v1 - v0, dim=0)
|
||||
e1 = F.normalize(v2 - v0, dim=0)
|
||||
e2 = F.normalize(torch.cross(e0, e1), dim=0)
|
||||
tri1_ctr, tri1_n = get_tri_center_normal(tri1)
|
||||
tri2_ctr, tri2_n = get_tri_center_normal(tri2)
|
||||
|
||||
coplanar2 = torch.zeros((3,), dtype=torch.bool, device=tri1.device)
|
||||
for i in range(3):
|
||||
if (tri2[i] - v0).dot(e2).abs() < eps:
|
||||
coplanar2[i] = 1
|
||||
coplanar2 = coplanar2.all()
|
||||
return coplanar2
|
||||
check1 = tri1_n.dot(tri2_n).abs() > 1 - eps # checks if parallel
|
||||
|
||||
dist12 = torch.norm(tri1.unsqueeze(1) - tri2.unsqueeze(0), dim=-1)
|
||||
dist12_argmax = dist12.argmax()
|
||||
i1 = dist12_argmax // 3
|
||||
i2 = dist12_argmax % 3
|
||||
assert dist12[i1, i2] == dist12.max()
|
||||
|
||||
check2 = (
|
||||
F.normalize(tri1[i1] - tri2[i2], dim=0).dot(tri1_n).abs() < eps
|
||||
) or F.normalize(tri1[i1] - tri2[i2], dim=0).dot(tri2_n).abs() < eps
|
||||
|
||||
return check1 and check2
|
||||
|
||||
|
||||
def coplanar_tri_plane(
|
||||
tri: torch.Tensor, plane: torch.Tensor, n: torch.Tensor, eps: float = DOT_EPS
|
||||
):
|
||||
"""
|
||||
Determines whether two triangle faces in 3D are coplanar
|
||||
Args:
|
||||
tri: tensor of shape (3, 3) of the vertices of the triangle
|
||||
plane: tensor of shape (4, 3) of the vertices of the plane
|
||||
n: tensor of shape (3,) of the unit "inside" direction on the plane
|
||||
Returns:
|
||||
is_coplanar: bool
|
||||
"""
|
||||
tri_ctr, tri_n = get_tri_center_normal(tri)
|
||||
|
||||
check1 = tri_n.dot(n).abs() > 1 - eps # checks if parallel
|
||||
|
||||
dist12 = torch.norm(tri.unsqueeze(1) - plane.unsqueeze(0), dim=-1)
|
||||
dist12_argmax = dist12.argmax()
|
||||
i1 = dist12_argmax // 4
|
||||
i2 = dist12_argmax % 4
|
||||
assert dist12[i1, i2] == dist12.max()
|
||||
|
||||
check2 = F.normalize(tri[i1] - plane[i2], dim=0).dot(n).abs() < eps
|
||||
|
||||
return check1 and check2
|
||||
|
||||
|
||||
def is_inside(
|
||||
@ -875,7 +1189,6 @@ def is_inside(
|
||||
n: torch.Tensor,
|
||||
points: torch.Tensor,
|
||||
return_proj: bool = True,
|
||||
eps: float = EPS,
|
||||
):
|
||||
"""
|
||||
Computes whether point is "inside" the plane.
