maintain essential topological invariants

This commit is contained in:
Irlan 2018-05-09 05:44:09 -03:00
parent 3f5494211d
commit 0fc1751ca1
2 changed files with 392 additions and 160 deletions

View File

@ -82,6 +82,8 @@ struct qhVertex
qhVertex* prev;
qhVertex* next;
//qhHalfEdge* edge;
b3Vec3 position;
qhFace* conflictFace;
@ -116,9 +118,18 @@ public:
// Get the number of iterations this algorithm ran.
u32 GetIterations() const;
// Validate this hull.
// Validate convexity.
// Called at each iteration.
void ValidateConvexity() const;
// Validate connectivity.
// Called at each iteration.
void Validate() const;
// Called anywhere.
void Validate(const qhFace* face) const;
// Called anywhere.
void Validate(const qhHalfEdge* edge) const;
// Draw this hull.
@ -136,6 +147,8 @@ private:
bool MergeLargeFace(qhFace* face);
void FixMerge(qhFace* face, qhHalfEdge* ein);
qhHalfEdge* FindHalfEdge(const qhVertex* v1, const qhVertex* v2) const;
//

View File

@ -193,6 +193,7 @@ void qhHull::Construct(const b3Vec3* vs, u32 count)
while (eye)
{
Validate();
ValidateConvexity();
AddEyeVertex(eye);
@ -202,7 +203,9 @@ void qhHull::Construct(const b3Vec3* vs, u32 count)
}
Validate();
ValidateConvexity();
#if 0
// Ensure the hull contains the original vertex set
for (u32 i = 0; i < count; ++i)
{
@ -211,9 +214,10 @@ void qhHull::Construct(const b3Vec3* vs, u32 count)
for (qhFace* f = m_faceList.head; f; f = f->next)
{
float32 d = b3Distance(v, f->plane);
//B3_ASSERT(d < m_tolerance);
B3_ASSERT(d < m_tolerance);
}
}
#endif
}
bool qhHull::BuildInitialHull(const b3Vec3* vertices, u32 vertexCount)
@ -500,7 +504,8 @@ void qhHull::FindHorizon(qhVertex* eye)
void qhHull::AddNewFaces(qhVertex* eye)
{
// Ensure CCW horizon order
// Ensure CCW horizon order.
// Usually it can fail hit if face merging is disable.
B3_ASSERT(m_horizonCount > 0);
for (u32 i = 0; i < m_horizonCount; ++i)
{
@ -524,8 +529,6 @@ void qhHull::AddNewFaces(qhVertex* eye)
b3Vec3 eyePosition = eye->position;
eye->conflictFace->conflictList.Remove(eye);
eye->conflictFace = NULL;
FreeVertex(eye);
// Add the eye point to the hull
@ -629,7 +632,7 @@ qhVertex* qhHull::AddVertex(const b3Vec3& position)
return v;
}
inline qhHalfEdge* qhHull::FindHalfEdge(const qhVertex* v1, const qhVertex* v2) const
qhHalfEdge* qhHull::FindHalfEdge(const qhVertex* v1, const qhVertex* v2) const
{
for (qhFace* face = m_faceList.head; face != NULL; face = face->next)
{
@ -637,6 +640,7 @@ inline qhHalfEdge* qhHull::FindHalfEdge(const qhVertex* v1, const qhVertex* v2)
do
{
B3_ASSERT(e->active == true);
B3_ASSERT(e->twin != NULL);
B3_ASSERT(e->twin->active == true);
if (e->tail == v1 && e->twin->tail == v2)
@ -660,7 +664,7 @@ static B3_FORCE_INLINE b3Vec3 b3Newell(const b3Vec3& a, const b3Vec3& b)
return b3Vec3((a.y - b.y) * (a.z + b.z), (a.z - b.z) * (a.x + b.x), (a.x - b.x) * (a.y + b.y));
}
static inline void b3ResetFaceData(qhFace* face)
static void b3ResetFaceData(qhFace* face)
{
b3Vec3 n;
n.SetZero();
@ -688,84 +692,257 @@ static inline void b3ResetFaceData(qhFace* face)
face->center = c;
float32 len = b3Length(n);
face->area = 0.5f * len;
if (len > B3_EPSILON)
{
n /= len;
}
B3_ASSERT(len > B3_EPSILON);
n /= len;
face->plane.normal = n;
face->plane.offset = b3Dot(n, c);
}
qhFace* qhHull::RemoveEdge(qhHalfEdge* e)
static u32 b3VertexCount(const qhFace* face)
{
qhFace* rightFace = e->face;
qhHalfEdge* twin = e->twin;
qhFace* leftFace = twin->face;
// Set right face to reference a non-deleted edge
rightFace->edge = e->prev;
// Absorb face
qhHalfEdge* te = twin->next;
u32 n = 0;
qhHalfEdge* e = face->edge;
do
{
B3_ASSERT(te->face == leftFace);
te->face = rightFace;
te = te->next;
} while (te != twin->next);
++n;
e = e->next;
} while (e != face->edge);
return n;
}
// Link edges
e->prev->next = twin->next;
e->next->prev = twin->prev;
twin->prev->next = e->next;
twin->next->prev = e->prev;
void qhHull::FixMerge(qhFace* face1, qhHalfEdge* ein)
{
qhHalfEdge* eout = ein->next;
// Remove edge
e->twin = NULL;
e->tail = NULL;
e->face = NULL;
e->prev = NULL;
e->next = NULL;
FreeEdge(e);
B3_ASSERT(ein->twin->face == eout->twin->face);
// Remove twin
twin->twin = NULL;
twin->tail = NULL;
twin->face = NULL;
twin->prev = NULL;
twin->next = NULL;
FreeEdge(twin);
qhFace* face3 = ein->twin->face;
// Move left conflict vertices into right
qhVertex* v = leftFace->conflictList.head;
u32 count = b3VertexCount(face3);
// Is the face 3 a triangle?
