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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"
#include "ImathNamespace.h"
IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
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;
}
IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
#endif // INCLUDED_IMATHLINEALGO_H
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