///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
//
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
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// notice, this list of conditions and the following disclaimer.
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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
// nearestPointOnTriangle(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"
namespace Imath {
template <class T>
bool closestPoints(const Line3<T>& line1,
const Line3<T>& line2,
Vec3<T>& point1,
Vec3<T>& point2)
{
//
// Compute the closest points on two lines. This was originally
// lifted from inventor. This function assumes that the line
// directions are normalized. The original math has been collapsed.
//
T A = line1.dir ^ line2.dir;
if ( A == 1 ) return false;
T denom = A * A - 1;
T B = (line1.dir ^ line1.pos) - (line1.dir ^ line2.pos);
T C = (line2.dir ^ line1.pos) - (line2.dir ^ line2.pos);
point1 = line1(( B - A * C ) / denom);
point2 = line2(( B * A - C ) / denom);
return true;
}
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)
{
// Intersect the line with a triangle.
// 1. find plane of triangle
// 2. find intersection point of ray and plane
// 3. pick plane to project point and triangle into
// 4. check each edge of triangle to see if point is inside it
//
// XXX TODO - this routine is way too long
// - the value of EPSILON is dubious
// - there should be versions of this
// routine that do not calculate the
// barycentric coordinates or the
// front flag
const float EPSILON = 1e-6;
T d, t, d01, d12, d20, vd0, vd1, vd2, ax, ay, az, sense;
Vec3<T> v01, v12, v20, c;
int axis0, axis1;
// calculate plane for polygon
v01 = v1 - v0;
v12 = v2 - v1;
// c is un-normalized normal
c = v12.cross(v01);
d = c.length();
if(d < EPSILON)
return false; // cant hit a triangle with no area
c = c * (1. / d);
// calculate distance to plane along ray
d = line.dir.dot(c);
if (d < EPSILON && d > -EPSILON)
return false; // line is parallel to plane containing triangle
t = (v0 - line.pos).dot(c) / d;
if(t < 0)
return false;
// calculate intersection point
pt = line.pos + t * line.dir;
// is point inside triangle? Project to 2d to find out
// use the plane that has the largest absolute value
// component in the normal
ax = c[0] < 0 ? -c[0] : c[0];
ay = c[1] < 0 ? -c[1] : c[1];
az = c[2] < 0 ? -c[2] : c[2];
if(ax > ay && ax > az)
{
// project on x=0 plane
axis0 = 1;
axis1 = 2;
sense = c[0] < 0 ? -1 : 1;
}
else if(ay > az)
{
axis0 = 2;
axis1 = 0;
sense = c[1] < 0 ? -1 : 1;
}
else
{
axis0 = 0;
axis1 = 1;
sense = c[2] < 0 ? -1 : 1;
}
// distance from v0-v1 must be less than distance from v2 to v0-v1
d01 = sense * ((pt[axis0] - v0[axis0]) * v01[axis1]
- (pt[axis1] - v0[axis1]) * v01[axis0]);
if(d01 < 0) return false;
vd2 = sense * ((v2[axis0] - v0[axis0]) * v01[axis1]
- (v2[axis1] - v0[axis1]) * v01[axis0]);
if(d01 > vd2) return false;
// distance from v1-v2 must be less than distance from v1 to v2-v0
d12 = sense * ((pt[axis0] - v1[axis0]) * v12[axis1]
- (pt[axis1] - v1[axis1]) * v12[axis0]);
if(d12 < 0) return false;
vd0 = sense * ((v0[axis0] - v1[axis0]) * v12[axis1]
- (v0[axis1] - v1[axis1]) * v12[axis0]);
if(d12 > vd0) return false;
// calculate v20, and do check on final side of triangle
v20 = v0 - v2;
d20 = sense * ((pt[axis0] - v2[axis0]) * v20[axis1]
- (pt[axis1] - v2[axis1]) * v20[axis0]);
if(d20 < 0) return false;
vd1 = sense * ((v1[axis0] - v2[axis0]) * v20[axis1]
- (v1[axis1] - v2[axis1]) * v20[axis0]);
if(d20 > vd1) return false;
// vd0, vd1, and vd2 will always be non-zero for a triangle
// that has non-zero area (we return before this for
// zero area triangles)
barycentric = Vec3<T>(d12 / vd0, d20 / vd1, d01 / vd2);
front = line.dir.dot(c) < 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>
nearestPointOnTriangle(const Vec3<T> &v0,
const Vec3<T> &v1,
const Vec3<T> &v2,
const Line3<T> &l)
{
Vec3<T> pt, barycentric;
bool front;
if (intersect (l, v0, v1, v2, pt, barycentric, front))
return pt;
//
// The line did not intersect the triangle, so to be picky, you should
// find the closest edge that it passed over/under, but chances are that
// 1) another triangle will be closer
// 2) the app does not need this much precision for a ray that does not
// intersect the triangle
// 3) the expense of the calculation is not worth it since this is the
// common case
//
// XXX TODO This is bogus -- nearestPointOnTriangle() should do
// what its name implies; it should return a point
// on an edge if some edge is closer to the line than
// any vertex. If the application does not want the
// extra calculations, it should be possible to specify
// that; it is not up to this nearestPointOnTriangle()
// to make the decision.
return closestVertex(v0, v1, v2, l);
}
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