// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics) // SPDX-FileCopyrightText: 2021 Jorrit Rouwe // SPDX-License-Identifier: MIT #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include JPH_NAMESPACE_BEGIN JPH_IMPLEMENT_SERIALIZABLE_VIRTUAL(ConvexHullShapeSettings) { JPH_ADD_BASE_CLASS(ConvexHullShapeSettings, ConvexShapeSettings) JPH_ADD_ATTRIBUTE(ConvexHullShapeSettings, mPoints) JPH_ADD_ATTRIBUTE(ConvexHullShapeSettings, mMaxConvexRadius) JPH_ADD_ATTRIBUTE(ConvexHullShapeSettings, mMaxErrorConvexRadius) JPH_ADD_ATTRIBUTE(ConvexHullShapeSettings, mHullTolerance) } ShapeSettings::ShapeResult ConvexHullShapeSettings::Create() const { if (mCachedResult.IsEmpty()) Ref shape = new ConvexHullShape(*this, mCachedResult); return mCachedResult; } ConvexHullShape::ConvexHullShape(const ConvexHullShapeSettings &inSettings, ShapeResult &outResult) : ConvexShape(EShapeSubType::ConvexHull, inSettings, outResult), mConvexRadius(inSettings.mMaxConvexRadius) { using BuilderFace = ConvexHullBuilder::Face; using Edge = ConvexHullBuilder::Edge; using Faces = Array; // Check convex radius if (mConvexRadius < 0.0f) { outResult.SetError("Invalid convex radius"); return; } // Build convex hull const char *error = nullptr; ConvexHullBuilder builder(inSettings.mPoints); ConvexHullBuilder::EResult result = builder.Initialize(cMaxPointsInHull, inSettings.mHullTolerance, error); if (result != ConvexHullBuilder::EResult::Success && result != ConvexHullBuilder::EResult::MaxVerticesReached) { outResult.SetError(error); return; } const Faces &builder_faces = builder.GetFaces(); // Check the consistency of the resulting hull if we fully built it if (result == ConvexHullBuilder::EResult::Success) { ConvexHullBuilder::Face *max_error_face; float max_error_distance, coplanar_distance; int max_error_idx; builder.DetermineMaxError(max_error_face, max_error_distance, max_error_idx, coplanar_distance); if (max_error_distance > 4.0f * max(coplanar_distance, inSettings.mHullTolerance)) // Coplanar distance could be bigger than the allowed tolerance if the points are far apart { outResult.SetError(StringFormat("Hull building failed, point %d had an error of %g (relative to tolerance: %g)", max_error_idx, (double)max_error_distance, double(max_error_distance / inSettings.mHullTolerance))); return; } } // Calculate center of mass and volume builder.GetCenterOfMassAndVolume(mCenterOfMass, mVolume); // Calculate covariance matrix // See: // - Why the inertia tensor is the inertia tensor - Jonathan Blow (http://number-none.com/blow/inertia/deriving_i.html) // - How to find the inertia tensor (or other mass properties) of a 3D solid body represented by a triangle mesh (Draft) - Jonathan Blow, Atman J Binstock (http://number-none.com/blow/inertia/bb_inertia.doc) Mat44 covariance_canonical(Vec4(1.0f / 60.0f, 1.0f / 120.0f, 1.0f / 120.0f, 0), Vec4(1.0f / 120.0f, 1.0f / 60.0f, 1.0f / 120.0f, 0), Vec4(1.0f / 120.0f, 1.0f / 120.0f, 1.0f / 60.0f, 0), Vec4(0, 0, 0, 1)); Mat44 covariance_matrix = Mat44::sZero(); for (BuilderFace *f : builder_faces) { // Fourth point of the tetrahedron is at the center of mass, we subtract it from the other points so we get a tetrahedron with one vertex at zero // The first point on the face will be used to form a triangle fan Edge *e = f->mFirstEdge; Vec3 v1 = inSettings.mPoints[e->mStartIdx] - mCenterOfMass; // Get the 2nd point e = e->mNextEdge; Vec3 v2 = inSettings.mPoints[e->mStartIdx] - mCenterOfMass; // Loop over the triangle fan for (e = e->mNextEdge; e != f->mFirstEdge; e = e->mNextEdge) { Vec3 v3 = inSettings.mPoints[e->mStartIdx] - mCenterOfMass; // Affine transform that transforms a unit tetrahedron (with vertices (0, 0, 0), (1, 0, 0), (0, 1, 0) and (0, 0, 1) to this tetrahedron Mat44 a(Vec4(v1, 0), Vec4(v2, 0), Vec4(v3, 0), Vec4(0, 0, 0, 1)); // Calculate covariance matrix for this tetrahedron float det_a = a.GetDeterminant3x3(); Mat44 c = det_a * (a * covariance_canonical * a.Transposed()); // Add it covariance_matrix += c; // Prepare for next triangle v2 = v3; } } // Calculate inertia matrix assuming density is 1, note that element (3, 3) is garbage mInertia = Mat44::sIdentity() * (covariance_matrix(0, 0) + covariance_matrix(1, 1) + covariance_matrix(2, 2)) - covariance_matrix; // Convert polygons from the builder to our internal representation using VtxMap = UnorderedMap; VtxMap vertex_map; vertex_map.reserve(VtxMap::size_type(inSettings.mPoints.size())); for (BuilderFace *builder_face : builder_faces) { // Determine where the vertices go JPH_ASSERT(mVertexIdx.size() <= 0xFFFF); uint16 first_vertex = (uint16)mVertexIdx.size(); uint16 num_vertices = 0; // Loop over vertices in face Edge *edge = builder_face->mFirstEdge; do { // Remap to new index, not all points in the original input set are required to form the hull uint8 new_idx; int original_idx = edge->mStartIdx; VtxMap::iterator m = vertex_map.find(original_idx); if (m != vertex_map.end()) { // Found, reuse new_idx = m->second; } else { // This is