if (count == 3)
{
u32 vn = b3VertexCount(ein->face);
// Unlink incoming edge from face 1
B3_ASSERT(ein->prev->next == ein);
ein->prev->next = ein->twin->next;
// Unlink incoming edge twin from face 3
B3_ASSERT(ein->twin->next->prev == ein->twin);
ein->twin->next->prev = ein->prev;
B3_ASSERT(ein->face == face1);
if (face1->edge == ein)
{
face1->edge = ein->prev;
}
// Set incoming edge twin face reference the face 1
B3_ASSERT(ein->twin->next->face == face3);
ein->twin->next->face = face1;
// Unlink outgoing edge from face 1
B3_ASSERT(eout->next->prev == eout);
eout->next->prev = eout->twin->prev;
B3_ASSERT(eout->twin->prev->next == eout->twin);
eout->twin->prev->next = eout->next;
B3_ASSERT(eout->face == face1);
if (face1->edge == eout)
{
face1->edge = eout->next;
}
// Reset face 1 data
b3ResetFaceData(face1);
// Validate face 1
Validate(face1);
// Remove outgoing vertex
m_vertexList.Remove(eout->tail);
FreeVertex(eout->tail);
// Remove incoming edge
FreeEdge(ein->twin);
FreeEdge(ein);
// Remove outgoing edge
FreeEdge(eout->twin);
FreeEdge(eout);
// Move face 3 conflict vertices into face 1
qhVertex* v = face3->conflictList.head;
while (v)
{
qhVertex* v0 = v;
v = face3->conflictList.Remove(v);
face1->conflictList.PushFront(v0);
v0->conflictFace = face1;
}
// Remove face 3
m_faceList.Remove(face3);
FreeFace(face3);
}
else
{
// Extend the incoming edge to the next vertex
B3_ASSERT(ein->twin->tail == eout->tail);
ein->twin->tail = eout->twin->tail;
// Remove outgoing vertex
m_vertexList.Remove(eout->tail);
FreeVertex(eout->tail);
// Unlink outgoing edge from face 1
B3_ASSERT(eout->prev->next == eout);
eout->prev->next = eout->next;
B3_ASSERT(eout->next->prev == eout);
eout->next->prev = eout->prev;
if (face1->edge == eout)
{
face1->edge = eout->next;
}
// Reset face 1 data
b3ResetFaceData(face1);
// Validate face 1
Validate(face1);
// Unlink outgoing edge twin from face 3
B3_ASSERT(eout->twin->prev->next == eout->twin);
eout->twin->prev->next = eout->twin->next;
B3_ASSERT(eout->twin->next->prev == eout->twin);
eout->twin->next->prev = eout->twin->prev;
if (face3->edge == eout->twin)
{
face3->edge = eout->twin->next;
}
// Remove outgoing edge
FreeEdge(eout->twin);
FreeEdge(eout);
}
}
qhFace* qhHull::RemoveEdge(qhHalfEdge* edge)
{
B3_ASSERT(edge->active == true);
qhFace* face1 = edge->face;
B3_ASSERT(face1->active == true);
B3_ASSERT(edge->twin->active == true);
qhFace* face2 = edge->twin->face;
// Edge must be shared.
