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#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <cmath>
using namespace std;
using Mat = vector< vector<double> >;
const double PI = 4.0 * atan( 1.0 );
//====
class Stl;
//
class Shape
{
public:
virtual void addToPlot( Stl &stl ) = 0;
};
//====
struct Pt
{
double x, y, z;
Pt( double x = 0, double y = 0, double z = 0 ) : x( x ), y( y ), z( z ) {}
};
//
Pt operator + ( const Pt &a, const Pt &b ){ return { a.x + b.x, a.y + b.y, a.z + b.z }; }
Pt operator  ( const Pt &a, const Pt &b ){ return { a.x  b.x, a.y  b.y, a.z  b.z }; }
Pt operator / ( const Pt &a, double d ){ return { a.x / d, a.y / d, a.z / d }; }
Pt operator * ( double d , const Pt &a ){ return { d * a.x, d * a.y, d * a.z }; }
Pt cross ( const Pt &a, const Pt &b ){ return { a.y * b.z  a.z * b.y, a.z * b.x  a.x * b.z, a.x * b.y  a.y * b.x }; }
double dot ( const Pt &a, const Pt &b ){ return a.x * b.x + a.y * b.y + a.z * b.z; }
double normsq ( const Pt &a ){ return dot( a, a ); }
double len ( const Pt &a ){ return sqrt( normsq( a ) ); }
ostream & operator << ( ostream &out, const Pt a ){ return out << a.x << " " << a.y << " " << a.z << " "; }
Pt operator * ( const Mat &M, const Pt &v )
{
return { M[0][0] * v.x + M[0][1] * v.y + M[0][2] * v.z,
M[1][0] * v.x + M[1][1] * v.y + M[1][2] * v.z,
M[2][0] * v.x + M[2][1] * v.y + M[2][2] * v.z };
}
Mat operator * ( const Mat &M, const Mat &N )
{
Mat R( M.size(), vector<double>( N[0].size(), 0.0 ) );
for ( int i = 0; i < M.size(); i++ )
{
for ( int j = 0; j < N[0].size(); j++ )
{
for ( int k = 0; k < N.size(); k++ ) R[i][j] += M[i][k] * N[k][j];
}
}
return R;
}
//====
Mat rotationMatrix( const Pt &axis, double radians )
{
Mat result( 3, vector<double>( 3, 0.0 ) );
Pt n = axis / len( axis );
double cosA = cos( radians ), sinA = sin( radians ), cosA1 = 1.0  cosA;
result[0][0] = cosA + n.x * n.x * cosA1;
result[0][1] = + n.x * n.y * cosA1  n.z * sinA;
result[0][2] = + n.x * n.z * cosA1 + n.y * sinA;
result[1][0] = + n.y * n.x * cosA1 + n.z * sinA;
result[1][1] = cosA + n.y * n.y * cosA1;
result[1][2] = + n.y * n.z * cosA1  n.x * sinA;
result[2][0] = + n.z * n.x * cosA1  n.y * sinA;
result[2][1] = + n.z * n.y * cosA1 + n.x * sinA;
result[2][2] = cosA + n.z * n.z * cosA1;
return result;
}
//
void axisAngle( const Mat &R, Pt &axis, double &angle )
{
angle = acos( 0.5 * ( R[0][0] + R[1][1] + R[2][2]  1 ) );
double s = sin( angle );
if ( abs( s ) < 1.0e6 ) axis = Pt( 1.0, 0.0, 0.0 );
else axis = ( 0.5 / s ) * Pt( R[2][1]  R[1][2], R[0][2]  R[2][0], R[1][0]  R[0][1] );
axis = axis / len( axis );
}
//====
struct Triangle
{
Pt v1, v2, v3;
Triangle( const Pt &v1, const Pt &v2, const Pt &v3 ) : v1( v1 ), v2( v2 ), v3( v3 ) {}
};
//====
class Stl
{
vector<Triangle> triangles;
public:
void add( Shape *S ) { S>addToPlot( *this ); }
void addTriangle( const Pt &v1, const Pt &v2, const Pt &v3 ) { triangles.push_back( Triangle( v1, v2, v3 ) ); }
void addRectangle( const Pt &v1, const Pt &v2, const Pt &v3, const Pt &v4 ) { addTriangle( v1, v2, v3 ); addTriangle( v1, v3, v4 ); }
void insert( const Stl &stl ) { triangles.insert( triangles.end(), stl.triangles.begin(), stl.triangles.end() ); }
void translate( const Pt &v ) { for ( Triangle &t : triangles ) t = Triangle( t.v1 + v, t.v2 + v, t.v3 + v ); }