a new point // Make relative to center of mass Vec3 p = inSettings.mPoints[original_idx] - mCenterOfMass; // Update local bounds mLocalBounds.Encapsulate(p); // Add to point list JPH_ASSERT(mPoints.size() <= 0xff); new_idx = (uint8)mPoints.size(); mPoints.push_back({ p }); vertex_map[original_idx] = new_idx; } // Append to vertex list JPH_ASSERT(mVertexIdx.size() < 0xffff); mVertexIdx.push_back(new_idx); num_vertices++; edge = edge->mNextEdge; } while (edge != builder_face->mFirstEdge); // Add face mFaces.push_back({ first_vertex, num_vertices }); // Add plane Plane plane = Plane::sFromPointAndNormal(builder_face->mCentroid - mCenterOfMass, builder_face->mNormal.Normalized()); mPlanes.push_back(plane); } // Test if GetSupportFunction can support this many points if (mPoints.size() > cMaxPointsInHull) { outResult.SetError(StringFormat("Internal error: Too many points in hull (%u), max allowed %d", (uint)mPoints.size(), cMaxPointsInHull)); return; } for (int p = 0; p < (int)mPoints.size(); ++p) { // For each point, find faces that use the point Array faces; for (int f = 0; f < (int)mFaces.size(); ++f) { const Face &face = mFaces[f]; for (int v = 0; v < face.mNumVertices; ++v) if (mVertexIdx[face.mFirstVertex + v] == p) { faces.push_back(f); break; } } if (faces.size() < 2) { outResult.SetError("A point must be connected to 2 or more faces!"); return; } // Find the 3 normals that form the largest tetrahedron // The largest tetrahedron we can get is ((1, 0, 0) x (0, 1, 0)) . (0, 0, 1) = 1, if the volume is only 5% of that, // the three vectors are too coplanar and we fall back to using only 2 plane normals float biggest_volume = 0.05f; int best3[3] = { -1, -1, -1 }; // When using 2 normals, we get the two with the biggest angle between them with a minimal difference of 1 degree // otherwise we fall back to just using 1 plane normal float smallest_dot = Cos(DegreesToRadians(1.0f)); int best2[2] = { -1, -1 }; for (int face1 = 0; face1 < (int)faces.size(); ++face1) { Vec3 normal1 = mPlanes[faces[face1]].GetNormal(); for (int face2 = face1 + 1; face2 < (int)faces.size(); ++face2) { Vec3 normal2 = mPlanes[faces[face2]].GetNormal(); Vec3 cross = normal1.Cross(normal2); // Determine the 2 face normals that are most apart float dot = normal1.Dot(normal2); if (dot < smallest_dot) { smallest_dot = dot; best2[0] = faces[face1]; best2[1] = faces[face2]; } // Determine the 3 face normals that form the largest tetrahedron for (int face3 = face2 + 1; face3 < (int)faces.size(); ++face3) { Vec3 normal3 = mPlanes[faces[face3]].GetNormal(); float volume = abs(cross.Dot(normal3)); if (volume > biggest_volume) { biggest_volume = volume; best3[0] = faces[face1]; best3[1] = faces[face2]; best3[2] = faces[face3]; } } } } // If we didn't find 3 planes, use 2, if we didn't find 2 use 1 if (best3[0] != -1) faces = { best3[0], best3[1], best3[2] }; else if (best2[0] != -1) faces = { best2[0], best2[1] }; else faces = { faces[0] }; // Copy the faces to the points buffer Point &point = mPoints[p]; point.mNumFaces = (int)faces.size(); for (int i = 0; i < (int)faces.size(); ++i) point.mFaces[i] = faces[i]; } // If the convex radius is already zero, there's no point in further reducing it if (mConvexRadius > 0.0f) { // Find out how thin the hull is by walking over all planes and checking the thickness of the hull in that direction float min_size = FLT_MAX; for (const Plane &plane : mPlanes) { // Take the point that is furthest away from the plane as thickness of this hull float max_dist = 0.0f; for (const Point &point : mPoints) { float dist = -plane.SignedDistance(point.mPosition); // Point is always behind plane, so we need to negate if (dist > max_dist) max_dist = dist; } min_size = min(min_size, max_dist); } // We need to fit in 2x the convex radius in min_size, so reduce the convex radius if it's bigger than that mConvexRadius = min(mConvexRadius, 0.5f * min_size); } // Now walk over all points and see if we have to further reduce the convex radius because of sharp edges if (mConvexRadius > 0.0f) { for (const Point &point : mPoints) if (point.mNumFaces != 1) // If we have a single face, shifting back is easy and we don't need to reduce the convex radius { // Get first two planes Plane p1 = mPlanes[point.mFaces[0]]; Plane p2 = mPlanes[point.mFaces[1]]; Plane p3; Vec3 offset_mask; if (point.mNumFaces == 3) { // Get third plane p3 = mPlanes[point.mFaces[2]]; // All 3 planes will be offset by the convex radius offset_mask = Vec3::sReplicate(1); } else { // Third plane has normal perpendicular to the other two planes and goes through the vertex position JPH_ASSERT(point.mNumFaces == 2); p3 = Plane::sFromPointAndNormal(point.mPosition, p1.GetNormal().Cross(p2.GetNormal())); // Only the first and 2nd plane will be offset, the 3rd plane is only there to guide the intersection point offset_mask = Vec3(1, 1, 0); } // Plane equation: point . normal + constant = 0 // Offsetting the plane backwards with convex radius r: point . normal + constant + r = 0 // To find the intersection 'point' of 3 planes we solve: // |n1x n1y n1z| |x| | r + c1 | // |n2x n2y n2z| |y| = - | r + c2 | <=> n point = -r (1, 1, 1) - (c1, c2, c3) // |n3x n3y n3z| |z| | r + c3 | // Where point = (x, y, z), n1x is the x component of the first plane, c1 = plane constant of plane 1, etc. // The relation between how much the intersection point shifts as a function of r is: -r * n^-1 (1, 1, 1) = r * offset // Where offset = -n^-1 (1, 1, 1) or -n^-1 (1, 1, 0) in case only the first 2 planes are offset // The error that is introduced by a convex radius r is: error = r * |offset| - r // So the max convex radius given error is: r = error / (|offset| - 1) Mat44 n = Mat44(Vec4(p1.GetNormal(), 0), Vec4(p2.GetNormal(), 0), Vec4(p3.GetNormal(), 0), Vec4(0, 0, 0, 1)).Transposed(); float det_n = n.GetDeterminant3x3(); if (det_n == 0.0f) { // If the determinant is zero, the matrix is not invertible so no solution exists to move the point backwards and we have to choose a convex radius of zero mConvexRadius = 0.0f; break; } Mat44 adj_n = n.Adjointed3x3(); float offset = ((adj_n * offset_mask) / det_n).Length(); JPH_ASSERT(offset > 1.0f); float max_convex_radius = inSettings.mMaxErrorConvexRadius / (offset - 1.0f); mConvexRadius = min(mConvexRadius, max_convex_radius); } } // Calculate the inner radius by getting the minimum distance from the origin to the planes of the hull mInnerRadius = FLT_MAX; for (const Plane &p : mPlanes) mInnerRadius = min(mInnerRadius, -p.GetConstant()); mInnerRadius = max(0.0f, mInnerRadius); // Clamp against zero, this should do nothing as the shape is centered around the center of mass but for flat convex hulls there may be numerical round off issues outResult.Set(this); } MassProperties ConvexHullShape::GetMassProperties() const { MassProperties p; float density = GetDensity(); // Calculate mass p.mMass = density * mVolume; // Calculate inertia matrix p.mInertia = density * mInertia; p.mInertia(3, 3) = 1.0f; return p; } Vec3 ConvexHullShape::GetSurfaceNormal(const SubShapeID &inSubShapeID, Vec3Arg inLocalSurfacePosition) const { JPH_ASSERT(inSubShapeID.IsEmpty(), "Invalid subshape ID"); const Plane &first_plane = mPlanes[0]; Vec3 best_normal = first_plane.GetNormal(); float best_dist = abs(first_plane.SignedDistance(inLocalSurfacePosition)); // Find the face that has the shortest distance to the surface point for (Array::size_type i = 1; i < mFaces.size(); ++i) { const Plane &plane = mPlanes[i]; Vec3 plane_normal = plane.GetNormal(); float dist = abs(plane.SignedDistance(inLocalSurfacePosition)); if (dist < best_dist) { best_dist = dist; best_normal = plane_normal; } } return best_normal; } class ConvexHullShape::HullNoConvex final : public Support { public: explicit HullNoConvex(float inConvexRadius) : mConvexRadius(inConvexRadius) { static_assert(sizeof(HullNoConvex) <= sizeof(SupportBuffer), "Buffer size too small"); JPH_ASSERT(IsAligned(this, alignof(HullNoConvex))); } virtual Vec3 GetSupport(Vec3Arg inDirection) const override { // Find the point with the highest projection on inDirection float best_dot = -FLT_MAX; Vec3 best_point = Vec3::sZero(); for (Vec3 point : mPoints) { // Check if its support is bigger than the current max float dot = point.Dot(inDirection); if (dot > best_dot) { best_dot = dot; best_point = point; } } return best_point; } virtual float GetConvexRadius() const override { return mConvexRadius; } using PointsArray = StaticArray; inline PointsArray & GetPoints() { return mPoints; } const PointsArray & GetPoints() const { return mPoints; } private: float mConvexRadius; PointsArray mPoints; }; class ConvexHullShape::HullWithConvex final : public Support { public: explicit HullWithConvex(const ConvexHullShape *inShape) : mShape(inShape) { static_assert(sizeof(HullWithConvex) <= sizeof(SupportBuffer), "Buffer size too small"); JPH_ASSERT(IsAligned(this, alignof(HullWithConvex))); } virtual Vec3 GetSupport(Vec3Arg inDirection) const override { // Find the point with the highest projection on inDirection float best_dot = -FLT_MAX; Vec3 best_point = Vec3::sZero(); for (const Point &point : mShape->mPoints) { // Check if its support is bigger than the current max float dot = point.mPosition.Dot(inDirection); if (dot > best_dot) { best_dot = dot; best_point = point.mPosition; } } return best_point; } virtual float GetConvexRadius() const override { return 0.0f; } private: const ConvexHullShape * mShape; }; class ConvexHullShape::HullWithConvexScaled final : public Support { public: HullWithConvexScaled(const ConvexHullShape *inShape, Vec3Arg inScale) : mShape(inShape), mScale(inScale) { static_assert(sizeof(HullWithConvexScaled) <= sizeof(SupportBuffer), "Buffer size too small"); JPH_ASSERT(IsAligned(this, alignof(HullWithConvexScaled))); } virtual Vec3 GetSupport(Vec3Arg inDirection) const override { // Find the point with the highest projection on inDirection float best_dot = -FLT_MAX; Vec3 best_point = Vec3::sZero(); for (const Point &point : mShape->mPoints) { // Calculate scaled position Vec3 pos = mScale * point.mPosition; // Check if its support is bigger than the current max float dot = pos.Dot(inDirection); if (dot > best_dot) { best_dot = dot; best_point = pos; } } return best_point; } virtual float GetConvexRadius() const override { return 0.0f; } private: const ConvexHullShape * mShape; Vec3 mScale; }; const ConvexShape::Support *ConvexHullShape::GetSupportFunction(ESupportMode inMode, SupportBuffer &inBuffer, Vec3Arg inScale) const { // If there's no convex radius, we don't need to shrink the hull if (mConvexRadius == 0.0f) { if (ScaleHelpers::IsNotScaled(inScale)) return new (&inBuffer) HullWithConvex(this); else return new (&inBuffer) HullWithConvexScaled(this, inScale); } switch (inMode) { case ESupportMode::IncludeConvexRadius: case ESupportMode::Default: if (ScaleHelpers::IsNotScaled(inScale)) return new (&inBuffer) HullWithConvex(this); else return new (&inBuffer) HullWithConvexScaled(this, inScale); case ESupportMode::ExcludeConvexRadius: if (ScaleHelpers::IsNotScaled(inScale)) { // Create support function HullNoConvex *hull = new (&inBuffer) HullNoConvex(mConvexRadius); HullNoConvex::PointsArray &transformed_points = hull->GetPoints(); JPH_ASSERT(mPoints.size() <= cMaxPointsInHull, "Not enough space, this should have been caught during shape creation!"); for (const Point &point : mPoints) { Vec3 new_point; if (point.mNumFaces == 1) { // Simply shift back by the convex radius using our 1 plane new_point = point.mPosition - mPlanes[point.mFaces[0]].GetNormal() * mConvexRadius; } else { // Get first two planes and offset inwards by convex radius Plane p1 = mPlanes[point.mFaces[0]].Offset(-mConvexRadius); Plane p2 = mPlanes[point.mFaces[1]].Offset(-mConvexRadius); Plane p3; if (point.mNumFaces == 3) { // Get third plane and offset inwards by convex radius p3 = mPlanes[point.mFaces[2]].Offset(-mConvexRadius); } else { // Third plane has normal perpendicular to the other two planes and goes through the vertex position JPH_ASSERT(point.mNumFaces == 2); p3 = Plane::sFromPointAndNormal(point.mPosition, p1.GetNormal().Cross(p2.GetNormal())); } // Find intersection point between the three planes if (!Plane::sIntersectPlanes(p1, p2, p3, new_point)) { // Fallback: Just push point back using the first plane new_point = point.mPosition - p1.GetNormal() * mConvexRadius; } } // Add point transformed_points.push_back(new_point); } return hull; } else { // Calculate scaled convex radius float convex_radius = ScaleHelpers::ScaleConvexRadius(mConvexRadius, inScale); // Create new support function HullNoConvex *hull = new (&inBuffer) HullNoConvex(convex_radius); HullNoConvex::PointsArray &transformed_points = hull->GetPoints(); JPH_ASSERT(mPoints.size() <= cMaxPointsInHull, "Not enough space, this should have been caught during shape creation!"); // Precalculate inverse scale Vec3 inv_scale = inScale.Reciprocal(); for (const Point &point : mPoints) { // Calculate scaled position Vec3 pos = inScale * point.mPosition; // Transform normals for plane 1 with scale Vec3 n1 = (inv_scale * mPlanes[point.mFaces[0]].GetNormal()).Normalized(); Vec3 new_point; if (point.mNumFaces == 1) { // Simply shift back by the convex radius using our 1 plane new_point = pos - n1 * convex_radius; } else { // Transform normals for plane 2 with scale Vec3 n2 = (inv_scale * mPlanes[point.mFaces[1]].GetNormal()).Normalized(); // Get first two planes and offset inwards by convex radius Plane p1 = Plane::sFromPointAndNormal(pos, n1).Offset(-convex_radius); Plane p2 = Plane::sFromPointAndNormal(pos, n2).Offset(-convex_radius); Plane p3; if (point.mNumFaces == 3) { // Transform last normal with scale Vec3 n3 = (inv_scale * mPlanes[point.mFaces[2]].GetNormal()).Normalized(); // Get third plane and offset inwards by convex radius p3 = Plane::sFromPointAndNormal(pos, n3).Offset(-convex_radius); } else { // Third plane has normal perpendicular to the other two planes and goes through the vertex position JPH_ASSERT(point.mNumFaces == 2); p3 = Plane::sFromPointAndNormal(pos, n1.Cross(n2)); } // Find intersection point between the three planes if (!Plane::sIntersectPlanes(p1, p2, p3, new_point)) { // Fallback: Just push point back using the first plane new_point = pos - n1 * convex_radius; } } // Add point transformed_points.push_back(new_point); } return hull; } } JPH_ASSERT(false); return nullptr; } void ConvexHullShape::GetSupportingFace(const SubShapeID &inSubShapeID, Vec3Arg inDirection, Vec3Arg inScale, Mat44Arg inCenterOfMassTransform, SupportingFace &outVertices) const { JPH_ASSERT(inSubShapeID.IsEmpty(), "Invalid subshape ID"); Vec3 inv_scale = inScale.Reciprocal(); // Need to transform the plane normals using inScale // Transforming a direction with matrix M is done through multiplying by (M^-1)^T // In this case M is a diagonal matrix with the scale vector, so we need to multiply our normal by 1 / scale and renormalize afterwards Vec3 plane0_normal = inv_scale * mPlanes[0].GetNormal(); float