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moab::HomXform Class Reference

Homogeneous coordinate transformation matrix. More...

#include <HomXform.hpp>

+ Collaboration diagram for moab::HomXform:

Public Member Functions

 HomXform (const int matrix[16])
 constructor from matrix
 HomXform ()
 bare constructor
 HomXform (const int rotate[9], const int scale[3], const int translate[3])
 constructor from rotation, scaling, translation
 HomXform (int i1, int i2, int i3, int i4, int i5, int i6, int i7, int i8, int i9, int i10, int i11, int i12, int i13, int i14, int i15, int i16)
 constructor taking 16 ints, useful for efficient operators
 HomXform (HomXform const &from)
 copy constructor
HomXform inverse () const
 return this.inverse
void three_pt_xform (const HomCoord &p1, const HomCoord &q1, const HomCoord &p2, const HomCoord &q2, const HomCoord &p3, const HomCoord &q3)
 compute a transform from three points
int operator[] (const int &count) const
 operators
int & operator[] (const int &count)
bool operator== (const HomXform &rhs) const
bool operator!= (const HomXform &rhs) const
HomXform & operator= (const HomXform &rhs)
HomXform & operator*= (const HomXform &rhs)
HomXform operator* (const HomXform &rhs2) const

Static Public Attributes

static MOAB_EXPORT HomXform IDENTITY

Private Attributes

int xForm [16]
 the matrix; don't bother storing the last column, since we assume for now it's always unused

Friends

class HomCoord

Detailed Description

Homogeneous coordinate transformation matrix.

Definition at line 147 of file HomXform.hpp.

Constructor & Destructor Documentation

moab::HomXform::HomXform ( const int  matrix[16]) [inline]

constructor from matrix

Definition at line 497 of file HomXform.hpp.

References xForm.

{
    for( int i = 0; i < 16; i++ )
        xForm[i] = matrix[i];
}
moab::HomXform::HomXform ( ) [inline]

bare constructor

Definition at line 503 of file HomXform.hpp.

Referenced by inverse(), operator*(), operator*=(), and three_pt_xform().

{}
moab::HomXform::HomXform ( const int  rotate[9],
const int  scale[3],
const int  translate[3] 
) [inline]

constructor from rotation, scaling, translation

Definition at line 505 of file HomXform.hpp.

References xForm.

{
    int i, j;
    for( i = 0; i < 3; i++ )
    {
        for( j = 0; j < 3; j++ )
            xForm[i * 4 + j] = rotate[i * 3 + j] * scale[j];

        xForm[12 + i] = translate[i];
    }
    xForm[3]  = 0;
    xForm[7]  = 0;
    xForm[11] = 0;
    xForm[15] = 1;
}
moab::HomXform::HomXform ( int  i1,
int  i2,
int  i3,
int  i4,
int  i5,
int  i6,
int  i7,
int  i8,
int  i9,
int  i10,
int  i11,
int  i12,
int  i13,
int  i14,
int  i15,
int  i16 
) [inline]

constructor taking 16 ints, useful for efficient operators

Definition at line 521 of file HomXform.hpp.

References xForm.

{
    xForm[0]  = i1;
    xForm[1]  = i2;
    xForm[2]  = i3;
    xForm[3]  = i4;
    xForm[4]  = i5;
    xForm[5]  = i6;
    xForm[6]  = i7;
    xForm[7]  = i8;
    xForm[8]  = i9;
    xForm[9]  = i10;
    xForm[10] = i11;
    xForm[11] = i12;
    xForm[12] = i13;
    xForm[13] = i14;
    xForm[14] = i15;
    xForm[15] = i16;
}
moab::HomXform::HomXform ( HomXform const &  from) [inline]

copy constructor

Definition at line 188 of file HomXform.hpp.

References xForm.

    {
        std::copy( from.xForm, from.xForm + 16, xForm );
    }

Member Function Documentation

HomXform moab::HomXform::inverse ( ) const [inline]

return this.inverse

Definition at line 716 of file HomXform.hpp.

References HomXform(), XFORM, and xForm.

Referenced by moab::HomCoord::operator/=().

