334 lines
9.2 KiB
C++
334 lines
9.2 KiB
C++
///////////////////////////////////////////////////////////////////////////
|
|
//
|
|
// 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
|
|
// met:
|
|
// * Redistributions of source code must retain the above copyright
|
|
// notice, this list of conditions and the following disclaimer.
|
|
// * Redistributions in binary form must reproduce the above
|
|
// copyright notice, this list of conditions and the following disclaimer
|
|
// in the documentation and/or other materials provided with the
|
|
// distribution.
|
|
// * Neither the name of Industrial Light & Magic nor the names of
|
|
// its contributors may be used to endorse or promote products derived
|
|
// from this software without specific prior written permission.
|
|
//
|
|
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
|
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
|
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
|
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
|
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
|
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
|
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
|
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
|
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
//
|
|
///////////////////////////////////////////////////////////////////////////
|
|
|
|
|
|
|
|
#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
|