best_dot = plane0_normal.Dot(inDirection) / plane0_normal.Length(); int best_face_idx = 0; for (Array::size_type i = 1; i < mPlanes.size(); ++i) { Vec3 plane_normal = inv_scale * mPlanes[i].GetNormal(); float dot = plane_normal.Dot(inDirection) / plane_normal.Length(); if (dot < best_dot) { best_dot = dot; best_face_idx = (int)i; } } // Get vertices const Face &best_face = mFaces[best_face_idx]; const uint8 *first_vtx = mVertexIdx.data() + best_face.mFirstVertex; const uint8 *end_vtx = first_vtx + best_face.mNumVertices; // If we have more than 1/2 the capacity of outVertices worth of vertices, we start skipping vertices (note we can't fill the buffer completely since extra edges will be generated by clipping). // TODO: This really needs a better algorithm to determine which vertices are important! int max_vertices_to_return = outVertices.capacity() / 2; int delta_vtx = (int(best_face.mNumVertices) + max_vertices_to_return) / max_vertices_to_return; // Calculate transform with scale Mat44 transform = inCenterOfMassTransform.PreScaled(inScale); if (ScaleHelpers::IsInsideOut(inScale)) { // Flip winding of supporting face for (const uint8 *v = end_vtx - 1; v >= first_vtx; v -= delta_vtx) outVertices.push_back(transform * mPoints[*v].mPosition); } else { // Normal winding of supporting face for (const uint8 *v = first_vtx; v < end_vtx; v += delta_vtx) outVertices.push_back(transform * mPoints[*v].mPosition); } } void ConvexHullShape::GetSubmergedVolume(Mat44Arg inCenterOfMassTransform, Vec3Arg inScale, const Plane &inSurface, float &outTotalVolume, float &outSubmergedVolume, Vec3 &outCenterOfBuoyancy JPH_IF_DEBUG_RENDERER(, RVec3Arg inBaseOffset)) const { // Trivially calculate total volume Vec3 abs_scale = inScale.Abs(); outTotalVolume = mVolume * abs_scale.GetX() * abs_scale.GetY() * abs_scale.GetZ(); // Check if shape has been scaled inside out bool is_inside_out = ScaleHelpers::IsInsideOut(inScale); // Convert the points to world space and determine the distance to the surface int num_points = int(mPoints.size()); PolyhedronSubmergedVolumeCalculator::Point *buffer = (PolyhedronSubmergedVolumeCalculator::Point *)JPH_STACK_ALLOC(num_points * sizeof(PolyhedronSubmergedVolumeCalculator::Point)); PolyhedronSubmergedVolumeCalculator submerged_vol_calc(inCenterOfMassTransform * Mat44::sScale(inScale), &mPoints[0].mPosition, sizeof(Point), num_points, inSurface, buffer JPH_IF_DEBUG_RENDERER(, inBaseOffset)); if (submerged_vol_calc.AreAllAbove()) { // We're above the water outSubmergedVolume = 0.0f; outCenterOfBuoyancy = Vec3::sZero(); } else if (submerged_vol_calc.AreAllBelow()) { // We're fully submerged outSubmergedVolume = outTotalVolume; outCenterOfBuoyancy = inCenterOfMassTransform.GetTranslation(); } else { // Calculate submerged volume int reference_point_idx = submerged_vol_calc.GetReferencePointIdx(); for (const Face &f : mFaces) { const uint8 *first_vtx = mVertexIdx.data() + f.mFirstVertex; const uint8 *end_vtx = first_vtx + f.mNumVertices; // If any of the vertices of this face are the reference point, the volume will be zero so we can skip this face bool degenerate = false; for (const uint8 *v = first_vtx; v < end_vtx; ++v) if (*v == reference_point_idx) { degenerate = true; break; } if (degenerate) continue; // Triangulate the face int i1 = *first_vtx; if (is_inside_out) { // Reverse winding for (const uint8 *v = first_vtx + 2; v < end_vtx; ++v) { int i2 = *(v - 1); int i3 = *v; submerged_vol_calc.AddFace(i1, i3, i2); } } else { // Normal winding for (const uint8 *v = first_vtx + 2; v < end_vtx; ++v) { int i2 = *(v - 1); int i3 = *v; submerged_vol_calc.AddFace(i1, i2, i3); } } } // Get the results submerged_vol_calc.GetResult(outSubmergedVolume, outCenterOfBuoyancy); } #ifdef JPH_DEBUG_RENDERER // Draw center of buoyancy if (sDrawSubmergedVolumes) DebugRenderer::sInstance->DrawWireSphere(inBaseOffset + outCenterOfBuoyancy, 0.05f, Color::sRed, 1); #endif // JPH_DEBUG_RENDERER } #ifdef JPH_DEBUG_RENDERER void ConvexHullShape::Draw(DebugRenderer *inRenderer, RMat44Arg inCenterOfMassTransform, Vec3Arg inScale, ColorArg inColor, bool inUseMaterialColors, bool inDrawWireframe) const { if (mGeometry == nullptr) { Array triangles; for (const Face &f : mFaces) { const uint8 *first_vtx = mVertexIdx.data() + f.mFirstVertex; const uint8 *end_vtx = first_vtx + f.mNumVertices; // Draw first triangle of polygon Vec3 v0 = mPoints[first_vtx[0]].mPosition; Vec3 v1 = mPoints[first_vtx[1]].mPosition; Vec3 v2 = mPoints[first_vtx[2]].mPosition; Vec3 uv_direction = (v1 - v0).Normalized(); triangles.push_back({ v0, v1, v2, Color::sWhite, v0, uv_direction }); // Draw any other triangles in this polygon for (const uint8 *v = first_vtx + 3; v < end_vtx; ++v) triangles.push_back({ v0, mPoints[*(v - 1)].mPosition, mPoints[*v].mPosition, Color::sWhite, v0, uv_direction }); } mGeometry = new DebugRenderer::Geometry(inRenderer->CreateTriangleBatch(triangles), GetLocalBounds()); } // Test if the shape is scaled inside out