B3_ASSERT(face2 != NULL);
B3_ASSERT(face2->active == true);
B3_ASSERT(face2 != face1);
// Merge face 2 into face 1
// Set face 2 edges owner face to face 1,
// except the twin edge which will be deleted
for (qhHalfEdge* e2 = edge->twin->next; e2 != edge->twin; e2 = e2->next)
{
B3_ASSERT(e2->face == face2);
e2->face = face1;
}
// Set the face 1 to reference a non-deleted edge
if (face1->edge == edge)
{
face1->edge = edge->next;
}
// Unlink edge from face 1
B3_ASSERT(edge->prev->next == edge);
edge->prev->next = edge->twin->next;
B3_ASSERT(edge->next->prev == edge);
edge->next->prev = edge->twin->prev;
B3_ASSERT(edge->twin->prev->next == edge->twin);
edge->twin->prev->next = edge->next;
B3_ASSERT(edge->twin->next->prev == edge->twin);
edge->twin->next->prev = edge->prev;
// Reset right face data
b3ResetFaceData(face1);
// Validate topology
Validate(face1);
// Move face 2 conflict vertices into face 1
qhVertex* v = face2->conflictList.head;
while (v)
{
qhVertex* v0 = v;
v = leftFace->conflictList.Remove(v);
v = face2->conflictList.Remove(v);
rightFace->conflictList.PushFront(v0);
v0->conflictFace = rightFace;
face1->conflictList.PushFront(v0);
v0->conflictFace = face1;
}
// Remove left face
leftFace->edge = NULL;
// Remove face 2
m_faceList.Remove(face2);
FreeFace(face2);
m_faceList.Remove(leftFace);
// Remove edge
FreeEdge(edge->twin);
FreeEdge(edge);
FreeFace(leftFace);
// Check for topological errors and apply a fix on them
// if detected.
// Reset face data
b3ResetFaceData(rightFace);
// Maintained invariants:
// - Each vertex must have at least three neighbor faces
// - Face 1 must be concave
return rightFace;
// Searching a redundant vertex in face 1 boils down to
// search for a incoming and outgoing edges in the face 1
// which have the same neighbour face.
qhHalfEdge* ein = face1->edge;
do
{
qhHalfEdge* eout = ein->next;
// Has a vertex in the face 1 become redundant?
if (ein->twin->face == eout->twin->face)
{
qhHalfEdge* ein0 = ein;
ein = eout;
// Fix error.
// This is were some edges and faces might
// be deleted.
FixMerge(face1, ein0);
continue;
}
ein = eout;
} while (ein != face1->edge);
// Return face 1
return face1;
}
qhFace* qhHull::AddFace(qhVertex* v1, qhVertex* v2, qhVertex* v3)
{
// Each vertex must be free.
//B3_ASSERT(v1->edge == NULL);
//B3_ASSERT(v2->edge == NULL);
//B3_ASSERT(v3->edge == NULL);
qhFace* face = AllocateFace();
qhHalfEdge* e1 = FindHalfEdge(v1, v2);
@ -786,13 +963,11 @@ qhFace* qhHull::AddFace(qhVertex* v1, qhVertex* v2, qhVertex* v3)
}
else
{
// Edge must be free.
B3_ASSERT(e1->face == NULL);
e1->face = face;
B3_ASSERT(e1->tail == v1);
if (e1->face == NULL)
{
e1->face = face;
}
B3_ASSERT(e1->twin != NULL);
B3_ASSERT(e1->twin->active == true);
B3_ASSERT(e1->twin->tail == v2);
@ -816,13 +991,11 @@ qhFace* qhHull::AddFace(qhVertex* v1, qhVertex* v2, qhVertex* v3)
}
else
{
// Edge must be free.
B3_ASSERT(e2->face == NULL);
e2->face = face;
B3_ASSERT(e2->tail == v2);
if (e2->face == NULL)
{
e2->face = face;
}
B3_ASSERT(e2->twin != NULL);
B3_ASSERT(e2->twin->active == true);
B3_ASSERT(e2->twin->tail == v3);
@ -842,36 +1015,44 @@ qhFace* qhHull::AddFace(qhVertex* v1, qhVertex* v2, qhVertex* v3)
e3->twin->face = NULL;
e3->twin->prev = NULL;
e3->twin->next = NULL;
e3->twin->twin = e3;
}
else
{
// Edge must be free.
