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  3. FSimpleIntrinsicEdgeFlipMesh

FSimpleIntrinsicEdgeFlipMesh

Intrinsic Meshes:

API > API/Plugins > API/Plugins/DynamicMesh > API/Plugins/DynamicMesh/Operations

Inheritance Hierarchy

References

   
Module DynamicMesh
Header /Engine/Plugins/Runtime/GeometryProcessing/Source/DynamicMesh/Public/Operations/IntrinsicTriangulationMesh.h
Include #include "Operations/IntrinsicTriangulationMesh.h"

Syntax

class FSimpleIntrinsicEdgeFlipMesh

Remarks

Intrinsic Meshes:

An Intrinsic Mesh can be thought of as a mesh that overlays another mesh, sharing the original surface. The edges of the intrinsic mesh are constrained to be on the original mesh surface, but need not align with the original mesh edges. The lengths of the intrinsic edges are measured on the surface of the original mesh (not the R3 distance). The original mesh vertices are a subset of the intrinsic mesh vertices and intrinsic edge splits and triangle pokes may introduce new intrinsic mesh vertices.

Note: the implementation is a simple triangle-based mesh but there is no restriction that edge(a, b) is unique (e.g. multiple intrinsic edges may connect the same two vertices with different paths). In fact this mesh allows triangles and edges with repeated vertices. Such structures arise naturally with intrinsic triangulation, for example an edge that starts and ends at the same vertex may encircle a mesh.

The bookkeeping that manages the correspondence between locations on the intrinsic mesh and on the surface mesh is implemented either using integer-based "Normal Coordinates" ( cf 'Integer Coordinates for Intrinsic Geometry Processing' M. Gillespie, N. Sharp, and K. Crane, TOG , Vol. 40, December 2021. ) as used by FIntrinsicEdgeFlipMesh and FIntrinsicMesh; or alternately floating-point based generalized directions "Signpost data" ( cf 'Signpost Coordinates inspired by "Navigating Intrinsic Triangulations' Sharp, Soliman and Crane [2019, ACM Transactions on Graphics]) as used by FIntrinsicTriangulation. The FSimpleIntrinsicEdgeFlipMesh is designed to work with the function FlipToDelaunay() to make an Intrinsic Delaunay Triangulation (IDT) of the same surface as a given FDynamicMesh, allowing for more robust cotangent-Laplacians (see LaplacianMatrixAssembly.h)

The vertices in this FSimpleIntrinsicEdgeFlipMesh are exactly those found in the surface mesh since it supports edge flips, but no other operations that change the mesh connectivity, and no operations that affect the vertices.

This mesh alone does not support computing the intersections of intrinsic edges with the surface mesh edges and as a result it can not be used to easily extract the path of an intrinsic edge. To do such computations FIntrinsicEdgeFlipMesh, FIntrinsicMesh or FIntrinsicTriangulation should be used.

The API of FIntrinsicEdgeFlipMesh is similar to FDynamicMesh3, but only has a minimal subset of methods and some such as ::FlipEdge() and ::GetEdgeOpposingV() have very different implementations.

In addition to managing vertices, triangles and edges this class also tracks edge lengths (as measured on the surface mesh) and for convenience the internal angles for each triangle.

Variables

  Type Name Description
Protected variable const int32[3] AddOneModThree  
Protected variable const int32[3] AddTwoModThree  
Protected variable TDynamicVector< double > EdgeLengths  
Protected variable FRefCountVector EdgeRefCounts  
Protected variable TDynamicVector< FEdge > Edges  
Protected variable TDynamicVector< FVector3d > InternalAngles  
Protected variable TDynamicVector< FIndex3i > TriangleEdges  
Protected variable FRefCountVector TriangleRefCounts  
Protected variable TDynamicVector< FIndex3i > Triangles  
Protected variable FSmallListSet VertexEdgeLists  
Protected variable FRefCountVector VertexRefCounts  
Protected variable TDynamicVector< FVector3d > Vertices  

Constructors

  Type Name Description
Public function    
Public function   Constructor does ID-matching deep copy the basic mesh topology (but no attributes or groups)
Public function    

Functions

  Type Name Description
Public function void

Clear ()

 Discard all data
Protected function Const FVector3d

ComputeTriInternalAnglesR ( const int32 TID
)

