ImathLineAlgo.h

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//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
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// from this software without specific prior written permission. 
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#ifndef INCLUDED_IMATHLINEALGO_H
#define INCLUDED_IMATHLINEALGO_H

//------------------------------------------------------------------
//
//  This file contains algorithms applied to or in conjunction
//  with lines (Imath::Line). These algorithms may require
//  more headers to compile. The assumption made is that these
//  functions are called much less often than the basic line
//  functions or these functions require more support classes
//
//  Contains:
//
//  bool closestPoints(const Line<T>& line1,
//             const Line<T>& line2,
//             Vec3<T>& point1,
//             Vec3<T>& point2)
//
//  bool intersect( const Line3<T> &line,
//          const Vec3<T> &v0,
//          const Vec3<T> &v1,
//          const Vec3<T> &v2,
//          Vec3<T> &pt,
//          Vec3<T> &barycentric,
//          bool &front)
//
//      V3f
//      closestVertex(const Vec3<T> &v0,
//                    const Vec3<T> &v1,
//                    const Vec3<T> &v2,
//                    const Line3<T> &l)
//
//  V3f
//  rotatePoint(const Vec3<T> p, Line3<T> l, float angle)
//
//------------------------------------------------------------------

#include "ImathLine.h"
#include "ImathVecAlgo.h"
#include "ImathFun.h"

namespace Imath {


template <class T>
bool
closestPoints
    (const Line3<T>& line1,
     const Line3<T>& line2,
     Vec3<T>& point1,
     Vec3<T>& point2)
{
    //
    // Compute point1 and point2 such that point1 is on line1, point2
    // is on line2 and the distance between point1 and point2 is minimal.
    // This function returns true if point1 and point2 can be computed,
    // or false if line1 and line2 are parallel or nearly parallel.
    // This function assumes that line1.dir and line2.dir are normalized.
    //

    Vec3<T> w = line1.pos - line2.pos;
    T d1w = line1.dir ^ w;
    T d2w = line2.dir ^ w;
    T d1d2 = line1.dir ^ line2.dir;
    T n1 = d1d2 * d2w - d1w;
    T n2 = d2w - d1d2 * d1w;
    T d = 1 - d1d2 * d1d2;
    T absD = abs (d);

    if ((absD > 1) ||
    (abs (n1) < limits<T>::max() * absD &&
     abs (n2) < limits<T>::max() * absD))
    {
    point1 = line1 (n1 / d);
    point2 = line2 (n2 / d);
    return true;
    }
    else
    {
    return false;
    }
}


template <class T>
bool
intersect
    (const Line3<T> &line,
     const Vec3<T> &v0,
     const Vec3<T> &v1,
     const Vec3<T> &v2,
     Vec3<T> &pt,
     Vec3<T> &barycentric,
     bool &front)
{
    //
    // Given a line and a triangle (v0, v1, v2), the intersect() function
    // finds the intersection of the line and the plane that contains the
    // triangle.
    //
    // If the intersection point cannot be computed, either because the
    // line and the triangle's plane are nearly parallel or because the
    // triangle's area is very small, intersect() returns false.
    //
    // If the intersection point is outside the triangle, intersect
    // returns false.
    //
    // If the intersection point, pt, is inside the triangle, intersect()
    // computes a front-facing flag and the barycentric coordinates of
    // the intersection point, and returns true.
    //
    // The front-facing flag is true if the dot product of the triangle's
    // normal, (v2-v1)%(v1-v0), and the line's direction is negative.
    //
    // The barycentric coordinates have the following property:
    //
    //     pt = v0 * barycentric.x + v1 * barycentric.y + v2 * barycentric.z
    //

    Vec3<T> edge0 = v1 - v0;
    Vec3<T> edge1 = v2 - v1;
    Vec3<T> normal = edge1 % edge0;

    T l = normal.length();

    if (l != 0)
    normal /= l;
    else
    return false;   // zero-area triangle

    //
    // d is the distance of line.pos from the plane that contains the triangle.
    // The intersection point is at line.pos + (d/nd) * line.dir.
    //

    T d = normal ^ (v0 - line.pos);
    T nd = normal ^ line.dir;

    if (abs (nd) > 1 || abs (d) < limits<T>::max() * abs (nd))
    pt = line (d / nd);
    else
    return false;  // line and plane are nearly parallel

    //
    // Compute the barycentric coordinates of the intersection point.
    // The intersection is inside the triangle if all three barycentric
    // coordinates are between zero and one.
    //

    {
    Vec3<T> en = edge0.normalized();
    Vec3<T> a = pt - v0;
    Vec3<T> b = v2 - v0;
    Vec3<T> c = (a - en * (en ^ a));
    Vec3<T> d = (b - en * (en ^ b));
    T e = c ^ d;
    T f = d ^ d;

    if (e >= 0 && e <= f)
        barycentric.z = e / f;
    else
        return false; // outside
    }

    {
    Vec3<T> en = edge1.normalized();
    Vec3<T> a = pt - v1;
    Vec3<T> b = v0 - v1;
    Vec3<T> c = (a - en * (en ^ a));
    Vec3<T> d = (b - en * (en ^ b));
    T e = c ^ d;
    T f = d ^ d;

    if (e >= 0 && e <= f)
        barycentric.x = e / f;
    else
        return false; // outside
    }

    barycentric.y = 1 - barycentric.x - barycentric.z;

    if (barycentric.y < 0)
    return false; // outside

    front = ((line.dir ^ normal) < 0);
    return true;
}


template <class T>
Vec3<T>
closestVertex
    (const Vec3<T> &v0,
     const Vec3<T> &v1,
     const Vec3<T> &v2,
     const Line3<T> &l)
{
    Vec3<T> nearest = v0;
    T neardot       = (v0 - l.closestPointTo(v0)).length2();
    
    T tmp           = (v1 - l.closestPointTo(v1)).length2();

    if (tmp < neardot)
    {
        neardot = tmp;
        nearest = v1;
    }

    tmp = (v2 - l.closestPointTo(v2)).length2();
    if (tmp < neardot)
    {
        neardot = tmp;
        nearest = v2;
    }

    return nearest;
}


template <class T>
Vec3<T>
rotatePoint (const Vec3<T> p, Line3<T> l, T angle)
{
    //
    // Rotate the point p around the line l by the given angle.
    //

    //
    // Form a coordinate frame with <x,y,a>. The rotation is the in xy
    // plane.
    //

    Vec3<T> q = l.closestPointTo(p);
    Vec3<T> x = p - q;
    T radius = x.length();

    x.normalize();
    Vec3<T> y = (x % l.dir).normalize();

    T cosangle = Math<T>::cos(angle);
    T sinangle = Math<T>::sin(angle);

    Vec3<T> r = q + x * radius * cosangle + y * radius * sinangle; 

    return r;
}


} // namespace Imath

#endif