al_Curve.hpp

#ifndef INCLUDE_AL_CURVE_HPP
#define INCLUDE_AL_CURVE_HPP
 
/*  Allocore --
  Multimedia / virtual environment application class library
 
  Copyright (C) 2009. AlloSphere Research Group, Media Arts & Technology, UCSB.
  Copyright (C) 2012. The Regents of the University of California.
  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 the University of California 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 HOLDER 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.
 
 
  File description:
  Utilities for computing features of curves
 
  File author(s):
  Lance Putnam, 2012, putnam.lance@gmail.com
*/
 
namespace al {
 
template <class V2>
void frenet(const V2& d1, V2& t, V2& n);
 
template <class V3>
void frenet(const V3& d1, const V3& d2, V3& t, V3& n, V3& b);
 
template <class V3>
void frenet(const V3& p2, const V3& p1, const V3& p0, V3& t, V3& n, V3& b);
 
 
 
template <class Vec3>
struct Frenet {
  Vec3 T;  
  Vec3 N;  
  Vec3 B;  
 
  Frenet(const Vec3& p2 = Vec3(0, -0.01, 0), const Vec3& p1 = Vec3(0, 0, 0)) {
    init(p2, p1);
  }
 
  const Vec3& point() const { return mp1; }
 
  const Vec3& db() const { return mdb; }
 
  const Vec3& df() const { return mdf; }
 
  Vec3 d2() const { return mdf - mdb; }
 
  void operator()(const Vec3& p0) { next<1, 1, 1, 1, 1>(p0); }
 
 
  template <bool NormalizeT, bool NormalizeN, bool NormalizeB, bool ComputeN,
            bool ComputeB>
  void next(const Vec3& p0) {
    mdb = mdf;       // bwd diff is previous fwd diff
    mdf = p0 - mp1;  // compute new fwd diff
    mp1 = p0;        // store previous
 
    // Consecutive points equal? If so, use previous frame...
    // if(mdb == Vec3(0) || mdf == Vec3(0)) return;
 
    T = mdb + mdf;  // central diff
                    // (really half this, but we only need eigenvector)
    if (NormalizeT) T.normalize();
 
    // Colinear? If so, use previous binormal and normal...
    /*if(angle(mdf, mdb) < 0.001){
      //printf("colinear\n");
      return;
    }*/
 
    if (ComputeB || ComputeN) {
      B = cross(mdb, mdf);
      // B = cross(T, mdf - mdb); // formally, we use 2nd difference
    }
 
    if (ComputeN) {
      N = cross(B, T);
      if (NormalizeN) N.normalize();
    }
 
    if (NormalizeB) B.normalize();
  }
 
  void init(const Vec3& p2, const Vec3& p1) {
    mdf = p1 - p2;
    mp1 = p1;
  }
 
  //  /// Get curvature one back back from previous input point
  //  value_type curvature() const {
  //    Vec3 d1 = (mdf + mdb) * 0.5;
  //    value_type d1MagSqr = d1.magSqr();
  //    return sqrt(cross(d1, md2).magSqr() / (d1MagSqr*d1MagSqr*d1MagSqr));
  //  }
 
 protected:
  Vec3 mp1;  // Previously input point
  Vec3 mdb;  // Backward first difference
  Vec3 mdf;  // Forward first difference
};
 
// Implementation
 
template <class V2>
inline void frenet(const V2& d1, V2& t, V2& n) {
  t = d1;
  t.normalize();
  // normal according to right-hand rule
  n[0] = -t[1];
  n[1] = t[0];
}
 
template <class V3>
inline void frenet(const V3& d1, const V3& d2, V3& t, V3& n, V3& b) {
  b = cross(d2, d1);
  n = cross(d1, b);
  t = d1;
  t.normalize();
  b.normalize();
  n.normalize();
}
 
template <class V3>
inline void frenet(const V3& p2, const V3& p1, const V3& p0, V3& t, V3& n,
                   V3& b) {
  V3 d1 = (p0 - p2);            // 1st (central) difference (scaled by 2)
  V3 d2 = (p0 - p1 * 2. + p2);  // 2nd difference
  frenet(d1, d2, t, n, b);
}
 
//
// template <class T, template <class> class NVec>
// T curvature(const NVec<T>& a, const NVec<T>& b, const NVec<T>& c);
//
// template <class T, template <class> class V>
// T curvature(const V<T>& a, const V<T>& b, const V<T>& c){
//
//  V<T> d1b = b-a;        // first backward difference
//  V<T> d1f = c-b;        // first forward difference
//  V<T> d1  = (d1f+d1b) * 0.5;  // first mid difference
//
//  V<T> d2  = d1f - d1b;    // second difference
//
//  T d1n = d1.norm();
//
//  return (d1.cross(d2)).norm() / (d1n*d1n*d1n);
//}
 
}  // namespace al
#endif