void scale( double s ) { for ( Triangle &t : triangles ) t = Triangle( s * t.v1, s * t.v2, s * t.v3 ); }
void scale( double s, const Pt ¢re ) { translate( 1 * centre ); scale( s ); translate( centre ); }
void rotate( const Mat &M ) { for ( Triangle &t : triangles ) t = Triangle( M * t.v1, M * t.v2, M * t.v3 ); }
void rotate( const Mat &M, const Pt ¢re ) { translate( 1 * centre ); rotate( M ); translate( centre ); }
void draw( const string &filename );
};
//
void Stl::draw( const string &filename )
{
ofstream out( filename );
out << "solid\n";
for ( Triangle t : triangles )
{
Pt n = cross( t.v2  t.v1, t.v3  t.v1 );
n = n / len( n );
out << " facet normal " << n << '\n';
out << " outer loop\n";
out << " vertex " << t.v1 << '\n';
out << " vertex " << t.v2 << '\n';
out << " vertex " << t.v3 << '\n';
out << " endloop\n";
out << " endfacet\n";
}
out << "endsolid\n";
}
//====
class Cuboid : public Shape
{
Pt centre;
Pt side1, side2, side3;
public:
Cuboid( const Pt &c, double L ) : centre( c ), side1( Pt( L, 0, 0 ) ), side2( Pt( 0, L, 0 ) ), side3( Pt( 0, 0, L ) ) {}
Cuboid( const Pt &c, const Pt &s1, const Pt &s2, const Pt &s3 ) : centre( c ), side1( s1 ), side2( s2 ), side3( s3 ) {}
void addToPlot( Stl &stl );
};
//
void Cuboid::addToPlot( Stl &stl )
{
Pt v1 = centre  0.5 * ( side1 + side2 + side3 );
Pt v2 = v1 + side1, v3 = v2 + side2, v4 = v3  side1;
Pt v5 = v1 + side3, v6 = v2 + side3, v7 = v3 + side3, v8 = v4 + side3;
stl.addRectangle( v1, v2, v6, v5 );
stl.addRectangle( v2, v3, v7, v6 );
stl.addRectangle( v3, v4, v8, v7 );
stl.addRectangle( v4, v1, v5, v8 );
stl.addRectangle( v1, v4, v3, v2 );
stl.addRectangle( v5, v6, v7, v8 );
}
//====
class Polymer
{
public:
double side;
Pt start;
vector< pair<Pt,double> > cubes;
Polymer( double side, const Pt &start, const vector< pair<Pt,double> > &cubes ) : side( side ), start( start ), cubes( cubes ) {}
void rotate( const Pt ¢re, const Pt &axis, double angle );
};
//
void Polymer::rotate( const Pt ¢re, const Pt &axis, double angle )
{
Mat M = rotationMatrix( axis, angle );
start = centre + M * ( start  centre );
for ( auto &C : cubes )
{
Mat P = rotationMatrix( C.first, C.second );
Mat R = M * P;
axisAngle( R, C.first, C.second );
}
}
//====
int main()
{
Polymer pb1( 1.0,
{ 10.0, 15.0, 5.0 },
{ { { 0.79948 , 0.504813 , 0.325568 }, 0.0888429 },
{ { 0.941624 , 0.0857279, 0.325568 }, 6.06663 },
{ { 0.940697 , 0.0953601, 0.325568 }, 0.454249 },
{ { 0.945361 , 0.017274 , 0.325568 }, 0.932644 },
{ { 0.936006 , 0.133785 , 0.325568 }, 0.585938 },
{ { 0.0287705, 0.945081 , 0.325568 }, 6.16575 },
{ { 0.190289 , 0.926173 , 0.325568 }, 1.48524 },
{ { 0.922358 , 0.207991 , 0.325568 }, 2.83318 },
{ { 0.0299494, 0.945044 , 0.325568 }, 2.60525 } } );
Polymer pb2 = pb1;
Pt reference = { 0.0, 0.0, 0.0 };
Pt axis = { 1.0, 0.0, 0.0 };
double angle = PI / 2.0;
pb2.rotate( reference, axis, angle );
// Add both polymers to plot
Stl stl;
Pt ex = { 1, 0, 0 }, ey = { 0, 1, 0 }, ez = { 0, 0, 1 };
for ( Polymer P : { pb1, pb2 } )
{
Pt start = P.start;
for ( auto &C : P.cubes )
{
Mat R = rotationMatrix( C.first, C.second );
Pt side1 = P.side * ( R * ex );
Pt side2 = P.side * ( R * ey );
Pt side3 = P.side * ( R * ez );
Pt centre = start + 0.5 * side3;
Cuboid cub( centre, side1, side2, side3 );
stl.add( &cub );
start = start + side3;
}
}
stl.draw( "stl.stl" );
}
 