B3_ASSERT(e3->face == NULL);
e3->face = face;
B3_ASSERT(e3->tail == v3);
if (e3->face == NULL)
{
e3->face = face;
}
B3_ASSERT(e3->twin != NULL);
B3_ASSERT(e3->twin->active == true);
B3_ASSERT(e3->twin->tail == v1);
}
B3_ASSERT(e1->prev == NULL);
e1->prev = e3;
B3_ASSERT(e1->next == NULL);
e1->next = e2;
B3_ASSERT(e2->prev == NULL);
e2->prev = e1;
B3_ASSERT(e2->next == NULL);
e2->next = e3;
B3_ASSERT(e3->prev == NULL);
e3->prev = e2;
B3_ASSERT(e3->next == NULL);
e3->next = e1;
face->edge = e1;
b3ResetFaceData(face);
face->conflictList.head = NULL;
face->conflictList.count = 0;
Validate(face);
m_faceList.PushFront(face);
return face;
@ -879,6 +1060,7 @@ qhFace* qhHull::AddFace(qhVertex* v1, qhVertex* v2, qhVertex* v3)
qhFace* qhHull::RemoveFace(qhFace* face)
{
// Conflict vertices must have been removed
B3_ASSERT(face->conflictList.count == 0);
// Remove half-edges
@ -888,33 +1070,19 @@ qhFace* qhHull::RemoveFace(qhFace* face)
qhHalfEdge* e0 = e;
e = e->next;
qhHalfEdge* twin = e0->twin;
// Is the edge a boundary?
if (twin->face == NULL)
if (e0->twin->face == NULL)
{
// Remove both half-edges if the edge is not shared.
e0->twin = NULL;
e0->tail = NULL;
e0->face = NULL;
e0->prev = NULL;
e0->next = NULL;
// Edge is non-shared.
FreeEdge(e0->twin);
FreeEdge(e0);
twin->twin = NULL;
twin->tail = NULL;
twin->face = NULL;
twin->prev = NULL;
twin->next = NULL;
FreeEdge(twin);
}
else
{
// Remove the non-shared half-edge.
// However, we preserve the edge, its twin, and their connection.
// Edge is shared.
// Mark the twin edge as a boundary edge.
B3_ASSERT(e0->twin != NULL);
B3_ASSERT(e0->twin->twin == e0);
//e0->tail = NULL;
e0->face = NULL;
e0->prev = NULL;
e0->next = NULL;
@ -922,35 +1090,31 @@ qhFace* qhHull::RemoveFace(qhFace* face)
} while (e != face->edge);
face->edge = NULL;
// Remove face
qhFace* nextFace = m_faceList.Remove(face);
FreeFace(face);
// Return the next face in the list of faces
return nextFace;
}
bool qhHull::MergeFace(qhFace* rightFace)
bool qhHull::MergeFace(qhFace* face1)
{
// Non-convex edge
qhHalfEdge* edge = NULL;
qhHalfEdge* e = rightFace->edge;
qhHalfEdge* e = face1->edge;
do
{
qhFace* leftFace = e->twin->face;
qhHalfEdge* twin = e->twin;
qhFace* face2 = twin->face;
//B3_ASSERT(leftFace != rightFace);
B3_ASSERT(face2 != NULL);
B3_ASSERT(face2 != face1);
if (leftFace == rightFace)
{
e = e->next;
continue;
}
float32 d1 = b3Distance(leftFace->center, rightFace->plane);
float32 d2 = b3Distance(rightFace->center, leftFace->plane);
float32 d1 = b3Distance(face2->center, face1->plane);
float32 d2 = b3Distance(face1->center, face2->plane);
if (d1 < -m_tolerance && d2 < -m_tolerance)
{
@ -963,7 +1127,7 @@ bool qhHull::MergeFace(qhFace* rightFace)
edge = e;
break;
} while (e != rightFace->edge);
} while (e != face1->edge);
if (edge)
{
@ -974,63 +1138,57 @@ bool qhHull::MergeFace(qhFace* rightFace)
return false;
}
bool qhHull::MergeLargeFace(qhFace* rightFace)
bool qhHull::MergeLargeFace(qhFace* face1)
{
// Non-convex edge
// Find a non-convex edge
qhHalfEdge* edge = NULL;
qhHalfEdge* e = rightFace->edge;
qhHalfEdge* e = face1->edge;
B3_ASSERT(e->face == rightFace);
B3_ASSERT(e->face == face1);
do
{
qhHalfEdge* twin = e->twin;
qhFace* face2 = twin->face;
qhFace* leftFace = twin->face;
B3_ASSERT(face2 != NULL);
B3_ASSERT(face2 != face1);
//B3_ASSERT(leftFace != rightFace);
if (leftFace == rightFace)
if (face1->area > face2->area)
{
e = e->next;
continue;
}
if (rightFace->area > leftFace->area)
{
// Right face merge
float32 d = b3Distance(leftFace->center, rightFace->plane);
// Face 1 merge
float32 d = b3Distance(face2->center, face1->plane);