{

    /*
    // original code:

      HomXform tmp;

        // assign the diagonal
      tmp[0] = xForm[0];
      tmp[5] = xForm[5];
      tmp[10] = xForm[10];
      tmp[15] = xForm[15];

        // invert the rotation matrix
      tmp[XFORM_INDEX(0,1)] = XFORM(1,0);
      tmp[XFORM_INDEX(0,2)] = XFORM(2,0);
      tmp[XFORM_INDEX(1,0)] = XFORM(0,1);
      tmp[XFORM_INDEX(1,2)] = XFORM(2,1);
      tmp[XFORM_INDEX(2,0)] = XFORM(0,2);
      tmp[XFORM_INDEX(2,1)] = XFORM(1,2);

        // negative translate * Rinv
      tmp[XFORM_INDEX(3,0)] = -(XFORM(3,0)*tmp.XFORM(0,0) + XFORM(3,1)*tmp.XFORM(1,0) +
    XFORM(3,2)*tmp.XFORM(2,0)); tmp[XFORM_INDEX(3,1)] = -(XFORM(3,0)*tmp.XFORM(0,1) +
    XFORM(3,1)*tmp.XFORM(1,1) + XFORM(3,2)*tmp.XFORM(2,1)); tmp[XFORM_INDEX(3,2)] =
    -(XFORM(3,0)*tmp.XFORM(0,2) + XFORM(3,1)*tmp.XFORM(1,2) + XFORM(3,2)*tmp.XFORM(2,2));

        // zero last column
      tmp[XFORM_INDEX(0,3)] = 0;
      tmp[XFORM_INDEX(1,3)] = 0;
      tmp[XFORM_INDEX(2,3)] = 0;

        // h factor
      tmp[XFORM_INDEX(3,3)] = 1;

      return tmp;
    */

    // more efficient, but somewhat confusing (remember, column-major):

    return HomXform(
        // row 0
        xForm[0], XFORM( 1, 0 ), XFORM( 2, 0 ), 0,
        // row 1
        XFORM( 0, 1 ), xForm[5], XFORM( 2, 1 ), 0,
        // row 2
        XFORM( 0, 2 ), XFORM( 1, 2 ), xForm[10], 0,
        // row 3
        -( XFORM( 3, 0 ) * xForm[0] + XFORM( 3, 1 ) * XFORM( 0, 1 ) + XFORM( 3, 2 ) * XFORM( 0, 2 ) ),
        -( XFORM( 3, 0 ) * XFORM( 1, 0 ) + XFORM( 3, 1 ) * xForm[5] + XFORM( 3, 2 ) * XFORM( 1, 2 ) ),
        -( XFORM( 3, 0 ) * XFORM( 2, 0 ) + XFORM( 3, 1 ) * XFORM( 2, 1 ) + XFORM( 3, 2 ) * xForm[10] ), 1 );
}
bool moab::HomXform::operator!= ( const HomXform &  rhs) const [inline]

Definition at line 706 of file HomXform.hpp.

References xForm.

{
    return ( xForm[0] != rhs.xForm[0] || xForm[1] != rhs.xForm[1] || xForm[2] != rhs.xForm[2] ||
             xForm[3] != rhs.xForm[3] || xForm[4] != rhs.xForm[4] || xForm[5] != rhs.xForm[5] ||
             xForm[6] != rhs.xForm[6] || xForm[7] != rhs.xForm[7] || xForm[8] != rhs.xForm[8] ||
             xForm[9] != rhs.xForm[9] || xForm[10] != rhs.xForm[10] || xForm[11] != rhs.xForm[11] ||
             xForm[12] != rhs.xForm[12] || xForm[13] != rhs.xForm[13] || xForm[14] != rhs.xForm[14] ||
             xForm[15] != rhs.xForm[15] );
}
HomXform moab::HomXform::operator* ( const HomXform &  rhs2) const [inline]

Definition at line 564 of file HomXform.hpp.

References HomXform(), and XFORM.

