// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics) // SPDX-FileCopyrightText: 2021 Jorrit Rouwe // SPDX-License-Identifier: MIT #include #include #include JPH_NAMESPACE_BEGIN bool OrientedBox::Overlaps(const AABox &inBox, float inEpsilon) const { // Taken from: Real Time Collision Detection - Christer Ericson // Chapter 4.4.1, page 103-105. // Note that the code is swapped around: A is the aabox and B is the oriented box (this saves us from having to invert the orientation of the oriented box) // Convert AABox to center / extent representation Vec3 a_center = inBox.GetCenter(); Vec3 a_half_extents = inBox.GetExtent(); // Compute rotation matrix expressing b in a's coordinate frame Mat44 rot(mOrientation.GetColumn4(0), mOrientation.GetColumn4(1), mOrientation.GetColumn4(2), mOrientation.GetColumn4(3) - Vec4(a_center, 0)); // Compute common subexpressions. Add in an epsilon term to // counteract arithmetic errors when two edges are parallel and // their cross product is (near) null (see text for details) Vec3 epsilon = Vec3::sReplicate(inEpsilon); Vec3 abs_r[3] { rot.GetAxisX().Abs() + epsilon, rot.GetAxisY().Abs() + epsilon, rot.GetAxisZ().Abs() + epsilon }; // Test axes L = A0, L = A1, L = A2 float ra, rb; for (int i = 0; i < 3; i++) { ra = a_half_extents[i]; rb = mHalfExtents[0] * abs_r[0][i] + mHalfExtents[1] * abs_r[1][i] + mHalfExtents[2] * abs_r[2][i]; if (abs(rot(i, 3)) > ra + rb) return false; } // Test axes L = B0, L = B1, L = B2 for (int i = 0; i < 3; i++) { ra = a_half_extents.Dot(abs_r[i]); rb = mHalfExtents[i]; if (abs(rot.GetTranslation().Dot(rot.GetColumn3(i))) > ra + rb) return false; } // Test axis L = A0 x B0 ra = a_half_extents[1] * abs_r[0][2] + a_half_extents[2] * abs_r[0][1]; rb = mHalfExtents[1] * abs_r[2][0] + mHalfExtents[2] * abs_r[1][0]; if (abs(rot(2, 3) * rot(1, 0) - rot(1, 3) * rot(2, 0)) > ra + rb) return false; // Test axis L = A0 x B1 ra = a_half_extents[1] * abs_r[1][2] + a_half_extents[2] * abs_r[1][1]; rb = mHalfExtents[0] * abs_r[2][0] + mHalfExtents[2] * abs_r[0][0]; if (abs(rot(2, 3) * rot(1, 1) - rot(1, 3) * rot(2, 1)) > ra + rb) return false; // Test axis L = A0 x B2 ra = a_half_extents[1] * abs_r[2][2] + a_half_extents[2] * abs_r[2][1]; rb = mHalfExtents[0] * abs_r[1][0] + mHalfExtents[1] * abs_r[0][0]; if (abs(rot(2, 3) * rot(1, 2) - rot(1, 3) * rot(2, 2)) > ra + rb) return false; // Test axis L = A1 x B0 ra = a_half_extents[0] * abs_r[0][2] + a_half_extents[2] * abs_r[0][0]; rb = mHalfExtents[1] * abs_r[2][1] + mHalfExtents[2] * abs_r[1][1]; if (abs(rot(0, 3) * rot(2, 0) - rot(2, 3) * rot(0, 0)) > ra + rb) return false; // Test axis L = A1 x B1 ra = a_half_extents[0] * abs_r[1][2] + a_half_extents[2] * abs_r[1][0]; rb = mHalfExtents[0] * abs_r[2][1] + mHalfExtents[2] * abs_r[0][1]; if (abs(rot(0, 3) * rot(2, 1) - rot(2, 3) * rot(0, 1)) > ra + rb) return false; // Test axis L = A1 x B2 ra = a_half_extents[0] * abs_r[2][2] + a_half_extents[2] * abs_r[2][0]; rb = mHalfExtents[0] * abs_r[1][1] + mHalfExtents[1] * abs_r[0][1]; if (abs(rot(0, 3) * rot(2, 2) - rot(2, 3) * rot(0, 2)) > ra + rb) return false; // Test axis L = A2 x B0 ra = a_half_extents[0] * abs_r[0][1] + a_half_extents[1] * abs_r[0][0]; rb = mHalfExtents[1] * abs_r[2][2] + mHalfExtents[2] * abs_r[1][2]; if (abs(rot(1, 3) * rot(0, 0) - rot(0, 3) * rot(1, 0)) > ra + rb) return false; // Test axis L = A2 x B1 ra = a_half_extents[0] * abs_r[1][1] + a_half_extents[1] * abs_r[1][0]; rb = mHalfExtents[0] * abs_r[2][2] + mHalfExtents[2] * abs_r[0][2]; if (abs(rot(1, 3) * rot(0, 1) - rot(0, 3) * rot(1, 1)) > ra + rb) return false; // Test axis L = A2 x B2 ra = a_half_extents[0] * abs_r[2][1] + a_half_extents[1] * abs_r[2][0]; rb = mHalfExtents[0] * abs_r[1][2] + mHalfExtents[1] * abs_r[0][2]; if (abs(rot(1, 3) * rot(0, 2) - rot(0, 3) * rot(1, 2)) > ra + rb) return false; // Since no separating axis is found, the OBB and AAB must be intersecting return true; } bool OrientedBox::Overlaps(const OrientedBox &inBox, float inEpsilon) const { // Taken from: Real Time Collision Detection - Christer Ericson // Chapter 4.4.1, page 103-105. // Note that A is this, B is inBox // Compute rotation matrix expressing b in a's coordinate frame Mat44 rot = mOrientation.InversedRotationTranslation() * inBox.mOrientation; // Compute common subexpressions. Add in an epsilon term to // counteract arithmetic errors when two edges are parallel and // their cross product is (near) null (see text for details) Vec3 epsilon = Vec3::sReplicate(inEpsilon); Vec3 abs_r[3] { rot.GetAxisX().Abs() + epsilon, rot.GetAxisY().Abs() + epsilon, rot.GetAxisZ().Abs() + epsilon }; // Test axes L = A0, L = A1, L = A2 float ra, rb; for (int i = 0; i < 3; i++) { ra = mHalfExtents[i]; rb = inBox.mHalfExtents[0] * abs_r[0][i] + inBox.mHalfExtents[1] * abs_r[1][i] + inBox.mHalfExtents[2] * abs_r[2][i]; if (abs(rot(i, 3)) > ra + rb) return false; } // Test axes L = B0, L = B1, L = B2 for (int i = 0; i < 3; i++) { ra = mHalfExtents.Dot(abs_r[i]); rb = inBox.mHalfExtents[i]; if (abs(rot.GetTranslation().Dot(rot.GetColumn3(i))) > ra + rb) return false; } // Test axis L = A0 x B0 ra = mHalfExtents[1] * abs_r[0][2] + mHalfExtents[2] * abs_r[0][1]; rb = inBox.mHalfExtents[1] * abs_r[2][0] + inBox.mHalfExtents[2] * abs_r[1][0]; if (abs(rot(2, 3) * rot(1, 0) - rot(1, 3) * rot(2, 0)) > ra + rb) return false; // Test axis L = A0 x B1 ra = mHalfExtents[1] * abs_r[1][2] + mHalfExtents[2] * abs_r[1][1]; rb = inBox.mHalfExtents[0] * abs_r[2][0] + inBox.mHalfExtents[2] * abs_r[0][0]; if (abs(rot(2, 3) * rot(1, 1) - rot(1, 3) * rot(2, 1)) > ra + rb) return false; // Test axis L = A0 x B2 ra = mHalfExtents[1] * abs_r[2][2] + mHalfExtents[2] * abs_r[2][1]; rb = inBox.mHalfExtents[0] * abs_r[1][0] + inBox.mHalfExtents[1] * abs_r[0][0]; if (abs(rot(2, 3) * rot(1, 2) - rot(1, 3) * rot(2, 2)) > ra + rb) return false; // Test axis L = A1 x B0 ra = mHalfExtents[0] * abs_r[0][2] + mHalfExtents[2] * abs_r[0][0]; rb = inBox.mHalfExtents[1] * abs_r[2][1] + inBox.mHalfExtents[2] * abs_r[1][1]; if (abs(rot(0, 3) * rot(2, 0) - rot(2, 3) * rot(0, 0)) > ra + rb) return false; // Test axis L = A1 x B1 ra = mHalfExtents[0] * abs_r[1][2] + mHalfExtents[2] * abs_r[1][0]; rb = inBox.mHalfExtents[0] * abs_r[2][1] + inBox.mHalfExtents[2] * abs_r[0][1]; if (abs(rot(0, 3) * rot(2, 1) - rot(2, 3) * rot(0, 1)) > ra + rb) return false; // Test axis L = A1 x B2 ra = mHalfExtents[0] * abs_r[2][2] + mHalfExtents[2] * abs_r[2][0]; rb = inBox.mHalfExtents[0] * abs_r[1][1] + inBox.mHalfExtents[1] * abs_r[0][1]; if (abs(rot(0, 3) * rot(2, 2) - rot(2, 3) * rot(0, 2)) > ra + rb) return false; // Test axis L = A2 x B0 ra = mHalfExtents[0] * abs_r[0][1] + mHalfExtents[1] * abs_r[0][0]; rb = inBox.mHalfExtents[1] * abs_r[2][2] + inBox.mHalfExtents[2] * abs_r[1][2]; if (abs(rot(1, 3) * rot(0, 0) - rot(0, 3) * rot(1, 0)) > ra + rb) return false; // Test axis L = A2 x B1 ra = mHalfExtents[0] * abs_r[1][1] + mHalfExtents[1] * abs_r[1][0]; rb = inBox.mHalfExtents[0] * abs_r[2][2] + inBox.mHalfExtents[2] * abs_r[0][2]; if (abs(rot(1, 3) * rot(0, 1) - rot(0, 3) * rot(1, 1)) > ra + rb) return false; // Test axis L = A2 x B2 ra = mHalfExtents[0] * abs_r[2][1] + mHalfExtents[1] * abs_r[2][0]; rb = inBox.mHalfExtents[0] * abs_r[1][2] + inBox.mHalfExtents[1] * abs_r[0][2]; if (abs(rot(1, 3) * rot(0, 2) - rot(0, 3) * rot(1, 2)) > ra + rb) return false; // Since no separating axis is found, the OBBs must be intersecting return true; } JPH_NAMESPACE_END