FEGregoryPatch.cpp

/*This file is part of the FEBio Studio source code and is licensed under the MIT license
listed below.

See Copyright-FEBio-Studio.txt for details.

Copyright (c) 2021 University of Utah, The Trustees of Columbia University in
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#include "stdafx.h"
#include "FEGregoryPatch.h"
#include <MeshLib/FEMesh.h>

FEGregoryPatch::FEGregoryPatch(void)
{
	m_w = m_h = 1;
	m_nx = m_ny = 5;
	m_mx = m_my = 5;

	AddDoubleParam(m_w, "w", "Width");
	AddDoubleParam(m_h, "h", "Height");
	AddIntParam(m_nx, "nx", "Nx"); // number of patches in x-direction
	AddIntParam(m_ny, "ny", "Ny"); // number of patches in y-direction
	AddIntParam(m_mx, "mx", "Mx"); // number of elements per patch in x-direction
	AddIntParam(m_my, "my", "My"); // number of elements per patch in y-direction
}

FEGregoryPatch::~FEGregoryPatch(void)
{
}

FSMesh* FEGregoryPatch::BuildMesh()
{
	// first, build the patches
	BuildPatches();

	// calcaulte the patch control data
	BuildPatchData();

	// next, we build the FE mesh
	return BuildFEMesh();
}

FSMesh* FEGregoryPatch::BuildFEMesh()
{
	// get the parameters
	m_w = GetFloatValue(W);
	m_h = GetFloatValue(H);
	m_nx = GetIntValue(NX);
	m_ny = GetIntValue(NY);
	m_mx = GetIntValue(MX);
	m_my = GetIntValue(MY);

	if (m_nx<1) m_nx = 1;
	if (m_ny<1) m_ny = 1;
	if (m_mx<1) m_mx = 1;
	if (m_my<1) m_my = 1;

	int nodes = (m_nx*m_mx+1)*(m_ny*m_my+1);
	int elems = m_nx*m_mx*m_ny*m_my;

	FSMesh* pm = new FSMesh();
	pm->Create(nodes, elems);

	// build the nodes
	int i, j, k, l, m, n;
	double r, s;
	FSNode *pn = pm->NodePtr();
	for (j=0; j<=m_ny*m_my; ++j)
		for (i=0; i<=m_nx*m_mx; ++i, ++pn)
		{
			k = j/m_my;
			if (k==m_ny) { k = m_ny-1; m = m_my; } else m = j%m_my;

			l = i/m_mx;
			if (l==m_nx) { l = m_nx-1; n = m_mx; } else n = i%m_mx;

			GPatch& p = m_GPatch[k*m_nx+l];

			r = (double) n / (double) m_mx;
			s = (double) m / (double) m_my;

			pn->r = EvalPatch(p, r, s);
		}

	// assign group ID's to nodes
	for (j=0; j<=m_ny; ++j)
		for (i=0; i<=m_nx; ++i)
		{
			FSNode& n = pm->Node(j*(m_nx*m_mx+1)*(m_my) + i*m_mx);
			n.m_gid = j*(m_nx+1)+i;
		}

	// build the elements
	int eid = 0;
	for (j=0; j<m_ny*m_my; ++j)
		for (i=0; i<m_nx*m_mx; ++i)
		{
			FEElement_* pe = pm->ElementPtr(eid++);

			pe->m_node[0] = NodeIndex(i  ,j);
			pe->m_node[1] = NodeIndex(i+1,j);
			pe->m_node[2] = NodeIndex(i+1,j+1);
			pe->m_node[3] = NodeIndex(i  ,j+1);

			pe->SetType(FE_QUAD4);
			pe->m_gid = 0;
		}

	BuildFaces(pm);

	pm->BuildMesh();

	return pm;
}

void FEGregoryPatch::BuildPatches()
{
	double w = GetFloatValue(W);
	double h = GetFloatValue(H);
	m_nx = GetIntValue(NX);
	m_ny = GetIntValue(NY);

	if (m_nx<1) m_nx = 1;
	if (m_ny<1) m_ny = 1;

	int NN = (m_nx+1)*(m_ny+1);
	int NP = m_nx*m_ny;

	m_GNode.resize(NN);
	m_GPatch.resize(NP);

	// calculate nodes
	int i, j, n;
	n = 0;
	double x, y, z;
	for (j=0; j<=m_ny; ++j)
		for (i=0; i<=m_nx; ++i, ++n)
		{
			x = -w*0.5 + i*w/m_nx;
			y = -h*0.5 + j*h/m_ny;
			z = 0;
			m_GNode[n].m_r = vec3d(x, y, z);
		}

	// create patches
	n = 0;
	for (j=0; j<m_ny; ++j)
		for (i=0; i<m_nx; ++i, ++n)
		{
			int* m = m_GPatch[n].m_node;
			m[0] = j*(m_nx+1) + i;
			m[1] = j*(m_nx+1) + i+1;
			m[2] = (j+1)*(m_nx+1) + i+1;
			m[3] = (j+1)*(m_nx+1) + i;
		}
}

void FEGregoryPatch::BuildPatchData()
{
	int i, j;

	int NN = (m_nx+1)*(m_ny+1);
	int NP = m_nx*m_ny;

	// zero node normals
	for (i=0; i<NN; ++i) m_GNode[i].m_n = vec3d(0,0,0);