{
    return HomXform(
        //  temp.XFORM(0,0)
        XFORM( 0, 0 ) * rhs2.XFORM( 0, 0 ) + XFORM( 0, 1 ) * rhs2.XFORM( 1, 0 ) + XFORM( 0, 2 ) * rhs2.XFORM( 2, 0 ) +
            XFORM( 0, 3 ) * rhs2.XFORM( 3, 0 ),
        //  temp.XFORM(0,1)
        XFORM( 0, 0 ) * rhs2.XFORM( 0, 1 ) + XFORM( 0, 1 ) * rhs2.XFORM( 1, 1 ) + XFORM( 0, 2 ) * rhs2.XFORM( 2, 1 ) +
            XFORM( 0, 3 ) * rhs2.XFORM( 3, 1 ),
        //  temp.XFORM(0,2)
        XFORM( 0, 0 ) * rhs2.XFORM( 0, 2 ) + XFORM( 0, 1 ) * rhs2.XFORM( 1, 2 ) + XFORM( 0, 2 ) * rhs2.XFORM( 2, 2 ) +
            XFORM( 0, 3 ) * rhs2.XFORM( 3, 2 ),
        //  temp.XFORM(0,3)
        XFORM( 0, 0 ) * rhs2.XFORM( 0, 3 ) + XFORM( 0, 1 ) * rhs2.XFORM( 1, 3 ) + XFORM( 0, 2 ) * rhs2.XFORM( 2, 3 ) +
            XFORM( 0, 3 ) * rhs2.XFORM( 3, 3 ),

        //  temp.XFORM(1,0)
        XFORM( 1, 0 ) * rhs2.XFORM( 0, 0 ) + XFORM( 1, 1 ) * rhs2.XFORM( 1, 0 ) + XFORM( 1, 2 ) * rhs2.XFORM( 2, 0 ) +
            XFORM( 1, 3 ) * rhs2.XFORM( 3, 0 ),
        //  temp.XFORM(1,1)
        XFORM( 1, 0 ) * rhs2.XFORM( 0, 1 ) + XFORM( 1, 1 ) * rhs2.XFORM( 1, 1 ) + XFORM( 1, 2 ) * rhs2.XFORM( 2, 1 ) +
            XFORM( 1, 3 ) * rhs2.XFORM( 3, 1 ),
        //  temp.XFORM(1,2)
        XFORM( 1, 0 ) * rhs2.XFORM( 0, 2 ) + XFORM( 1, 1 ) * rhs2.XFORM( 1, 2 ) + XFORM( 1, 2 ) * rhs2.XFORM( 2, 2 ) +
            XFORM( 1, 3 ) * rhs2.XFORM( 3, 2 ),
        //  temp.XFORM(1,3)
        XFORM( 1, 0 ) * rhs2.XFORM( 0, 3 ) + XFORM( 1, 1 ) * rhs2.XFORM( 1, 3 ) + XFORM( 1, 2 ) * rhs2.XFORM( 2, 3 ) +
            XFORM( 1, 3 ) * rhs2.XFORM( 3, 3 ),

        //  temp.XFORM(2,0)
        XFORM( 2, 0 ) * rhs2.XFORM( 0, 0 ) + XFORM( 2, 1 ) * rhs2.XFORM( 1, 0 ) + XFORM( 2, 2 ) * rhs2.XFORM( 2, 0 ) +
            XFORM( 2, 3 ) * rhs2.XFORM( 3, 0 ),
        //  temp.XFORM(2,1)
        XFORM( 2, 0 ) * rhs2.XFORM( 0, 1 ) + XFORM( 2, 1 ) * rhs2.XFORM( 1, 1 ) + XFORM( 2, 2 ) * rhs2.XFORM( 2, 1 ) +
            XFORM( 2, 3 ) * rhs2.XFORM( 3, 1 ),
        //  temp.XFORM(2,2)
        XFORM( 2, 0 ) * rhs2.XFORM( 0, 2 ) + XFORM( 2, 1 ) * rhs2.XFORM( 1, 2 ) + XFORM( 2, 2 ) * rhs2.XFORM( 2, 2 ) +
            XFORM( 2, 3 ) * rhs2.XFORM( 3, 2 ),
        //  temp.XFORM(2,3)
        XFORM( 2, 0 ) * rhs2.XFORM( 0, 3 ) + XFORM( 2, 1 ) * rhs2.XFORM( 1, 3 ) + XFORM( 2, 2 ) * rhs2.XFORM( 2, 3 ) +
            XFORM( 2, 3 ) * rhs2.XFORM( 3, 3 ),

