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fix: exact collision checking for polytopes via iterative projection #1

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fix: exact collision checking for polytopes via iterative projection #1

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29 changes: 22 additions & 7 deletions src/impl/vamp/collision/sphere_polytope.hh
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Original file line number Diff line number Diff line change
Expand Up @@ -24,22 +24,37 @@ namespace vamp::collision
return obb_dist;
}

DataT max_dist = DataT::fill(-std::numeric_limits<float>::max());
// iteratively project (cx, cy, cz) onto the polytope and test distance between original centers and
// projected centers

DataT lower_bound_dist = DataT::fill(-std::numeric_limits<float>::max());
DataT cx_proj = cx;
DataT cy_proj = cy;
DataT cz_proj = cz;

// TODO: Proper GJK? Seems OK for now.
for (auto i = 0U; i < p.num_planes; ++i)
{
// dist = n.C - d - r (positive = separated)
auto dist = dot_3(p.nx[i], p.ny[i], p.nz[i], cx, cy, cz) - p.d[i] - r;
max_dist = max_dist.max(dist);
const DataT dot_product = dot_3(p.nx[i], p.ny[i], p.nz[i], cx_proj, cy_proj, cz_proj);
const DataT n_scale = (dot_product - p.d[i]).max(0.0);

// project c onto the halfspace by subtracting out the part parallel to n that lies beyond the
// plane

cx_proj = cx_proj - n_scale * p.nx[i];
cy_proj = cy_proj - n_scale * p.ny[i];
cz_proj = cz_proj - n_scale * p.nz[i];

lower_bound_dist = sql2_3(cx, cy, cz, cx_proj, cy_proj, cz_proj) - rsq;

if (max_dist.test_zero())
// if projected centers are all sufficiently far away from the original centers, we have proven
// the sphere is not in collision
if (lower_bound_dist.test_all_greater_equal(0.0))
{
break;
}
}

return max_dist;
return lower_bound_dist;
}

template <typename DataT>
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