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Triangle.cpp
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#include <iostream>
#include <cstdlib>
#include <cmath>
#include "Edge.h"
#include "Triangle.h"
using namespace std;
Triangle::Triangle( double* x1, double* x2, double* x3, int _order ) {
int i;
a[0] = x1[0];
a[1] = x1[1];
b[0] = x2[0];
b[1] = x2[1];
c[0] = x3[0];
c[1] = x3[1];
order = _order;
if( order == 1 ) {
nq = 1;
}
else if( order == 2 ) {
nq = 3;
}
else if( order == 3 || order == 4 ) {
nq = 6;
}
else if( order == 5 ) {
nq = 10;
}
else if( order == 6 ) {
nq = 11;
}
else if( order == 7 ) {
nq = 15;
}
else if( order == 8 ) {
nq = 16;
}
else {
cerr << "triangle quadrature order: " << order << "not implemented" << endl;
abort();
}
wi = new double[nq];
qi = new double*[nq];
for( i = 0; i < nq; i++ ) {
qi[i] = new double[2];
}
Init();
ab = new Edge( a, b );
bc = new Edge( b, c );
ca = new Edge( c, a );
}
Triangle::~Triangle() {
int i;
for( i = 0; i < nq; i++ ) {
delete[] qi[i];
}
delete[] qi;
delete[] wi;
delete ab;
delete bc;
delete ca;
}
void Triangle::Init() {
int i;
double tmp[16][2];
/* calculate the area */
area = 0.5*fabs( (b[0] - a[0])*(c[1] - a[1]) - (b[1] - a[1])*(c[0] - a[0]) );
if( order == 1 ) {
wi[0] = 1.0;
tmp[0][0] = 1.0/3.0;
tmp[0][1] = 1.0/3.0;
}
else if( order == 2 ) {
wi[0] = 1.0/3;
wi[1] = 1.0/3;
wi[2] = 1.0/3;
tmp[0][0] = 1.0/6.0;
tmp[0][1] = 2.0/3.0;
tmp[1][0] = 2.0/3.0;
tmp[1][1] = 1.0/6.0;
tmp[2][0] = 1.0/6.0;
tmp[2][1] = 1.0/6.0;
}
else if( order == 3 || order == 4 ) {
wi[0] = 0.109951743655321843;
wi[1] = 0.109951743655321857;
wi[2] = 0.109951743655321885;
wi[3] = 0.223381589678011389;
wi[4] = 0.223381589678011527;
wi[5] = 0.223381589678011527;
tmp[0][0] = 0.091576213509770466;
tmp[1][0] = 0.816847572980458514;
tmp[2][0] = 0.091576213509771076;
tmp[3][0] = 0.108103018168070275;
tmp[4][0] = 0.445948490915965612;
tmp[5][0] = 0.445948490915964113;
tmp[0][1] = 0.816847572980458514;
tmp[1][1] = 0.091576213509771076;
tmp[2][1] = 0.091576213509770466;
tmp[3][1] = 0.445948490915964113;
tmp[4][1] = 0.108103018168070275;
tmp[5][1] = 0.445948490915965612;
}
else if( order == 5 ) {
wi[0] = 1.31356049751916795e-02;
wi[1] = 1.31358306034076201e-02;
wi[2] = 1.37081973800151392e-02;
wi[3] = 1.17419193291163376e-01;
wi[4] = 1.17420611913379477e-01;
wi[5] = 1.24012589655715613e-01;
wi[6] = 1.24015246126072495e-01;
wi[7] = 1.25930230276426303e-01;
wi[8] = 1.25933026682913923e-01;
wi[9] = 2.25289469095714456e-01;
tmp[0][0] = 0.00000000000000000e+00;
tmp[1][0] = 1.00000000000000000e+00;
tmp[2][0] = 0.00000000000000000e+00;
tmp[3][0] = 2.67327353118498978e-01;
tmp[4][0] = 6.72817552946136210e-01;
tmp[5][0] = 6.49236350054349654e-02;
tmp[6][0] = 6.71649853904175198e-01;
tmp[7][0] = 6.54032456800035522e-02;
tmp[8][0] = 2.69376706913982855e-01;
tmp[9][0] = 3.38673850389605513e-01;
tmp[0][1] = 1.00000000000000000e+00;
tmp[1][1] = 0.00000000000000000e+00;