if (d < -m_tolerance)
{
// Edge is convex wrt to the right face
// Edge is convex wrt to the face 1
e = e->next;
continue;
}
// Edge is concave or coplanar wrt to the right face
// Edge is concave or coplanar wrt to the face 1
edge = e;
break;
}
else
{
// Left face merge
float32 d = b3Distance(rightFace->center, leftFace->plane);
// Face 2 merge
float32 d = b3Distance(face1->center, face2->plane);
if (d < -m_tolerance)
{
// Edge is convex wrt to the left face
// Edge is convex wrt to the face 2
e = e->next;
continue;
}
// Edge is concave or coplanar wrt to the left face
// Edge is concave or coplanar wrt to the face 2
edge = e;
break;
}
e = e->next;
} while (e != rightFace->edge);
} while (e != face1->edge);
if (edge)
{
@ -1087,6 +1245,41 @@ void qhHull::Translate(const b3Vec3& translation)
}
}
void qhHull::ValidateConvexity() const
{
for (qhFace* face = m_faceList.head; face != NULL; face = face->next)
{
B3_ASSERT(face->active == true);
const qhHalfEdge* edge = face->edge;
do
{
B3_ASSERT(edge->active == true);
B3_ASSERT(edge->face == face);
B3_ASSERT(edge->twin != NULL);
B3_ASSERT(edge->twin->active == true);
qhFace* other = edge->twin->face;
// Ensure closed volume
B3_ASSERT(other != NULL);
B3_ASSERT(other->active == true);
// Ensure topological health
B3_ASSERT(face != other);
// Ensure face convexity
float32 d1 = b3Distance(other->center, face->plane);
B3_ASSERT(d1 < -m_tolerance);
float32 d2 = b3Distance(face->center, other->plane);
B3_ASSERT(d2 < -m_tolerance);
edge = edge->next;
} while (edge != face->edge);
}
}
void qhHull::Validate(const qhHalfEdge* edge) const
{
B3_ASSERT(edge->active == true);
@ -1107,20 +1300,27 @@ void qhHull::Validate(const qhHalfEdge* edge) const
B3_ASSERT(next->active == true);
B3_ASSERT(twin->tail == next->tail);
u32 count = 0;
const qhHalfEdge* begin = edge;
bool found = false;
const qhFace* face = edge->face;
const qhHalfEdge* e = face->edge;
do
{
++count;
const qhHalfEdge* next = edge->next;
edge = next->twin;
} while (edge != begin);
if (e == edge)
{
found = true;
break;
}
e = e->next;
} while (e != face->edge);
B3_ASSERT(found == true);
}
void qhHull::Validate(const qhFace* face) const
{
B3_ASSERT(face->active == true);
// CCW
const qhHalfEdge* begin = face->edge;
const qhHalfEdge* edge = begin;
do
@ -1130,27 +1330,35 @@ void qhHull::Validate(const qhFace* face) const
B3_ASSERT(edge->twin != NULL);
B3_ASSERT(edge->twin->active == true);
qhFace* other = edge->twin->face;
if (other != NULL)
if (edge->twin->face != NULL)
{
// Ensure face convexity
B3_ASSERT(other->active == true);
//B3_ASSERT(face != other);
//float32 d1 = b3Distance(other->center, face->plane);
//float32 d2 = b3Distance(face->center, other->plane);
//B3_ASSERT(d1 < -m_tolerance);
//B3_ASSERT(d2 < -m_tolerance);
// Vertex redundancy
// B3_ASSERT(edge->next->twin->face != edge->twin->face);
B3_ASSERT(edge->twin->face->active == true);
B3_ASSERT(edge->twin->face != face);
}
edge = edge->next;
} while (edge != begin);
// CW
edge = begin;
do
{
B3_ASSERT(edge->active == true);
B3_ASSERT(edge->face == face);
B3_ASSERT(edge->twin != NULL);
B3_ASSERT(edge->twin->active == true);
if (edge->twin->face != NULL)
{
B3_ASSERT(edge->twin->face->active == true);
B3_ASSERT(edge->twin->face != face);
}
edge = edge->prev;
} while (edge != begin);
Validate(face->edge);
}
@ -1170,6 +1378,17 @@ void qhHull::Validate() const
B3_ASSERT(vertex->active == true);
}
// Ensure each vertex has at least three neighbor faces
qhHalfEdge* ein = face->edge;
do
{
qhHalfEdge* eout = ein->next;
B3_ASSERT(ein->twin->face != eout->twin->face);
ein = eout;
} while (ein != face->edge);
Validate(face);
}
}