289 lines
7.7 KiB
C++
289 lines
7.7 KiB
C++
///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas
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// Digital Ltd. LLC
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//
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// All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following disclaimer
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// in the documentation and/or other materials provided with the
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// distribution.
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// * Neither the name of Industrial Light & Magic nor the names of
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// its contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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///////////////////////////////////////////////////////////////////////////
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#ifndef INCLUDED_IMATHLINEALGO_H
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#define INCLUDED_IMATHLINEALGO_H
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//------------------------------------------------------------------
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//
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// This file contains algorithms applied to or in conjunction
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// with lines (Imath::Line). These algorithms may require
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// more headers to compile. The assumption made is that these
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// functions are called much less often than the basic line
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// functions or these functions require more support classes
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//
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// Contains:
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//
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// bool closestPoints(const Line<T>& line1,
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// const Line<T>& line2,
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// Vec3<T>& point1,
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// Vec3<T>& point2)
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//
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// bool intersect( const Line3<T> &line,
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// const Vec3<T> &v0,
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// const Vec3<T> &v1,
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// const Vec3<T> &v2,
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// Vec3<T> &pt,
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// Vec3<T> &barycentric,
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// bool &front)
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//
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// V3f
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// closestVertex(const Vec3<T> &v0,
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// const Vec3<T> &v1,
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// const Vec3<T> &v2,
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// const Line3<T> &l)
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//
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// V3f
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// rotatePoint(const Vec3<T> p, Line3<T> l, float angle)
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//
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//------------------------------------------------------------------
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#include "ImathLine.h"
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#include "ImathVecAlgo.h"
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#include "ImathFun.h"
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#include "ImathNamespace.h"
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IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
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template <class T>
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bool
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closestPoints
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(const Line3<T>& line1,
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const Line3<T>& line2,
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Vec3<T>& point1,
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Vec3<T>& point2)
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{
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//
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// Compute point1 and point2 such that point1 is on line1, point2
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// is on line2 and the distance between point1 and point2 is minimal.
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// This function returns true if point1 and point2 can be computed,
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// or false if line1 and line2 are parallel or nearly parallel.
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// This function assumes that line1.dir and line2.dir are normalized.
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//
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Vec3<T> w = line1.pos - line2.pos;
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T d1w = line1.dir ^ w;
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T d2w = line2.dir ^ w;
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T d1d2 = line1.dir ^ line2.dir;
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T n1 = d1d2 * d2w - d1w;
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T n2 = d2w - d1d2 * d1w;
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T d = 1 - d1d2 * d1d2;
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T absD = abs (d);
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if ((absD > 1) ||
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(abs (n1) < limits<T>::max() * absD &&
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abs (n2) < limits<T>::max() * absD))
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{
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point1 = line1 (n1 / d);
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point2 = line2 (n2 / d);
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return true;
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}
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else
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{
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return false;
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}
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}
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template <class T>
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bool
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intersect
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(const Line3<T> &line,
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const Vec3<T> &v0,
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const Vec3<T> &v1,
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const Vec3<T> &v2,
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Vec3<T> &pt,
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Vec3<T> &barycentric,
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bool &front)
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{
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//
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// Given a line and a triangle (v0, v1, v2), the intersect() function
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// finds the intersection of the line and the plane that contains the
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// triangle.
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//
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// If the intersection point cannot be computed, either because the
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// line and the triangle's plane are nearly parallel or because the
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// triangle's area is very small, intersect() returns false.
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//
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// If the intersection point is outside the triangle, intersect
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// returns false.
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//
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// If the intersection point, pt, is inside the triangle, intersect()
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// computes a front-facing flag and the barycentric coordinates of
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// the intersection point, and returns true.
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//
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// The front-facing flag is true if the dot product of the triangle's
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// normal, (v2-v1)%(v1-v0), and the line's direction is negative.
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//
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// The barycentric coordinates have the following property:
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//
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// pt = v0 * barycentric.x + v1 * barycentric.y + v2 * barycentric.z
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//
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Vec3<T> edge0 = v1 - v0;
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Vec3<T> edge1 = v2 - v1;
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Vec3<T> normal = edge1 % edge0;
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T l = normal.length();
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if (l != 0)
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normal /= l;
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else
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return false; // zero-area triangle
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//
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// d is the distance of line.pos from the plane that contains the triangle.
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// The intersection point is at line.pos + (d/nd) * line.dir.
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//
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T d = normal ^ (v0 - line.pos);
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T nd = normal ^ line.dir;
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if (abs (nd) > 1 || abs (d) < limits<T>::max() * abs (nd))
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pt = line (d / nd);
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else
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return false; // line and plane are nearly parallel
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//
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// Compute the barycentric coordinates of the intersection point.
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// The intersection is inside the triangle if all three barycentric
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// coordinates are between zero and one.
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//
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{
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Vec3<T> en = edge0.normalized();
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Vec3<T> a = pt - v0;
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Vec3<T> b = v2 - v0;
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Vec3<T> c = (a - en * (en ^ a));
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Vec3<T> d = (b - en * (en ^ b));
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T e = c ^ d;
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T f = d ^ d;
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if (e >= 0 && e <= f)
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barycentric.z = e / f;
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else
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return false; // outside
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}
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{
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Vec3<T> en = edge1.normalized();
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Vec3<T> a = pt - v1;
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Vec3<T> b = v0 - v1;
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Vec3<T> c = (a - en * (en ^ a));
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Vec3<T> d = (b - en * (en ^ b));
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T e = c ^ d;
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T f = d ^ d;
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if (e >= 0 && e <= f)
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barycentric.x = e / f;
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else
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return false; // outside
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}
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barycentric.y = 1 - barycentric.x - barycentric.z;
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if (barycentric.y < 0)
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return false; // outside
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front = ((line.dir ^ normal) < 0);
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return true;
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}
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template <class T>
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Vec3<T>
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closestVertex
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(const Vec3<T> &v0,
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const Vec3<T> &v1,
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const Vec3<T> &v2,
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const Line3<T> &l)
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{
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Vec3<T> nearest = v0;
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T neardot = (v0 - l.closestPointTo(v0)).length2();
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T tmp = (v1 - l.closestPointTo(v1)).length2();
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if (tmp < neardot)
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{
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neardot = tmp;
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nearest = v1;
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}
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tmp = (v2 - l.closestPointTo(v2)).length2();
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if (tmp < neardot)
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{
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neardot = tmp;
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nearest = v2;
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}
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return nearest;
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}
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template <class T>
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Vec3<T>
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rotatePoint (const Vec3<T> p, Line3<T> l, T angle)
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{
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//
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// Rotate the point p around the line l by the given angle.
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//
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//
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// Form a coordinate frame with <x,y,a>. The rotation is the in xy
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// plane.
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//
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Vec3<T> q = l.closestPointTo(p);
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Vec3<T> x = p - q;
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T radius = x.length();
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x.normalize();
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Vec3<T> y = (x % l.dir).normalize();
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T cosangle = Math<T>::cos(angle);
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T sinangle = Math<T>::sin(angle);
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Vec3<T> r = q + x * radius * cosangle + y * radius * sinangle;
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return r;
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}
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IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
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#endif // INCLUDED_IMATHLINEALGO_H
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