tmp[2][1] = 0.00000000000000000e+00;
tmp[3][1] = 6.72819921871012694e-01;
tmp[4][1] = 2.67328859948191944e-01;
tmp[5][1] = 6.71653011149382917e-01;
tmp[6][1] = 6.49251690028951334e-02;
tmp[7][1] = 2.69378936645285116e-01;
tmp[8][1] = 6.54054874919145490e-02;
tmp[9][1] = 3.38679989302702156e-01;
}
else if( order == 6 ) {
wi[0] = 3.80680718529555623e-02;
wi[1] = 3.83793553077528410e-02;
wi[2] = 4.62004567445618367e-02;
wi[3] = 5.34675894441989999e-02;
wi[4] = 8.37558269657456833e-02;
wi[5] = 1.01644833025517037e-01;
wi[6] = 1.01861524461366940e-01;
wi[7] = 1.11421831660001677e-01;
wi[8] = 1.12009450262946106e-01;
wi[9] = 1.24787571437558295e-01;
wi[10] = 1.88403488837394911e-01;
tmp[0][0] = 5.72549866774768601e-02;
tmp[1][0] = 8.95362640024579104e-01;
tmp[2][0] = 6.84475748456514044e-01;
tmp[3][0] = 6.87462559150295305e-02;
tmp[4][0] = 6.15676205575839575e-01;
tmp[5][0] = 6.27946141197789465e-01;
tmp[6][0] = 6.29091383418635686e-02;
tmp[7][0] = 6.83782119205099126e-02;
tmp[8][0] = 2.87529458374392255e-01;
tmp[9][0] = 3.28783556413134614e-01;
tmp[10][0] = 3.12290405013644801e-01;
tmp[0][1] = 8.95498146789879490e-01;
tmp[1][1] = 6.18282212503219533e-02;
tmp[2][1] = 2.33437384976827311e-02;
tmp[3][1] = 6.00302757472630025e-02;
tmp[4][1] = 3.33461808341377175e-01;
tmp[5][1] = 1.59189185992151483e-01;
tmp[6][1] = 6.55295093705452469e-01;
tmp[7][1] = 3.09117685428267230e-01;
tmp[8][1] = 6.36426509179620181e-01;
tmp[9][1] = 7.70240056424634223e-02;
tmp[10][1] = 3.52344786445899505e-01;
}
else if( order == 7 ) {
wi[0] = 5.12790870460473960e-03;
wi[1] = 5.12790870460473960e-03;
wi[2] = 5.12790870460473960e-03;
wi[3] = 5.58023523323444987e-02;
wi[4] = 5.58023523323445195e-02;
wi[5] = 5.58023523323445819e-02;
wi[6] = 5.58023523323446027e-02;
wi[7] = 5.58023523323446166e-02;
wi[8] = 5.58023523323446582e-02;
wi[9] = 8.39887797667335373e-02;
wi[10] = 8.39887797667336067e-02;
wi[11] = 8.39887797667336206e-02;
wi[12] = 1.32611940197305850e-01;
wi[13] = 1.32611940197305905e-01;
wi[15] = 1.32611940197305933e-01;
tmp[0][0] = 1.00000000000000000e+00;
tmp[1][0] = 0.00000000000000000e+00;
tmp[2][0] = 0.00000000000000000e+00;
tmp[3][0] = 1.73896050734549223e-01;
tmp[4][0] = 7.83965665101213904e-01;
tmp[5][0] = 4.21382841642368722e-02;
tmp[6][0] = 1.73896050734549223e-01;
tmp[7][0] = 7.83965665101213904e-01;
tmp[8][0] = 4.21382841642368722e-02;
tmp[9][0] = 4.74388086175152879e-01;
tmp[10][0] = 5.12238276496914668e-02;
tmp[11][0] = 4.74388086175155654e-01;
tmp[12][0] = 2.38561530018069179e-01;
tmp[13][0] = 5.22876939963858534e-01;
tmp[14][0] = 2.38561530018072343e-01;
tmp[0][1] = 0.00000000000000000e+00;
tmp[1][1] = 1.00000000000000000e+00;
tmp[2][1] = 0.00000000000000000e+00;
tmp[3][1] = 7.83965665101213904e-01;
tmp[4][1] = 4.21382841642368722e-02;
tmp[5][1] = 1.73896050734549223e-01;
tmp[6][1] = 4.21382841642368722e-02;
tmp[7][1] = 1.73896050734549223e-01;