        //  temp.XFORM(3,0)
        //  xForm[12]*rhs2.xForm[0] + xForm[13]*rhs2.xForm[4] + xForm[14]*rhs2.xForm[8] +
        //  xForm[15]*rhs2.xForm[12]
        XFORM( 3, 0 ) * rhs2.XFORM( 0, 0 ) + XFORM( 3, 1 ) * rhs2.XFORM( 1, 0 ) + XFORM( 3, 2 ) * rhs2.XFORM( 2, 0 ) +
            XFORM( 3, 3 ) * rhs2.XFORM( 3, 0 ),
        //  temp.XFORM(3,1)
        //  xForm[12]*rhs2.xForm[1] + xForm[13]*rhs2.xForm[5] + xForm[14]*rhs2.xForm[9] +
        //  xForm[15]*rhs2.xForm[13]
        XFORM( 3, 0 ) * rhs2.XFORM( 0, 1 ) + XFORM( 3, 1 ) * rhs2.XFORM( 1, 1 ) + XFORM( 3, 2 ) * rhs2.XFORM( 2, 1 ) +
            XFORM( 3, 3 ) * rhs2.XFORM( 3, 1 ),
        //  temp.XFORM(3,2)
        //  xForm[12]*rhs2.xForm[2] + xForm[13]*rhs2.xForm[6] + xForm[14]*rhs2.xForm[10] +
        //  xForm[15]*rhs2.xForm[14]
        XFORM( 3, 0 ) * rhs2.XFORM( 0, 2 ) + XFORM( 3, 1 ) * rhs2.XFORM( 1, 2 ) + XFORM( 3, 2 ) * rhs2.XFORM( 2, 2 ) +
            XFORM( 3, 3 ) * rhs2.XFORM( 3, 2 ),
        //  temp.XFORM(3,3)
        //  xForm[12]*rhs2.xForm[3] + xForm[13]*rhs2.xForm[7] + xForm[14]*rhs2.xForm[11] +
        //  xForm[15]*rhs2.xForm[15]
        XFORM( 3, 0 ) * rhs2.XFORM( 0, 3 ) + XFORM( 3, 1 ) * rhs2.XFORM( 1, 3 ) + XFORM( 3, 2 ) * rhs2.XFORM( 2, 3 ) +
            XFORM( 3, 3 ) * rhs2.XFORM( 3, 3 ) );
}
HomXform & moab::HomXform::operator*= ( const HomXform &  rhs) [inline]

Definition at line 628 of file HomXform.hpp.

References HomXform(), and XFORM.

{
    *this = HomXform(
        //  temp.XFORM(0,0)
        XFORM( 0, 0 ) * rhs2.XFORM( 0, 0 ) + XFORM( 0, 1 ) * rhs2.XFORM( 1, 0 ) + XFORM( 0, 2 ) * rhs2.XFORM( 2, 0 ) +
            XFORM( 0, 3 ) * rhs2.XFORM( 3, 0 ),
        //  temp.XFORM(0,1)
        XFORM( 0, 0 ) * rhs2.XFORM( 0, 1 ) + XFORM( 0, 1 ) * rhs2.XFORM( 1, 1 ) + XFORM( 0, 2 ) * rhs2.XFORM( 2, 1 ) +
            XFORM( 0, 3 ) * rhs2.XFORM( 3, 1 ),
        //  temp.XFORM(0,2)
        XFORM( 0, 0 ) * rhs2.XFORM( 0, 2 ) + XFORM( 0, 1 ) * rhs2.XFORM( 1, 2 ) + XFORM( 0, 2 ) * rhs2.XFORM( 2, 2 ) +
            XFORM( 0, 3 ) * rhs2.XFORM( 3, 2 ),
        //  temp.XFORM(0,3)
        XFORM( 0, 0 ) * rhs2.XFORM( 0, 3 ) + XFORM( 0, 1 ) * rhs2.XFORM( 1, 3 ) + XFORM( 0, 2 ) * rhs2.XFORM( 2, 3 ) +
            XFORM( 0, 3 ) * rhs2.XFORM( 3, 3 ),