DebugRenderer::ECullMode cull_mode = ScaleHelpers::IsInsideOut(inScale)? DebugRenderer::ECullMode::CullFrontFace : DebugRenderer::ECullMode::CullBackFace; // Determine the draw mode DebugRenderer::EDrawMode draw_mode = inDrawWireframe? DebugRenderer::EDrawMode::Wireframe : DebugRenderer::EDrawMode::Solid; // Draw the geometry Color color = inUseMaterialColors? GetMaterial()->GetDebugColor() : inColor; RMat44 transform = inCenterOfMassTransform.PreScaled(inScale); inRenderer->DrawGeometry(transform, color, mGeometry, cull_mode, DebugRenderer::ECastShadow::On, draw_mode); // Draw the outline if requested if (sDrawFaceOutlines) for (const Face &f : mFaces) { const uint8 *first_vtx = mVertexIdx.data() + f.mFirstVertex; const uint8 *end_vtx = first_vtx + f.mNumVertices; // Draw edges of face inRenderer->DrawLine(transform * mPoints[*(end_vtx - 1)].mPosition, transform * mPoints[*first_vtx].mPosition, Color::sGrey); for (const uint8 *v = first_vtx + 1; v < end_vtx; ++v) inRenderer->DrawLine(transform * mPoints[*(v - 1)].mPosition, transform * mPoints[*v].mPosition, Color::sGrey); } } void ConvexHullShape::DrawShrunkShape(DebugRenderer *inRenderer, RMat44Arg inCenterOfMassTransform, Vec3Arg inScale) const { // Get the shrunk points SupportBuffer buffer; const HullNoConvex *support = mConvexRadius > 0.0f? static_cast(GetSupportFunction(ESupportMode::ExcludeConvexRadius, buffer, inScale)) : nullptr; RMat44 transform = inCenterOfMassTransform * Mat44::sScale(inScale); for (int p = 0; p < (int)mPoints.size(); ++p) { const Point &point = mPoints[p]; RVec3 position = transform * point.mPosition; RVec3 shrunk_point = support != nullptr? transform * support->GetPoints()[p] : position; // Draw difference between shrunk position and position inRenderer->DrawLine(position, shrunk_point, Color::sGreen); // Draw face normals that are contributing for (int i = 0; i < point.mNumFaces; ++i) inRenderer->DrawLine(position, position + 0.1f * mPlanes[point.mFaces[i]].GetNormal(), Color::sYellow); // Draw point index inRenderer->DrawText3D(position, ConvertToString(p), Color::sWhite, 0.1f); } } #endif // JPH_DEBUG_RENDERER bool ConvexHullShape::CastRayHelper(const RayCast &inRay, float &outMinFraction, float &outMaxFraction) const { if (mFaces.size() == 2) { // If we have only 2 faces, we're a flat convex hull and we need to test edges instead of planes // Check if plane is parallel to ray const Plane &p = mPlanes.front(); Vec3 plane_normal = p.GetNormal(); float direction_projection = inRay.mDirection.Dot(plane_normal); if (abs(direction_projection) >= 1.0e-12f) { // Calculate intersection point float distance_to_plane = inRay.mOrigin.Dot(plane_normal) + p.GetConstant(); float fraction = -distance_to_plane / direction_projection; if (fraction < 0.0f || fraction > 1.0f) { // Does not hit plane, no hit outMinFraction = 0.0f; outMaxFraction = 1.0f + FLT_EPSILON; return false; } Vec3 intersection_point = inRay.mOrigin + fraction * inRay.mDirection; // Test all edges to see if point is inside polygon const Face &f = mFaces.front(); const uint8 *first_vtx = mVertexIdx.data() + f.mFirstVertex; const uint8 *end_vtx = first_vtx + f.mNumVertices; Vec3 p1 = mPoints[*end_vtx].mPosition; for (const uint8 *v = first_vtx; v < end_vtx; ++v) { Vec3 p2 = mPoints[*v].mPosition; if ((p2 - p1).Cross(intersection_point - p1).Dot(plane_normal) < 0.0f) { // Outside polygon, no hit outMinFraction = 0.0f; outMaxFraction = 1.0f + FLT_EPSILON; return false; } p1 = p2; } // Inside polygon, a hit outMinFraction = fraction; outMaxFraction = fraction; return true; } else { // Parallel ray doesn't hit outMinFraction = 0.0f; outMaxFraction = 1.0f + FLT_EPSILON; return false; } } else { // Clip ray against all planes int fractions_set = 0; bool all_inside = true; float min_fraction = 0.0f, max_fraction = 1.0f + FLT_EPSILON; for (const Plane &p : mPlanes) { // Check if the ray origin is behind this plane Vec3 plane_normal = p.GetNormal(); float distance_to_plane = inRay.mOrigin.Dot(plane_normal) + p.GetConstant(); bool is_outside = distance_to_plane > 0.0f; all_inside &= !is_outside; // Check if plane is parallel to ray float direction_projection = inRay.mDirection.Dot(plane_normal); if (abs(direction_projection) >= 1.0e-12f) { // Get intersection fraction between ray and plane float fraction = -distance_to_plane / direction_projection; // Update interval of ray that is inside the hull if (direction_projection < 0.0f) { min_fraction = max(fraction, min_fraction); fractions_set |= 1; } else { max_fraction = min(fraction, max_fraction); fractions_set |= 2; } } else if (is_outside) return false; // Outside the plane and parallel, no hit! } // Test if both min and max have been set if (fractions_set == 3) { // Output fractions outMinFraction = min_fraction; outMaxFraction = max_fraction; // Test if the infinite ray intersects with the hull (the length will be checked later) return min_fraction <= max_fraction && max_fraction >= 0.0f; } else { // Degenerate case, either the ray