	// calculate node normals
	vec3d r1, r2, y;
	for (i=0; i<NP; ++i)
	{
		GPatch& p = m_GPatch[i];
		for (j=0; j<4; ++j)
		{
			GNode& n0 = m_GNode[ p.m_node[j] ];
			GNode& n1 = m_GNode[ p.m_node[(j+1)%4] ];
			GNode& n2 = m_GNode[ p.m_node[(j+3)%4] ];

			r1 = n1.m_r - n0.m_r;
			r2 = n2.m_r - n0.m_r;

			y = r1^r2;
			y.Normalize();

			n0.m_n += y;
		}
	}

	// normalize normals
	for (i=0; i<NN; ++i) m_GNode[i].m_n.Normalize();

	// calculate the edge control points for each patch
	vec3d y0, y3, m0, m3, c0, c1, c2;
	for (i=0; i<NP; ++i)
	{
		GPatch& p = m_GPatch[i];
		for (j=0; j<4; ++j)
		{
			GNode& n0 = m_GNode[ p.m_node[j] ];
			GNode& n3 = m_GNode[ p.m_node[(j+1)%4] ];

			y0 = n0.m_r;
			m0 = n0.m_n;

			y3 = n3.m_r;
			m3 = n3.m_n;

			c0 = ((y3 - y0)-m0*((y3 - y0)*m0))/3.0;
			c2 = ((y3 - y0)-m3*((y3 - y0)*m3))/3.0;

			p.m_ye[j][0] = y0 + c0;
			p.m_ye[j][1] = y3 - c2;
		}
	}

	// calculate the interior control points for each patch
	vec3d y1, y2, a0, a3, b0, b1, b2, b3;
	double k0, k1, h0, h1;
	for (i=0; i<NP; ++i)
	{
		GPatch& p = m_GPatch[i];
		for (j=0; j<4; ++j)
		{
			GNode& n0 = m_GNode[ p.m_node[j] ];
			GNode& n3 = m_GNode[ p.m_node[(j+1)%4] ];
			y0 = n0.m_r; m0 = n0.m_n;
			y3 = n3.m_r; m3 = n3.m_n;
			y1 = p.m_ye[j][0];
			y2 = p.m_ye[j][1];

			a0 = m0^(y3-y0); a0.Normalize();
			a3 = m3^(y3-y0); a3.Normalize();

			b0 = p.m_ye[(j+3)%4][1] - y0;
			b3 = p.m_ye[(j+1)%4][0] - y3;

			c0 = y1 - y0;
			c1 = y2 - y1;
			c2 = y3 - y2;

			k0 = a0*b0;	h0 = (c0*b0)/(c0*c0);
			k1 = a3*b3;	h1 = (c2*b3)/(c2*c2);

			b1 = (a0*(k1 + k0) + a3*k0 + c1*(2.0*h0) + c0*h1)/3;
			b2 = (a3*(k1 + k0) + a0*k1 + c1*(2.0*h1) + c2*h0)/3;

			p.m_yi[j][0] = y1 + b1;
			p.m_yi[j][1] = y2 + b2;
		}
	}
}

vec3d FEGregoryPatch::EvalPatch(FEGregoryPatch::GPatch &p, double r, double s)
{
	// calculate internal control points
	vec3d x[4][4];
	x[0][0] = m_GNode[p.m_node[0]].m_r;
	x[3][0] = m_GNode[p.m_node[1]].m_r;
	x[3][3] = m_GNode[p.m_node[2]].m_r;
	x[0][3] = m_GNode[p.m_node[3]].m_r;

	x[1][0] = p.m_ye[0][0]; x[2][0] = p.m_ye[0][1];
	x[3][1] = p.m_ye[1][0]; x[3][2] = p.m_ye[1][1];
	x[2][3] = p.m_ye[2][0]; x[1][3] = p.m_ye[2][1];
	x[0][2] = p.m_ye[3][0]; x[0][1] = p.m_ye[3][1];

	x[1][1] = (r+s   == 0? vec3d(0,0,0) : (p.m_yi[0][0]*(r  ) + p.m_yi[3][1]*(s  ))/(r+s));
	x[2][1] = (1-r+s == 0? vec3d(0,0,0) : (p.m_yi[0][1]*(1-r) + p.m_yi[1][0]*(s  ))/(1-r+s));
	x[1][2] = (r+1-s == 0? vec3d(0,0,0) : (p.m_yi[2][1]*(r  ) + p.m_yi[3][0]*(1-s))/(r+1-s));
	x[2][2] = (2-r-s == 0? vec3d(0,0,0) : (p.m_yi[2][0]*(1-r) + p.m_yi[1][1]*(1-s))/(2-r-s));

	// calculate Bezier coefficients
	double B[2][4];
	B[0][0] = (1-r)*(1-r)*(1-r);
	B[0][1] = 3*r*(1-r)*(1-r);
	B[0][2] = 3*r*r*(1-r);
	B[0][3] = r*r*r;

	B[1][0] = (1-s)*(1-s)*(1-s);
	B[1][1] = 3*s*(1-s)*(1-s);
	B[1][2] = 3*s*s*(1-s);
	B[1][3] = s*s*s;

	// calculate the final position
	int i, j;
	vec3d y(0,0,0);
	for (i=0; i<4; ++i)
		for (j=0; j<4; ++j) y += x[i][j]*(B[0][i]*B[1][j]);

	return y;
}

void FEGregoryPatch::BuildFaces(FSMesh* pm)
{
	int faces = pm->Elements();
	pm->Create(0,0,faces);
	for (int i=0; i<faces; ++i)
	{
		FSFace& f = pm->Face(i);
		FSElement& e = pm->Element(i);
		f.SetType(FE_FACE_QUAD4);
		f.n[0] = e.m_node[0];
		f.n[1] = e.m_node[1];
		f.n[2] = e.m_node[2];
		f.n[3] = e.m_node[3];
		f.m_gid = e.m_gid;
		e.m_gid = 0;
	}
}