        //  temp.XFORM(1,0)
        XFORM( 1, 0 ) * rhs2.XFORM( 0, 0 ) + XFORM( 1, 1 ) * rhs2.XFORM( 1, 0 ) + XFORM( 1, 2 ) * rhs2.XFORM( 2, 0 ) +
            XFORM( 1, 3 ) * rhs2.XFORM( 3, 0 ),
        //  temp.XFORM(1,1)
        XFORM( 1, 0 ) * rhs2.XFORM( 0, 1 ) + XFORM( 1, 1 ) * rhs2.XFORM( 1, 1 ) + XFORM( 1, 2 ) * rhs2.XFORM( 2, 1 ) +
            XFORM( 1, 3 ) * rhs2.XFORM( 3, 1 ),
        //  temp.XFORM(1,2)
        XFORM( 1, 0 ) * rhs2.XFORM( 0, 2 ) + XFORM( 1, 1 ) * rhs2.XFORM( 1, 2 ) + XFORM( 1, 2 ) * rhs2.XFORM( 2, 2 ) +
            XFORM( 1, 3 ) * rhs2.XFORM( 3, 2 ),
        //  temp.XFORM(1,3)
        XFORM( 1, 0 ) * rhs2.XFORM( 0, 3 ) + XFORM( 1, 1 ) * rhs2.XFORM( 1, 3 ) + XFORM( 1, 2 ) * rhs2.XFORM( 2, 3 ) +
            XFORM( 1, 3 ) * rhs2.XFORM( 3, 3 ),

        //  temp.XFORM(2,0)
        XFORM( 2, 0 ) * rhs2.XFORM( 0, 0 ) + XFORM( 2, 1 ) * rhs2.XFORM( 1, 0 ) + XFORM( 2, 2 ) * rhs2.XFORM( 2, 0 ) +
            XFORM( 2, 3 ) * rhs2.XFORM( 3, 0 ),
        //  temp.XFORM(2,1)
        XFORM( 2, 0 ) * rhs2.XFORM( 0, 1 ) + XFORM( 2, 1 ) * rhs2.XFORM( 1, 1 ) + XFORM( 2, 2 ) * rhs2.XFORM( 2, 1 ) +
            XFORM( 2, 3 ) * rhs2.XFORM( 3, 1 ),
        //  temp.XFORM(2,2)
        XFORM( 2, 0 ) * rhs2.XFORM( 0, 2 ) + XFORM( 2, 1 ) * rhs2.XFORM( 1, 2 ) + XFORM( 2, 2 ) * rhs2.XFORM( 2, 2 ) +
            XFORM( 2, 3 ) * rhs2.XFORM( 3, 2 ),
        //  temp.XFORM(2,3)
        XFORM( 2, 0 ) * rhs2.XFORM( 0, 3 ) + XFORM( 2, 1 ) * rhs2.XFORM( 1, 3 ) + XFORM( 2, 2 ) * rhs2.XFORM( 2, 3 ) +
            XFORM( 2, 3 ) * rhs2.XFORM( 3, 3 ),