|
||||
@ -900,12 +1213,13 @@ def is_inside(
|
||||
p_proj: tensor of shape (P, 3) of the projected point on plane
|
||||
"""
|
||||
device = plane.device
|
||||
v0, v1, v2, v3 = plane
|
||||
e0 = F.normalize(v1 - v0, dim=0)
|
||||
e1 = F.normalize(v2 - v0, dim=0)
|
||||
if not torch.allclose(e0.dot(n), torch.zeros((1,), device=device), atol=1e-6):
|
||||
v0, v1, v2, v3 = plane.unbind(0)
|
||||
plane_ctr = plane.mean(0)
|
||||
e0 = F.normalize(v0 - plane_ctr, dim=0)
|
||||
e1 = F.normalize(v1 - plane_ctr, dim=0)
|
||||
if not torch.allclose(e0.dot(n), torch.zeros((1,), device=device), atol=1e-2):
|
||||
raise ValueError("Input n is not perpendicular to the plane")
|
||||
if not torch.allclose(e1.dot(n), torch.zeros((1,), device=device), atol=1e-6):
|
||||
if not torch.allclose(e1.dot(n), torch.zeros((1,), device=device), atol=1e-2):
|
||||
raise ValueError("Input n is not perpendicular to the plane")
|
||||
|
||||
add_dim = False
|
||||
@ -914,7 +1228,7 @@ def is_inside(
|
||||
add_dim = True
|
||||
|
||||
assert points.shape[1] == 3
|
||||
# Every point p can be written as p = v0 + a e0 + b e1 + c n
|
||||
# Every point p can be written as p = ctr + a e0 + b e1 + c n
|
||||
|
||||
# If return_proj is True, we need to solve for (a, b)
|
||||
p_proj = None
|
||||
@ -924,16 +1238,17 @@ def is_inside(
|
||||
[[1.0, e0.dot(e1)], [e0.dot(e1), 1.0]], dtype=torch.float32, device=device
|
||||
)
|
||||
B = torch.zeros((2, points.shape[0]), dtype=torch.float32, device=device)
|
||||
B[0, :] = torch.sum((points - v0.view(1, 3)) * e0.view(1, 3), dim=-1)
|
||||
B[1, :] = torch.sum((points - v0.view(1, 3)) * e1.view(1, 3), dim=-1)
|
||||
|
||||
B[0, :] = torch.sum((points - plane_ctr.view(1, 3)) * e0.view(1, 3), dim=-1)
|
||||
B[1, :] = torch.sum((points - plane_ctr.view(1, 3)) * e1.view(1, 3), dim=-1)
|
||||
ab = A.inverse() @ B # (2, P)
|
||||
p_proj = v0.view(1, 3) + ab.transpose(0, 1) @ torch.stack((e0, e1), dim=0)
|
||||
p_proj = plane_ctr.view(1, 3) + ab.transpose(0, 1) @ torch.stack(
|
||||
(e0, e1), dim=0
|
||||
)
|
||||
|
||||
# solving for c
|
||||
# c = (point - v0 - a * e0 - b * e1).dot(n)
|
||||
c = torch.sum((points - v0.view(1, 3)) * n.view(1, 3), dim=-1)
|
||||
ins = c > -eps
|
||||
# c = (point - ctr - a * e0 - b * e1).dot(n)
|
||||
direc = torch.sum((points - plane_ctr.view(1, 3)) * n.view(1, 3), dim=-1)
|
||||
ins = direc >= 0.0
|
||||
|
||||
if add_dim:
|
||||
assert p_proj.shape[0] == 1
|
||||
@ -942,7 +1257,7 @@ def is_inside(
|
||||
return ins, p_proj
|
||||
|
||||
|
||||
def plane_edge_point_of_intersection(plane, n, p0, p1):
|
||||
def plane_edge_point_of_intersection(plane, n, p0, p1, eps: float = DOT_EPS):
|
||||
"""
|
||||
Finds the point of intersection between a box plane and
|
||||
a line segment connecting (p0, p1).
|
||||
@ -961,11 +1276,17 @@ def plane_edge_point_of_intersection(plane, n, p0, p1):
|
||||
# The point of intersection can be parametrized
|
||||
# p = p0 + a (p1 - p0) where a in [0, 1]
|
||||
# We want to find a such that p is on plane
|
||||
# <p - v0, n> = 0
|
||||
v0, v1, v2, v3 = plane
|
||||
a = -(p0 - v0).dot(n) / (p1 - p0).dot(n)
|
||||
p = p0 + a * (p1 - p0)
|
||||
return p, a
|
||||
# <p - ctr, n> = 0
|
||||
|
||||
# if segment (p0, p1) is parallel to plane (it can only be on it)
|
||||
direc = F.normalize(p1 - p0, dim=0)
|
||||
if direc.dot(n).abs() < eps:
|
||||
return (p1 + p0) / 2.0, 0.5
|
||||
else:
|
||||
ctr = plane.mean(0)
|
||||
a = -(p0 - ctr).dot(n) / ((p1 - p0).dot(n))
|
||||
p = p0 + a * (p1 - p0)
|
||||
return p, a
|
||||
|
||||
|
||||
"""
|
||||
@ -983,7 +1304,6 @@ def clip_tri_by_plane_oneout(
|
||||
vout: torch.Tensor,
|
||||
vin1: torch.Tensor,
|
||||
vin2: torch.Tensor,
|
||||
eps: float = EPS,
|
||||
) -> Tuple[torch.Tensor, torch.Tensor]:
|
||||
"""
|
||||
Case (a).
