tetrahedron< PT, PD > Class Template Reference

Tetrahedron properties. More...

#include <tetrahedron.h>

Inheritance diagram for tetrahedron< PT, PD >:

Collaboration diagram for tetrahedron< PT, PD >:

List of all members.

Public Types
typedef PT	PTtype
typedef PD	PDtype
typedef void(triangle3D< PT, PD >::*	Fptr )(PT &) const
Public Member Functions
	tetrahedron ()
	Unconstructed tetrahedron.
	tetrahedron (PT const &p0_, PT const &p1_, PT const &p2_, PT const &p3_)
	The first three points form the inner base with a clockwise winding.
void	construct (PT const &p0_, PT const &p1_, PT const &p2_, PT const &p3_)
	The first three points form the inner base with a clockwise winding.
void	constructUnordered (PT const &p0_, PT const &p1_, PT const &p2_, PT const &p3_)
	A tetrahedron is formed, but there is no guarantee of point order as they are swapped to get a correctly ordered tetrahedron.
void	centroid (PT &x) const
	The average of the four points.
void	equilaterali (PT &x, uint i) const
	Generalizing the equilateral triangle to a tetrahedron, i indexes the face opposite point i, construct a point which has all sides of the new tetrahedron with the same triangle.
void	circumcenter (PT &x) const
	Center of sphere.
void	circumcenter (PT &x, uintc i) const
	Center of triangle opposite vertex i.
void	verticiespoint (PT &x, uintc i) const
void	triangleverticiespoint (PT &x, uintc i) const
	Calculate the altitude to point on a triangle face.
void	trianglei (triangle3D< PT, PD > &x, uintc i) const
	From vertex i extend a line bisecting the angle in half.
boolc	valid () const
	If the point representation is invalid and NDEBUG is not definded the function asserts.
void	applytoself (tetrahedron< PT, PD > &tet, Fptr fn) const
	Apply a function to generate a point from each side of the tetrahedron from the 3D triangle, the four points form another tetrahedron.
void	applytoself (tetrahedron< PT, PD > &tet, Fptr fn, uintc n) const
Public Attributes
PT	pi [4]
	The four points of the tetrahedron.

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Detailed Description

template<typename PT, typename PD>
class tetrahedron< PT, PD >

Tetrahedron properties.

PT is the point type. PD is the data type comprising the point.

Definition at line 21 of file tetrahedron.h.

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Member Typedef Documentation

template<typename PT, typename PD>

typedef void(triangle3D<PT,PD>::* tetrahedron< PT, PD >::Fptr)(PT &) const

template<typename PT, typename PD>

typedef PD tetrahedron< PT, PD >::PDtype

Definition at line 26 of file tetrahedron.h.

template<typename PT, typename PD>

typedef PT tetrahedron< PT, PD >::PTtype

Definition at line 25 of file tetrahedron.h.

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Constructor & Destructor Documentation

template<typename PT, typename PD>

tetrahedron< PT, PD >::tetrahedron

(

)

[inline]

Unconstructed tetrahedron.

Definition at line 32 of file tetrahedron.h.

{}

template<typename PT, typename PD >

tetrahedron< PT, PD >::tetrahedron	(	PT const &	p0_,
		PT const &	p1_,
		PT const &	p2_,
		PT const &	p3_
	)			[inline]

The first three points form the inner base with a clockwise winding.

Definition at line 537 of file tetrahedron.h.

{
  construct(p0,p1,p2,p3);
}

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Member Function Documentation

template<typename PT, typename PD>

void tetrahedron< PT, PD >::applytoself	(	tetrahedron< PT, PD > &	tet,
		Fptr	fn,
		uintc	n
	)			const

template<typename PT, typename PD>

void tetrahedron< PT, PD >::applytoself	(	tetrahedron< PT, PD > &	tet,
		Fptr	fn
	)			const

Apply a function to generate a point from each side of the tetrahedron from the 3D triangle, the four points form another tetrahedron.

Referenced by tetrahedrontest::test02().

template<typename PT, typename PD >

void tetrahedron< PT, PD >::centroid

(

PT &

x

)

const [inline]

The average of the four points.

Definition at line 220 of file tetrahedron.h.

References tetrahedron< PT, PD >::pi.

{
  x = pi[0];
  x += pi[1];
  x += pi[2];
  x += pi[3];
  x *= 0.25;
}

template<typename PT, typename PD >

void tetrahedron< PT, PD >::circumcenter	(	PT &	x,
		uintc	i
	)			const [inline]

Center of triangle opposite vertex i.

Definition at line 282 of file tetrahedron.h.