is parallel to all planes or the ray has zero length outMinFraction = 0.0f; outMaxFraction = 1.0f + FLT_EPSILON; // Return if the origin is inside the hull return all_inside; } } } bool ConvexHullShape::CastRay(const RayCast &inRay, const SubShapeIDCreator &inSubShapeIDCreator, RayCastResult &ioHit) const { // Determine if ray hits the shape float min_fraction, max_fraction; if (CastRayHelper(inRay, min_fraction, max_fraction) && min_fraction < ioHit.mFraction) // Check if this is a closer hit { // Better hit than the current hit ioHit.mFraction = min_fraction; ioHit.mSubShapeID2 = inSubShapeIDCreator.GetID(); return true; } return false; } void ConvexHullShape::CastRay(const RayCast &inRay, const RayCastSettings &inRayCastSettings, const SubShapeIDCreator &inSubShapeIDCreator, CastRayCollector &ioCollector, const ShapeFilter &inShapeFilter) const { // Test shape filter if (!inShapeFilter.ShouldCollide(this, inSubShapeIDCreator.GetID())) return; // Determine if ray hits the shape float min_fraction, max_fraction; if (CastRayHelper(inRay, min_fraction, max_fraction) && min_fraction < ioCollector.GetEarlyOutFraction()) // Check if this is closer than the early out fraction { // Better hit than the current hit RayCastResult hit; hit.mBodyID = TransformedShape::sGetBodyID(ioCollector.GetContext()); hit.mSubShapeID2 = inSubShapeIDCreator.GetID(); // Check front side hit if (inRayCastSettings.mTreatConvexAsSolid || min_fraction > 0.0f) { hit.mFraction = min_fraction; ioCollector.AddHit(hit); } // Check back side hit if (inRayCastSettings.mBackFaceModeConvex == EBackFaceMode::CollideWithBackFaces && max_fraction < ioCollector.GetEarlyOutFraction()) { hit.mFraction = max_fraction; ioCollector.AddHit(hit); } } } void ConvexHullShape::CollidePoint(Vec3Arg inPoint, const SubShapeIDCreator &inSubShapeIDCreator, CollidePointCollector &ioCollector, const ShapeFilter &inShapeFilter) const { // Test shape filter if (!inShapeFilter.ShouldCollide(this, inSubShapeIDCreator.GetID())) return; // Check if point is behind all planes for (const Plane &p : mPlanes) if (p.SignedDistance(inPoint) > 0.0f) return; // Point is inside ioCollector.AddHit({ TransformedShape::sGetBodyID(ioCollector.GetContext()), inSubShapeIDCreator.GetID() }); } void ConvexHullShape::CollideSoftBodyVertices(Mat44Arg inCenterOfMassTransform, Vec3Arg inScale, const CollideSoftBodyVertexIterator &inVertices, uint inNumVertices, int inCollidingShapeIndex) const { Mat44 inverse_transform = inCenterOfMassTransform.InversedRotationTranslation(); Vec3 inv_scale = inScale.Reciprocal(); bool is_not_scaled = ScaleHelpers::IsNotScaled(inScale); float scale_flip = ScaleHelpers::IsInsideOut(inScale)? -1.0f : 1.0f; for (CollideSoftBodyVertexIterator v = inVertices, sbv_end = inVertices + inNumVertices; v != sbv_end; ++v) if (v.GetInvMass() > 0.0f) { Vec3 local_pos = inverse_transform * v.GetPosition(); // Find most facing plane float max_distance = -FLT_MAX; Vec3 max_plane_normal = Vec3::sZero(); uint max_plane_idx = 0; if (is_not_scaled) { // Without scale, it is trivial to calculate the distance to the hull for (const Plane &p : mPlanes) { float distance = p.SignedDistance(local_pos); if (distance > max_distance) { max_distance = distance; max_plane_normal = p.GetNormal(); max_plane_idx = uint(&p - mPlanes.data()); } } } else { // When there's scale we need to calculate the planes first for (uint i = 0; i < (uint)mPlanes.size(); ++i) { // Calculate plane normal and point by scaling the original plane Vec3 plane_normal = (inv_scale * mPlanes[i].GetNormal()).Normalized(); Vec3 plane_point = inScale * mPoints[mVertexIdx[mFaces[i].mFirstVertex]].mPosition; float distance = plane_normal.Dot(local_pos - plane_point); if (distance > max_distance) { max_distance = distance; max_plane_normal = plane_normal; max_plane_idx = i; } } } bool is_outside = max_distance > 0.0f; // Project point onto that plane Vec3 closest_point = local_pos - max_distance * max_plane_normal; // Check edges if we're outside the hull (when inside we know the closest face is also the closest point to the surface) if (is_outside) { // Loop over edges float closest_point_dist_sq = FLT_MAX; const Face &face = mFaces[max_plane_idx]; for (const uint8 *v_start = &mVertexIdx[face.mFirstVertex], *v1 = v_start, *v_end = v_start + face.mNumVertices; v1 < v_end; ++v1) { // Find second point const uint8 *v2 = v1 + 1; if (v2 == v_end) v2 = v_start; // Get edge points Vec3 p1 = inScale * mPoints[*v1].mPosition; Vec3 p2 = inScale * mPoints[*v2].mPosition; // Check if the position is outside the edge (if not, the face will be closer) Vec3 edge_normal = (p2 - p1).Cross(max_plane_normal); if (scale_flip * edge_normal.Dot(local_pos - p1) > 0.0f) { // Get closest point on edge uint32 set; Vec3 closest = ClosestPoint::GetClosestPointOnLine(p1 - local_pos, p2 - local_pos, set); float distance_sq = closest.LengthSq(); if (distance_sq < closest_point_dist_sq) closest_point = local_pos + closest; } } } // Check if this is the