+++ /dev/null
-///////////////////////////////////////////////////////////////////////////
-//
-// 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
projects / opencv / blobdiff