{
assert(false);
/*
// <TODO>
//  T N3(hi[i].nml);

  T a(pi[(i+1)%4]);
  T b(pi[(i+2)%4]);
  T c(pi[(i+3)%4]);

  crossprod< T > cross;
  T N1,N2;
  cross( N1, a-b, N3 );
  cross( N2, c-b, N3 );

  T mba = (b+a)*0.5;
  T mbc = (b+c)*0.5;

  T t0, t1;

  d2matsolve
  (
    t0, t1,
    N1.x, -N2.x, 
    N1.y, -N2.y, 
    mbc.x - mba.x,
    mbc.y - mba.y
  );

  return N1*t0 + mba;
*/
}

template<typename PT, typename PD >

void tetrahedron< PT, PD >::circumcenter

(

PT &

x

)

const [inline]

Center of sphere.

ie distances to verticies are all equal.

Definition at line 244 of file tetrahedron.h.

References gausselim< T >::columnC(), gausselim< T >::eval(), and tetrahedron< PT, PD >::pi.

Referenced by visualize_tetrahedron< T >::eval(), and cpsphere::update().

{
  // Translate the points : p[0] is at the origin.
  PT p[4];
  for (uint i=0; i<4; ++i)
  {
    p[i] = pi[i];
    p[i] -= pi[0];
  };

  PD e[] = 
  {
    p[1].x, p[1].y, p[1].z, p[1].dot()*0.5,
    p[2].x, p[2].y, p[2].z, p[2].dot()*0.5,
    p[3].x, p[3].y, p[3].z, p[3].dot()*0.5
  };

  //gausselim<PD,3> g(e,1E-15);
  gausselim<PD> g(e,3);
//cout << "Initial system" << endl;
//  g.print();
  g.eval();
//cout << "Solve system." << endl;
//g.print();

  PD s[3];
  g.columnC(s);

  x = pi[0];
  x.x += s[0];
  x.y += s[1];
  x.z += s[2];
  
//  return pi[0]+(PT)(s[0],s[1],s[2]);
}

template<typename PT, typename PD >

void tetrahedron< PT, PD >::construct	(	PT const &	p0_,
		PT const &	p1_,
		PT const &	p2_,
		PT const &	p3_
	)			[inline]

The first three points form the inner base with a clockwise winding.

Definition at line 549 of file tetrahedron.h.

{
  pi[0] = p0;
  pi[1] = p1;
  pi[2] = p2;
  pi[3] = p3;

  assert(valid());
}

template<typename PT, typename PD >

void tetrahedron< PT, PD >::constructUnordered	(	PT const &	p0_,
		PT const &	p1_,
		PT const &	p2_,
		PT const &	p3_
	)			[inline]

A tetrahedron is formed, but there is no guarantee of point order as they are swapped to get a correctly ordered tetrahedron.

Definition at line 566 of file tetrahedron.h.

{
  pi[0] = p0;
  pi[1] = p1;
  pi[2] = p2;
  pi[3] = p3;

  if (valid()==false)
  {
    pi[0] = p2;
    pi[2] = p0;

    assert(valid());
  }
}

template<typename PT, typename PD >

void tetrahedron< PT, PD >::equilaterali	(	PT &	x,
		uint	i
	)			const [inline]

Generalizing the equilateral triangle to a tetrahedron, i indexes the face opposite point i, construct a point which has all sides of the new tetrahedron with the same triangle.

Definition at line 170 of file tetrahedron.h.

References triangle3D< PT, PD >::centroid(), triangle3D< PT, PD >::normal(), triangle3D< PT, PD >::pi, solvequadratic(), and tetrahedron< PT, PD >::trianglei().

{
  triangle3D<PT,PD> w;
  trianglei(w,i);
  PT a;
  w.centroid(a);
  PT b;
  w.normal(b);
  PT a2(a-w.pi[0]);
  // The distance between point 1 and 2, squared.
  PD l0 = (w.pi[1]-w.pi[2]).dot();

  // Currently must solve in doubles.
  PD t0;
  PD t1;
  //double t0;
  //double t1;
  solvequadratic(t0,t1,b.dot(),a2.dot(b)*2.0,a2.dot()-l0);
  PD t=t0;
  if (t<0)
    t=t1;
  assert(t>0);

  x = a+b*t;
}

template<typename PT, typename PD>

void tetrahedron< PT, PD >::trianglei	(	triangle3D< PT, PD > &	x,
		uintc	i
	)			const [inline]

From vertex i extend a line bisecting the angle in half.

Return where this line intersects the triangles edge. The triangle opposite the point i with anticlockwise point ordering facing outside the tetrahedron, arbitary orientation.

Definition at line 198 of file tetrahedron.h.

References triangle3D< PT, PD >::construct(), halfspaceD3< PT, PD >::isInside(), and triangle3D< PT, PD >::pi.

Referenced by tetrahedron< PT, PD >::equilaterali().

{
  PT q;
  switch (i)
  {
    case 0: x.construct(pi[3],pi[2],pi[1]); break;
    case 1: x.construct(pi[0],pi[2],pi[3]); break;
    case 2: x.construct(pi[1],pi[0],pi[3]); break;
    case 3: x.construct(pi[0],pi[1],pi[2]); break;
    default: assert(false); return;
  }

#ifndef NDEBUG
  halfspaceD3<PT,PD> h(x.pi[2],x.pi[1],x.pi[0]);
  assert( h.isInside(pi[i]) );
#endif
}

template<typename PT, typename PD >

void tetrahedron< PT, PD >::triangleverticiespoint	(	PT &	x,
		uintc	i
	)			const [inline]

Calculate the altitude to point on a triangle face.