largest penetration Vec3 normal = local_pos - closest_point; float normal_length = normal.Length(); float penetration = normal_length; if (is_outside) penetration = -penetration; else normal = -normal; if (v.UpdatePenetration(penetration)) { // Calculate contact plane normal = normal_length > 0.0f? normal / normal_length : max_plane_normal; Plane plane = Plane::sFromPointAndNormal(closest_point, normal); // Store collision v.SetCollision(plane.GetTransformed(inCenterOfMassTransform), inCollidingShapeIndex); } } } class ConvexHullShape::CHSGetTrianglesContext { public: CHSGetTrianglesContext(Mat44Arg inTransform, bool inIsInsideOut) : mTransform(inTransform), mIsInsideOut(inIsInsideOut) { } Mat44 mTransform; bool mIsInsideOut; size_t mCurrentFace = 0; }; void ConvexHullShape::GetTrianglesStart(GetTrianglesContext &ioContext, const AABox &inBox, Vec3Arg inPositionCOM, QuatArg inRotation, Vec3Arg inScale) const { static_assert(sizeof(CHSGetTrianglesContext) <= sizeof(GetTrianglesContext), "GetTrianglesContext too small"); JPH_ASSERT(IsAligned(&ioContext, alignof(CHSGetTrianglesContext))); new (&ioContext) CHSGetTrianglesContext(Mat44::sRotationTranslation(inRotation, inPositionCOM) * Mat44::sScale(inScale), ScaleHelpers::IsInsideOut(inScale)); } int ConvexHullShape::GetTrianglesNext(GetTrianglesContext &ioContext, int inMaxTrianglesRequested, Float3 *outTriangleVertices, const PhysicsMaterial **outMaterials) const { static_assert(cGetTrianglesMinTrianglesRequested >= 12, "cGetTrianglesMinTrianglesRequested is too small"); JPH_ASSERT(inMaxTrianglesRequested >= cGetTrianglesMinTrianglesRequested); CHSGetTrianglesContext &context = (CHSGetTrianglesContext &)ioContext; int total_num_triangles = 0; for (; context.mCurrentFace < mFaces.size(); ++context.mCurrentFace) { const Face &f = mFaces[context.mCurrentFace]; const uint8 *first_vtx = mVertexIdx.data() + f.mFirstVertex; const uint8 *end_vtx = first_vtx + f.mNumVertices; // Check if there is still room in the output buffer for this face int num_triangles = f.mNumVertices - 2; inMaxTrianglesRequested -= num_triangles; if (inMaxTrianglesRequested < 0) break; total_num_triangles += num_triangles; // Get first triangle of polygon Vec3 v0 = context.mTransform * mPoints[first_vtx[0]].mPosition; Vec3 v1 = context.mTransform * mPoints[first_vtx[1]].mPosition; Vec3 v2 = context.mTransform * mPoints[first_vtx[2]].mPosition; v0.StoreFloat3(outTriangleVertices++); if (context.mIsInsideOut) { // Store first triangle in this polygon flipped v2.StoreFloat3(outTriangleVertices++); v1.StoreFloat3(outTriangleVertices++); // Store other triangles in this polygon flipped for (const uint8 *v = first_vtx + 3; v < end_vtx; ++v) { v0.StoreFloat3(outTriangleVertices++); (context.mTransform * mPoints[*v].mPosition).StoreFloat3(outTriangleVertices++); (context.mTransform * mPoints[*(v - 1)].mPosition).StoreFloat3(outTriangleVertices++); } } else { // Store first triangle in this polygon v1.StoreFloat3(outTriangleVertices++); v2.StoreFloat3(outTriangleVertices++); // Store other triangles in this polygon for (const uint8 *v = first_vtx + 3; v < end_vtx; ++v) { v0.StoreFloat3(outTriangleVertices++); (context.mTransform * mPoints[*(v - 1)].mPosition).StoreFloat3(outTriangleVertices++); (context.mTransform * mPoints[*v].mPosition).StoreFloat3(outTriangleVertices++); } } } // Store materials if (outMaterials != nullptr) { const PhysicsMaterial *material = GetMaterial(); for (const PhysicsMaterial **m = outMaterials, **m_end = outMaterials + total_num_triangles; m < m_end; ++m) *m = material; } return total_num_triangles; } void ConvexHullShape::SaveBinaryState(StreamOut &inStream) const { ConvexShape::SaveBinaryState(inStream); inStream.Write(mCenterOfMass); inStream.Write(mInertia); inStream.Write(mLocalBounds.mMin); inStream.Write(mLocalBounds.mMax); inStream.Write(mPoints); inStream.Write(mFaces); inStream.Write(mPlanes); inStream.Write(mVertexIdx); inStream.Write(mConvexRadius); inStream.Write(mVolume); inStream.Write(mInnerRadius); } void ConvexHullShape::RestoreBinaryState(StreamIn &inStream) { ConvexShape::RestoreBinaryState(inStream); inStream.Read(mCenterOfMass); inStream.Read(mInertia); inStream.Read(mLocalBounds.mMin); inStream.Read(mLocalBounds.mMax); inStream.Read(mPoints); inStream.Read(mFaces); inStream.Read(mPlanes); inStream.Read(mVertexIdx); inStream.Read(mConvexRadius); inStream.Read(mVolume); inStream.Read(mInnerRadius); } Shape::Stats ConvexHullShape::GetStats() const { // Count number of triangles uint triangle_count = 0; for (const Face &f : mFaces) triangle_count += f.mNumVertices - 2; return Stats( sizeof(*this) + mPoints.size() * sizeof(Point) + mFaces.size() * sizeof(Face) + mPlanes.size() * sizeof(Plane) + mVertexIdx.size() * sizeof(uint8), triangle_count); } void ConvexHullShape::sRegister() { ShapeFunctions &f = ShapeFunctions::sGet(EShapeSubType::ConvexHull); f.mConstruct = []() -> Shape * { return new ConvexHullShape; }; f.mColor = Color::sGreen; } JPH_NAMESPACE_END