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MeshTri3.h
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Wed, Jul 17, 08:48

MeshTri3.h
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/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MESHTRI3_H
#define GOOSEFEM_MESHTRI3_H
// -------------------------------------------------------------------------------------------------
#include "Mesh.h"
// ===================================== GooseFEM::Mesh::Tri3 =====================================
namespace GooseFEM {
namespace Mesh {
namespace Tri3 {
// ========================================== REGULAR MESH =========================================
class Regular
{
private:
size_t m_nx; // number of 'pixels' horizontal direction (length == "m_nx * m_h")
size_t m_ny; // number of 'pixels' vertical direction (length == "m_ny * m_h")
double m_h; // size of the element edge (equal in both directions)
size_t m_nelem; // number of elements
size_t m_nnode; // number of nodes
size_t m_nne=3; // number of nodes-per-element
size_t m_ndim=2; // number of dimensions
public:
// mesh with "nx" pixels in horizontal direction, "ny" in vertical direction and "h" the edge size
Regular(size_t nx, size_t ny, double h=1.);
// sizes
size_t nelem(); // number of elements
size_t nnode(); // number of nodes
size_t nne(); // number of nodes-per-element
size_t ndim(); // number of dimensions
// mesh
MatD coor(); // nodal positions [ nnode , ndim ]
MatS conn(); // connectivity [ nelem , nne ]
// boundary nodes: edges
ColS nodesBottomEdge(); // nodes along the bottom edge
ColS nodesTopEdge(); // nodes along the top edge
ColS nodesLeftEdge(); // nodes along the left edge
ColS nodesRightEdge(); // nodes along the right edge
// boundary nodes: corners
size_t nodesBottomLeftCorner(); // bottom - left corner node
size_t nodesBottomRightCorner(); // bottom - right corner node
size_t nodesTopLeftCorner(); // top - left corner node
size_t nodesTopRightCorner(); // top - right corner node
// boundary nodes: corners (aliases)
size_t nodesLeftBottomCorner(); // bottom - left corner node
size_t nodesLeftTopCorner(); // top - left corner node
size_t nodesRightBottomCorner(); // bottom - right corner node
size_t nodesRightTopCorner(); // top - right corner node
// periodicity
MatS nodesPeriodic(); // periodic node pairs [:,2]: (independent, dependent)
size_t nodesOrigin(); // bottom-left node, to be used as reference for periodicity
MatS dofs(); // DOF-numbers for each component of each node (sequential)
MatS dofsPeriodic(); // DOF-numbers for each component of each node (sequential)
};
// ========================================= MESH ANALYSIS =========================================
// read / set the orientation (-1 / +1) of all triangles
inline ColI getOrientation(const MatD &coor, const MatS &conn );
inline MatS setOrientation(const MatD &coor, const MatS &conn, int orientation=-1);
inline MatS setOrientation(const MatD &coor, const MatS &conn, const ColI &val, int orientation=-1);
// ======================================= RE-TRIANGULATION ========================================
// simple interface to compute the full re-triangulation; it uses, depending on the input mesh:
// (1) the minimal evasive "TriUpdate"
// (2) the more rigorous "TriCompute"
inline MatS retriangulate(const MatD &coor, const MatS &conn, int orientation=-1);
// ------------------------- support class - update existing triangulation -------------------------
// minimal evasive re-triangulation which only flips edges of the existing connectivity
class TriUpdate
{
private:
MatS m_edge; // the element that neighbors along each edge (m_nelem: no neighbor)
MatS m_conn; // connectivity (updated)
MatD m_coor; // nodal positions (does not change)
size_t m_nelem; // #elements
size_t m_nnode; // #nodes
size_t m_nne; // #nodes-per-element
size_t m_ndim; // #dimensions
ColS m_elem; // the two elements involved in the last element change (see below)
ColS m_node; // the four nodes involved in the last element change (see below)
// old: m_elem(0) = [ m_node(0) , m_node(1) , m_node(2) ]
// m_elem(1) = [ m_node(1) , m_node(3) , m_node(2) ]
// new: m_elem(0) = [ m_node(0) , m_node(3) , m_node(2) ]
// m_elem(1) = [ m_node(0) , m_node(1) , m_node(3) ]
// compute neighbors per edge of all elements
void edge();
// update edges around renumbered elements
void chedge(size_t edge, size_t old_elem, size_t new_elem);
public:
TriUpdate(){};
TriUpdate(const MatD &coor, const MatS &conn);
bool eval (); // re-triangulate the full mesh (returns "true" if changed)
bool increment(); // one re-triangulation step (returns "true" if changed)
MatS conn () { return m_conn; }; // return (new) connectivity
MatS ch_elem () { return m_elem; }; // return element involved in last element change
MatS ch_node () { return m_node; }; // return nodes involved in last element change
};
// ================================ SUPPORT CLASS - EDGE DEFINITION ================================
// support class to allow the storage of a list of edges
class Edge {
public:
size_t n1 ; // node 1 (edge from node 1-2)
size_t n2 ; // node 2 (edge from node 1-2)
size_t elem; // element to which the edge belong
size_t edge; // edge index within the element (e.g. edge==1 -> n1=conn(0,elem), n2=conn(1,elem))
Edge(){};
Edge(size_t i, size_t j, size_t el, size_t ed, bool sort=false);
};
// -------------------------------------------------------------------------------------------------
// compare edges
inline bool Edge_cmp (Edge a, Edge b); // check equality
inline bool Edge_sort(Edge a, Edge b); // check if "a" is smaller than "b" in terms of node-numbers
// =================================================================================================
}}} // namespace ...
#endif

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