Definition at line 439 of file tetrahedron.h.

References d2matsolve(), crossproduct::eval(), and tetrahedron< PT, PD >::pi.

{
  PT a,b,c;

  switch(i)
  {
    case 0:
      a=pi[1]; b=pi[2]; c=pi[3];
      break;

    case 1:
      a=pi[0]; b=pi[2]; c=pi[3];
      break;

    case 2:
      a=pi[0]; b=pi[1]; c=pi[3];
//cout << SHOW(a) << endl;
//cout << SHOW(b) << endl;
//cout << SHOW(c) << endl;
      break;

    case 3:
      a=pi[0]; b=pi[1]; c=pi[2];
      break;
   
    default:
      assert(false);
  }

  PT ab = b - a;
  PT ac = c - a;

//cout << SHOW(ab) << endl;
//cout << SHOW(ac) << endl;

  PT w;
  crossproduct::eval(w,ab,ac);
  //crossprod< T > cross;
  //cross(w,ab,ac);

  PT act;
  PT abt;
  crossproduct::eval(act,w,ac);
  crossproduct::eval(abt,w,ab);
  //cross(act,w,ac);
  //cross(abt,w,ab);

  PT t0, t1;

  // Usually only one solving is necessary.
  // However if the determinant is zero, try
  // all the other combinations, one should be ok.

  // Assuming that the object is a tetrahedron: all the 
  // four points are unique.

  bool test = 
  d2matsolve
  (
    t0, t1,
    abt.x, -act.x,
    abt.y, -act.y,
    b.x - c.x,
    b.y - c.y
  );

  if (!test)
  {
    test = 
    d2matsolve
    (
      t0, t1,
      abt.x, -act.x,
       abt.z, -act.z,
      b.x - c.x,
      b.z - c.z
    );
  }

  if (!test)
  {
    test = 
    d2matsolve
    (
      t0, t1,
      abt.y, -act.y,
       abt.z, -act.z,
      b.y - c.y,
      b.z - c.z
    );
  }

  x = c + abt * t0;
}

template<typename PT , typename PD >

boolc tetrahedron< PT, PD >::valid

(

)

const [inline]

If the point representation is invalid and NDEBUG is not definded the function asserts.

Definition at line 230 of file tetrahedron.h.

References crossproduct::evalxyz(), and tetrahedron< PT, PD >::pi.

{
  PT a0(pi[1]-pi[0]);
  PT a1(pi[2]-pi[0]);
  PT a2;
  crossproduct::evalxyz(a2,a1,a0);

  PT q(pi[3]-pi[0]);
  bool res = (q.x*a2.x+q.y*a2.y+q.z*a2.z>0);

  return res;
}

template<typename PT, typename PD >

void tetrahedron< PT, PD >::verticiespoint	(	PT &	x,
		uintc	i
	)			const [inline]

Definition at line 386 of file tetrahedron.h.

References crossproduct::eval(), and tetrahedron< PT, PD >::pi.

Referenced by visualize_tetrahedron< T >::eval().

{
  PT a,b,c,d;

  // Let d be the opposite point.
  // Choose a as vector vertex.

  switch(i)
  {
    case 0:
      a=pi[3]; b=pi[2]; c=pi[1]; d=pi[0];
      break;

    case 1:
      a=pi[0]; b=pi[2]; c=pi[3]; d=pi[1];
      break;

    case 2:
      a=pi[0]; b=pi[1]; c=pi[3]; d=pi[2];
//cout << SHOW(a) << endl;
//cout << SHOW(b) << endl;
//cout << SHOW(c) << endl;
      break;

    case 3:
      a=pi[0]; b=pi[1]; c=pi[2]; d=pi[3];
      break;
   
    default:
      assert(false);
  }

  // ab
  PT A(b-a);
  // ac
  PT B(c-a);

  PT N;
  crossproduct::eval(N,A,B);
  //crossprod< T >()(N,A,B);
  assert(N.dot()!=0.0);
  
  x = N*( N.dot(a-d) / N.dot() )+ d;
}

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Member Data Documentation

template<typename PT, typename PD>

PT tetrahedron< PT, PD >::pi[4]

The four points of the tetrahedron.

Definition at line 29 of file tetrahedron.h.

Referenced by tetrahedron< PT, PD >::centroid(), tetrahedron< PT, PD >::circumcenter(), visualize_tetrahedron< T >::eval(), tetrahedron< PT, PD >::triangleverticiespoint(), tetrahedron< PT, PD >::valid(), and tetrahedron< PT, PD >::verticiespoint().

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The documentation for this class was generated from the following file:

• primshpcenters/tetrahedron.h