        //  temp.XFORM(3,0)
        XFORM( 3, 0 ) * rhs2.XFORM( 0, 0 ) + XFORM( 3, 1 ) * rhs2.XFORM( 1, 0 ) + XFORM( 3, 2 ) * rhs2.XFORM( 2, 0 ) +
            XFORM( 3, 3 ) * rhs2.XFORM( 3, 0 ),
        //  temp.XFORM(3,1)
        XFORM( 3, 0 ) * rhs2.XFORM( 0, 1 ) + XFORM( 3, 1 ) * rhs2.XFORM( 1, 1 ) + XFORM( 3, 2 ) * rhs2.XFORM( 2, 1 ) +
            XFORM( 3, 3 ) * rhs2.XFORM( 3, 1 ),
        //  temp.XFORM(3,2)
        XFORM( 3, 0 ) * rhs2.XFORM( 0, 2 ) + XFORM( 3, 1 ) * rhs2.XFORM( 1, 2 ) + XFORM( 3, 2 ) * rhs2.XFORM( 2, 2 ) +
            XFORM( 3, 3 ) * rhs2.XFORM( 3, 2 ),
        //  temp.XFORM(3,3)
        XFORM( 3, 0 ) * rhs2.XFORM( 0, 3 ) + XFORM( 3, 1 ) * rhs2.XFORM( 1, 3 ) + XFORM( 3, 2 ) * rhs2.XFORM( 2, 3 ) +
            XFORM( 3, 3 ) * rhs2.XFORM( 3, 3 ) );

    return *this;
}
HomXform & moab::HomXform::operator= ( const HomXform &  rhs) [inline]

Definition at line 556 of file HomXform.hpp.

References xForm.

{
    for( int i = 0; i < 16; i++ )
        xForm[i] = rhs.xForm[i];

    return *this;
}
bool moab::HomXform::operator== ( const HomXform &  rhs) const [inline]

Definition at line 696 of file HomXform.hpp.

References xForm.

{
    return ( xForm[0] == rhs.xForm[0] && xForm[1] == rhs.xForm[1] && xForm[2] == rhs.xForm[2] &&
             xForm[3] == rhs.xForm[3] && xForm[4] == rhs.xForm[4] && xForm[5] == rhs.xForm[5] &&
             xForm[6] == rhs.xForm[6] && xForm[7] == rhs.xForm[7] && xForm[8] == rhs.xForm[8] &&
             xForm[9] == rhs.xForm[9] && xForm[10] == rhs.xForm[10] && xForm[11] == rhs.xForm[11] &&
             xForm[12] == rhs.xForm[12] && xForm[13] == rhs.xForm[13] && xForm[14] == rhs.xForm[14] &&
             xForm[15] == rhs.xForm[15] );
}
int moab::HomXform::operator[] ( const int &  count) const [inline]

operators

Definition at line 686 of file HomXform.hpp.

References xForm.

{
    return xForm[count];
}
int & moab::HomXform::operator[] ( const int &  count) [inline]

Definition at line 691 of file HomXform.hpp.

References xForm.

{
    return xForm[count];
}
void moab::HomXform::three_pt_xform ( const HomCoord &  p1,
const HomCoord &  q1,
const HomCoord &  p2,
const HomCoord &  q2,
const HomCoord &  p3,
const HomCoord &  q3 
)

compute a transform from three points

Definition at line 33 of file HomXform.cpp.

References moab::HomCoord::homCoord, HomXform(), moab::HomCoord::i(), IDENTITY, moab::HomCoord::j(), moab::HomCoord::k(), moab::HomCoord::length_squared(), moab::HomCoord::normalize(), moab::HomCoord::set(), and t.

Referenced by moab::SweptElementData::add_vsequence(), and moab::ScdElementData::add_vsequence().

{
    // pmin and pmax are min and max bounding box corners which are mapped to
    // qmin and qmax, resp.  qmin and qmax are not necessarily min/max corners,
    // since the mapping can change the orientation of the box in the q reference
    // frame.  Re-interpreting the min/max bounding box corners does not change
    // the mapping.

    // change that: base on three points for now (figure out whether we can
    // just use two later); three points are assumed to define an orthogonal
    // system such that (p2-p1)%(p3-p1) = 0

    // use the three point rule to compute the mapping, from Mortensen,
    // "Geometric Modeling".  If p1, p2, p3 and q1, q2, q3 are three points in
    // the two coordinate systems, the three pt rule is:
    //
    // v1 = p2 - p1
    // v2 = p3 - p1
    // v3 = v1 x v2
    // w1-w3 similar, with q1-q3
    // V = matrix with v1-v3 as rows
    // W similar, with w1-w3
    // R = V^-1 * W
    // t = q1 - p1 * W
    // Form transform matrix M from R, t

