85 lines
2.3 KiB
C++
85 lines
2.3 KiB
C++
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// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla Public License
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// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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// obtain one at http://mozilla.org/MPL/2.0/.
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#include "random_quaternion.h"
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#include "PI.h"
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template <typename Scalar>
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IGL_INLINE Eigen::Quaternion<Scalar> igl::random_quaternion()
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{
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const auto & unit_rand = []()->Scalar
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{
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return ((Scalar)rand() / (Scalar)RAND_MAX);
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};
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#ifdef false
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// http://mathproofs.blogspot.com/2005/05/uniformly-distributed-random-unit.html
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const Scalar t0 = 2.*igl::PI*unit_rand();
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const Scalar t1 = acos(1.-2.*unit_rand());
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const Scalar t2 = 0.5*(igl::PI*unit_rand() + acos(unit_rand()));
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return Eigen::Quaternion<Scalar>(
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1.*sin(t0)*sin(t1)*sin(t2),
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1.*cos(t0)*sin(t1)*sin(t2),
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1.*cos(t1)*sin(t2),
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1.*cos(t2));
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#elif false
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// "Uniform Random Rotations" [Shoemake 1992] method 1
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const auto & uurand = [&unit_rand]()->Scalar
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{
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return unit_rand()*2.-1.;
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};
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Scalar x = uurand();
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Scalar y = uurand();
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Scalar z = uurand();
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Scalar w = uurand();
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const auto & hype = [&uurand](Scalar & x, Scalar & y)->Scalar
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{
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Scalar s1;
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while((s1 = x*x + y*y) > 1.0)
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{
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x = uurand();
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y = uurand();
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}
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return s1;
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};
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Scalar s1 = hype(x,y);
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Scalar s2 = hype(z,w);
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Scalar num1 = -2.*log(s1);
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Scalar num2 = -2.*log(s2);
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Scalar r = num1 + num2;
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Scalar root1 = sqrt((num1/s1)/r);
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Scalar root2 = sqrt((num2/s2)/r);
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return Eigen::Quaternion<Scalar>(
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x*root1,
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y*root1,
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z*root2,
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w*root2);
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#else
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// Shoemake method 2
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const Scalar x0 = unit_rand();
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const Scalar x1 = unit_rand();
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const Scalar x2 = unit_rand();
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const Scalar r1 = sqrt(1.0 - x0);
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const Scalar r2 = sqrt(x0);
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const Scalar t1 = 2.*igl::PI*x1;
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const Scalar t2 = 2.*igl::PI*x2;
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const Scalar c1 = cos(t1);
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const Scalar s1 = sin(t1);
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const Scalar c2 = cos(t2);
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const Scalar s2 = sin(t2);
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return Eigen::Quaternion<Scalar>(
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s1*r1,
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c1*r1,
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s2*r2,
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c2*r2);
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#endif
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}
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#ifdef IGL_STATIC_LIBRARY
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// Explicit template instantiation
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template Eigen::Quaternion<double, 0> igl::random_quaternion<double>();
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#endif
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