 Computes the angles based on the edge lengths, so must have valid EdgeLengths for this tri before calling.
Public function Const double

EdgeCotanWeight ( int32 EID
)

 Return 1/2 ( cot(alpha_{ij}) + cot(beta_{ij}) ) where alpha_{ij} and beta_{ij} are the to interior angles opposite the specified edge, EID.
Public function Const int32  
Public function Const FRefCountVector::IndexEnumerable  
Public function Const FVector2d

EdgeOpposingAngles ( int32 EID
)

 Return FVector2( alpha_{ij} , beta_{ij} ) where alpha_{ij} and beta_{ij} are the two interior angles opposite the specified edge, EID.
Public function EMeshResult

FlipEdge ( int32 EID,
FEdgeFlipInfo& EdgeFlipInfo
)

 Flip a single edge in the Intrinsic Mesh.
Protected function EMeshResult

FlipEdgeTopology ( int32 eab,
FEdgeFlipInfo& FlipInfo
)

 Update the mesh topology (e.g. triangles and edges) by doing an edge flip, but does not update the intrinsic edge lengths or angles.
Public function Const FEdge

GetEdge ( int32 EdgeID
)

  
Public function Const double

GetEdgeLength ( int32 EID
)

  
Protected function Const FVector3d

GetEdgeLengthTriple ( const FIndex3i& EIDs
)

  
Public function Const FIndex2i

GetEdgeOpposingV ( int32 EID
)

  
Public function Const FIndex2i

GetEdgeT ( int32 EdgeID
)

  
Public function Const FIndex2i

GetEdgeV ( int32 EdgeID
)

  
Protected function Const double  
Protected function Const FIndex2i

GetOrientedEdgeV ( int32 EID,
int32 TID
)

  
Public function Const FIndex3i

GetTriangle ( int32 TriangleID
)

  
Public function Const const FIndex3i &

GetTriangleRef ( int TriangleID
)

  
Public function Const FVector3d

GetTriEdgeLengths ( const int32 TID
)

  
Public function Const FIndex3i

GetTriEdges ( int32 TriangleID
)

  
Public function Const double

GetTriInternalAngleR ( const int32 TID,
const int32 IndexOf
)

  
Public function Const FVector3d

GetVertex ( int32 VertexID
)

  
Public function Const int32

GetVtxEdgeCount ( int32 VID
)

  
Public function Const bool

IsBoundaryEdge ( int32 EdgeID
)

  
Public function Const bool

IsBoundaryVertex ( int32 VertexID
)

  
Public function Const bool

IsEdge ( int32 EdgeID
)

  
Public function Const bool

IsTriangle ( int32 TriangleID
)

  
Public function Const bool

IsVertex ( int32 VertexID
)

  
Public function Const int32  
Public function Const int32  
Public function Const int32  
Public function Const Vector3Type

Permute ( int32 Index,
const Vector3Type& Src
)

 Cyclic permutation of the src vector such that the 'Index' entry in the src is the first entry in the result NB: Index must be 0, 1, or 2.
Protected function int32

ReplaceEdgeTriangle ( int32 eID,
int32 tOld,
int32 tNew
)

 Replace tOld with tNew in an existing edge
Protected function int32

ReplaceTriangleEdge ( int32 tID,
int32 eOld,
int32 eNew
)

 Replace eOld with eNew in and existing triangle
Public function void

Reset ( const FDynamicMesh3& SrcMesh
)

 Reset the mesh to an ID-matching deep copy the basic mesh topology (but no attributes or groups)
Protected function void

SetEdgeTrianglesInternal ( int32 EdgeID,
int32 t0,
int32 t1
)

 Update the existing edge to reference triangles t0 and t1
Protected function void

SetEdgeVerticesInternal ( int32 EdgeID,
int32 a,
int32 b
)

 Update the existing edge to reference vertices 'a' and 'b'.
Public function Const int32  
Public function Const FRefCountVector::IndexEnumerable  
Public function Const FSmallListSet::ValueEnumerable

VtxEdgesItr ( int32 VID
)

  

Typedefs

Name Description
FEdge  
FEdgeFlipInfo  

Constants

Name Description
InvalidID InvalidID indicates that a vertex/edge/triangle ID is invalid

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