|
||||
@ -1004,10 +1324,10 @@ def clip_tri_by_plane_oneout(
|
||||
device = plane.device
|
||||
# point of intersection between plane and (vin1, vout)
|
||||
pint1, a1 = plane_edge_point_of_intersection(plane, n, vin1, vout)
|
||||
assert a1 >= -eps and a1 <= 1.0 + eps, a1
|
||||
assert a1 >= -0.0001 and a1 <= 1.0001, a1
|
||||
# point of intersection between plane and (vin2, vout)
|
||||
pint2, a2 = plane_edge_point_of_intersection(plane, n, vin2, vout)
|
||||
assert a2 >= -eps and a2 <= 1.0 + eps, a2
|
||||
assert a2 >= -0.0001 and a2 <= 1.0001, a2
|
||||
|
||||
verts = torch.stack((vin1, pint1, pint2, vin2), dim=0) # 4x3
|
||||
faces = torch.tensor(
|
||||
@ -1022,7 +1342,6 @@ def clip_tri_by_plane_twoout(
|
||||
vout1: torch.Tensor,
|
||||
vout2: torch.Tensor,
|
||||
vin: torch.Tensor,
|
||||
eps: float = EPS,
|
||||
) -> Tuple[torch.Tensor, torch.Tensor]:
|
||||
"""
|
||||
Case (b).
|
||||
@ -1042,10 +1361,10 @@ def clip_tri_by_plane_twoout(
|
||||
device = plane.device
|
||||
# point of intersection between plane and (vin, vout1)
|
||||
pint1, a1 = plane_edge_point_of_intersection(plane, n, vin, vout1)
|
||||
assert a1 >= -eps and a1 <= 1.0 + eps, a1
|
||||
assert a1 >= -0.0001 and a1 <= 1.0001, a1
|
||||
# point of intersection between plane and (vin, vout2)
|
||||
pint2, a2 = plane_edge_point_of_intersection(plane, n, vin, vout2)
|
||||
assert a2 >= -eps and a2 <= 1.0 + eps, a2
|
||||
assert a2 >= -0.0001 and a2 <= 1.0001, a2
|
||||
|
||||
verts = torch.stack((vin, pint1, pint2), dim=0) # 3x3
|
||||
faces = torch.tensor(
|
||||
@ -1071,6 +1390,9 @@ def clip_tri_by_plane(plane, n, tri_verts) -> Union[List, torch.Tensor]:
|
||||
tri_verts: tensor of shape (K, 3, 3) of the vertex coordinates of the triangles formed
|
||||
after clipping. All K triangles are now "inside" the plane.
|
||||
"""
|
||||
if coplanar_tri_plane(tri_verts, plane, n):
|
||||
return tri_verts.view(1, 3, 3)
|
||||
|
||||
v0, v1, v2 = tri_verts.unbind(0)
|
||||
isin0, _ = is_inside(plane, n, v0)
|
||||
isin1, _ = is_inside(plane, n, v1)
|
||||
@ -1191,7 +1513,7 @@ def box3d_overlap_naive(box1: torch.Tensor, box2: torch.Tensor):
|
||||
for i2 in range(tri_verts2.shape[0]):
|
||||
if (
|
||||
coplanar_tri_faces(tri_verts1[i1], tri_verts2[i2])
|
||||
and tri_verts_area(tri_verts1[i1]) > 1e-4
|
||||
and tri_verts_area(tri_verts1[i1]) > AREA_EPS
|
||||
):
|
||||
keep2[i2] = 0
|
||||
keep2 = keep2.nonzero()[:, 0]
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user