tmp[8][1] = 7.83965665101213904e-01;
tmp[9][1] = 4.74388086175155654e-01;
tmp[10][1] = 4.74388086175152879e-01;
tmp[11][1] = 5.12238276496914668e-02;
tmp[12][1] = 5.22876939963858534e-01;
tmp[13][1] = 2.38561530018072343e-01;
tmp[14][1] = 2.38561530018069179e-01;
}
else if( order == 8 ) {
wi[0] = 2.72303141744348991e-02;
wi[1] = 2.72303141744349199e-02;
wi[2] = 2.72303141744349199e-02;
wi[3] = 2.72303141744349789e-02;
wi[4] = 2.72303141744349789e-02;
wi[5] = 2.72303141744349997e-02;
wi[6] = 3.24584976231980793e-02;
wi[7] = 3.24584976231980793e-02;
wi[8] = 3.24584976231981001e-02;
wi[9] = 9.50916342672845638e-02;
wi[10] = 9.50916342672846193e-02;
wi[11] = 9.50916342672846193e-02;
wi[12] = 1.03217370534718286e-01;
wi[13] = 1.03217370534718314e-01;
wi[14] = 1.03217370534718314e-01;
wi[15] = 1.44315607677787283e-01;
tmp[0][0] = 7.28492392955404355e-01;
tmp[1][0] = 8.39477740995753056e-03;
tmp[2][0] = 2.63112829634638112e-01;
tmp[3][0] = 8.39477740995753056e-03;
tmp[4][0] = 7.28492392955404355e-01;
tmp[5][0] = 2.63112829634638112e-01;
tmp[6][0] = 5.05472283170310122e-02;
tmp[7][0] = 5.05472283170309566e-02;
tmp[8][0] = 8.98905543365938087e-01;
tmp[9][0] = 4.59292588292723236e-01;
tmp[10][0] = 8.14148234145536387e-02;
tmp[11][0] = 4.59292588292723125e-01;
tmp[12][0] = 1.70569307751760324e-01;
tmp[13][0] = 1.70569307751760046e-01;
tmp[14][0] = 6.58861384496479685e-01;
tmp[15][0] = 3.33333333333333370e-01;
tmp[0][1] = 8.39477740995753056e-03;
tmp[1][1] = 2.63112829634638112e-01;
tmp[2][1] = 7.28492392955404355e-01;
tmp[3][1] = 7.28492392955404355e-01;
tmp[4][1] = 2.63112829634638112e-01;
tmp[5][1] = 8.39477740995753056e-03;
tmp[6][1] = 5.05472283170309566e-02;
tmp[7][1] = 8.98905543365938087e-01;
tmp[8][1] = 5.05472283170310122e-02;
tmp[9][1] = 8.14148234145536387e-02;
tmp[10][1] = 4.59292588292723125e-01;
tmp[11][1] = 4.59292588292723236e-01;
tmp[12][1] = 6.58861384496479685e-01;
tmp[13][1] = 1.70569307751760324e-01;
tmp[14][1] = 1.70569307751760046e-01;
tmp[15][1] = 3.33333333333333370e-01;
}
/* generate the coordinates of the quadrature points from the barycentric coordinates */
for( i = 0; i < nq; i++ ) {
qi[i][0] = a[0]*tmp[i][0] + b[0]*tmp[i][1] + c[0]*(1.0 - tmp[i][0] - tmp[i][1]);
qi[i][1] = a[1]*tmp[i][0] + b[1]*tmp[i][1] + c[1]*(1.0 - tmp[i][0] - tmp[i][1]);
}
}
double Triangle::CrossProduct( int origin ) {
double p1[2], p2[2], p3[2], x12, y12, x13, y13;
if( origin == 1 ) {
p1[0] = a[0]; p2[0] = b[0]; p3[0] = c[0];
p1[1] = a[1]; p2[1] = b[1]; p3[1] = c[1];
}
else if( origin == 2 ) {
p1[0] = b[0]; p2[0] = c[0]; p3[0] = a[0];
p1[1] = b[1]; p2[1] = c[1]; p3[1] = a[1];
}
else if( origin == 3 ) {
p1[0] = c[0]; p2[0] = a[0]; p3[0] = b[0];
p1[1] = c[1]; p2[1] = a[1]; p3[1] = b[1];
}
else {
cerr << "invalid origin vertex index (must be 1-3)" << endl;
abort();
}
x12 = p2[0] - p1[0];
y12 = p2[1] - p1[1];
x13 = p3[0] - p1[0];
y13 = p3[1] - p1[1];
return x12*y13 - y12*x13;
}