    // check to see whether unity transform applies
    if( p1 == q1 && p2 == q2 && p3 == q3 )
    {
        *this = HomXform::IDENTITY;
        return;
    }

    // first, construct 3 pts from input
    HomCoord v1 = p2 - p1;
    assert( v1.i() != 0 || v1.j() != 0 || v1.k() != 0 );
    HomCoord v2 = p3 - p1;
    HomCoord v3 = v1 * v2;

    if( v3.length_squared() == 0 )
    {
        // 1d coordinate system; set one of v2's coordinates such that
        // it's orthogonal to v1
        if( v1.i() == 0 )
            v2.set( 1, 0, 0 );
        else if( v1.j() == 0 )
            v2.set( 0, 1, 0 );
        else if( v1.k() == 0 )
            v2.set( 0, 0, 1 );
        else
            assert( false );
        v3 = v1 * v2;
        assert( v3.length_squared() != 0 );
    }
    // assert to make sure they're each orthogonal
    assert( v1 % v2 == 0 && v1 % v3 == 0 && v2 % v3 == 0 );
    v1.normalize();
    v2.normalize();
    v3.normalize();
    // Make sure h is set to zero here, since it'll mess up things if it's one
    v1.homCoord[3] = v2.homCoord[3] = v3.homCoord[3] = 0;

    HomCoord w1 = q2 - q1;
    assert( w1.i() != 0 || w1.j() != 0 || w1.k() != 0 );
    HomCoord w2 = q3 - q1;
    HomCoord w3 = w1 * w2;

    if( w3.length_squared() == 0 )
    {
        // 1d coordinate system; set one of w2's coordinates such that
        // it's orthogonal to w1
        if( w1.i() == 0 )
            w2.set( 1, 0, 0 );
        else if( w1.j() == 0 )
            w2.set( 0, 1, 0 );
        else if( w1.k() == 0 )
            w2.set( 0, 0, 1 );
        else
            assert( false );
        w3 = w1 * w2;
        assert( w3.length_squared() != 0 );
    }
    // assert to make sure they're each orthogonal
    assert( w1 % w2 == 0 && w1 % w3 == 0 && w2 % w3 == 0 );
    w1.normalize();
    w2.normalize();
    w3.normalize();
    // Make sure h is set to zero here, since it'll mess up things if it's one
    w1.homCoord[3] = w2.homCoord[3] = w3.homCoord[3] = 0;

    // form v^-1 as transpose (ok for orthogonal vectors); put directly into
    // transform matrix, since it's eventually going to become R
    *this = HomXform( v1.i(), v2.i(), v3.i(), 0, v1.j(), v2.j(), v3.j(), 0, v1.k(), v2.k(), v3.k(), 0, 0, 0, 0, 1 );

    // multiply by w to get R
    *this *= HomXform( w1.i(), w1.j(), w1.k(), 0, w2.i(), w2.j(), w2.k(), 0, w3.i(), w3.j(), w3.k(), 0, 0, 0, 0, 1 );

    // compute t and put into last row
    HomCoord t              = q1 - p1 * *this;
    ( *this ).XFORM( 3, 0 ) = t.i();
    ( *this ).XFORM( 3, 1 ) = t.j();
    ( *this ).XFORM( 3, 2 ) = t.k();

    // M should transform p to q
    assert( ( q1 == p1 * *this ) && ( q2 == p2 * *this ) && ( q3 == p3 * *this ) );
}

Friends And Related Function Documentation

friend class HomCoord [friend]

Definition at line 156 of file HomXform.hpp.

Member Data Documentation

HomXform moab::HomXform::IDENTITY [static]

Definition at line 158 of file HomXform.hpp.

Referenced by three_pt_xform().

int moab::HomXform::xForm[16] [private]

the matrix; don't bother storing the last column, since we assume for now it's always unused

Definition at line 153 of file HomXform.hpp.

Referenced by HomXform(), inverse(), operator!=(), moab::HomCoord::operator*(), moab::HomCoord::operator*=(), operator=(), operator==(), and operator[]().

List of all members.

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