geom3

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// Copyright (C) 2010, Guy Barrand. All rights reserved.
// See the file tools.license for terms.
 
#ifndef tools_geom3
#define tools_geom3
 
#include "line"
#include "plane"
#include "vec3"
 
namespace tools {
 
template <class T>
class cubic {
public:
  cubic(const vec3<T>& a_p0,const vec3<T>& a_v0,
        const vec3<T>& a_p1,const vec3<T>& a_v1) {
    // Construct a cubic given 2 points and their tangents.
    initialize(a_p0.x(),a_p0.y(),a_p0.z(),
               a_v0.x(),a_v0.y(),a_v0.z(),
               a_p1.x(),a_p1.y(),a_p1.z(),
               a_v1.x(),a_v1.y(),a_v1.z());
  }
  cubic(const T& a_p0_x,const T& a_p0_y,const T& a_p0_z,
        const T& a_v0_x,const T& a_v0_y,const T& a_v0_z,
        const T& a_p1_x,const T& a_p1_y,const T& a_p1_z,
        const T& a_v1_x,const T& a_v1_y,const T& a_v1_z){
    initialize(a_p0_x,a_p0_y,a_p0_z,
               a_v0_x,a_v0_y,a_v0_z,
               a_p1_x,a_p1_y,a_p1_z,
               a_v1_x,a_v1_y,a_v1_z);
  }
 
  virtual ~cubic() {}
public:
  cubic(const cubic& a_from)
  :m_a(a_from.m_a)
  ,m_b(a_from.m_b)
  ,m_c(a_from.m_c)
  ,m_d(a_from.m_d)
  {}
  cubic& operator=(const cubic& a_from) {
    m_a = a_from.m_a;
    m_b = a_from.m_b;
    m_c = a_from.m_c;
    m_d = a_from.m_d;
    return *this;
  }
public:
  void get_point(unsigned int a_index,unsigned int a_num,vec3<T>& a_p){
    //a_index = 0        is a_p0
    //a_index = a_num-1  is a_p1
    T s = T(a_index)/T(a_num-1);
    T s2 = s*s;
    T s3 = s2*s;
    a_p = m_a*s3 + m_b*s2 + m_c*s + m_d;
  }
  void get_point(unsigned int a_index,unsigned int a_num,T& a_x,T& a_y,T& a_z){
    //a_index = 0        is a_p0
    //a_index = a_num-1  is a_p1
    T s = T(a_index)/T(a_num-1);
    T s2 = s*s;
    T s3 = s2*s;
    a_x = m_a.x()*s3 + m_b.x()*s2 + m_c.x()*s + m_d.x();
    a_y = m_a.y()*s3 + m_b.y()*s2 + m_c.y()*s + m_d.y();
    a_z = m_a.z()*s3 + m_b.z()*s2 + m_c.z()*s + m_d.z();
  }
protected:
  void initialize(const T& a_p0_x,const T& a_p0_y,const T& a_p0_z,
                  const T& a_v0_x,const T& a_v0_y,const T& a_v0_z,
                  const T& a_p1_x,const T& a_p1_y,const T& a_p1_z,
                  const T& a_v1_x,const T& a_v1_y,const T& a_v1_z){
    // Construct a cubic given 2 points and their tangents.
 
    //  f(s) = a s**3 + b s**2 + c s + d
    // f'(s) = 3 a s**2 + 2 b s + c
 
    //  f(0) = d = p0
    // f'(0) = c = v0
 
    //  f(1) =   a +   b + v0 + p0 = p1
    // f'(1) = 3 a + 2 b + v0 = v1
 
    //  f(1) =   a +   b = p1 - v0 - p0
    // f'(1) = 3 a + 2 b = v1 - v0
 
    // b = 3(p1-v0-p0)-(v1-v0)
    // a = p1-v0-p0 - b = p1-v0-p0-3(p1-v0-p0)+(v1-v0)
    // a = -2p1 + v0 + 2p0 + v1
 
    T a_x = -2*a_p1_x + a_v0_x + 2*a_p0_x + a_v1_x;
    T a_y = -2*a_p1_y + a_v0_y + 2*a_p0_y + a_v1_y;
    T a_z = -2*a_p1_z + a_v0_z + 2*a_p0_z + a_v1_z;
    m_a.set_value(a_x,a_y,a_z);
 
    T b_x = 3*(a_p1_x - a_v0_x - a_p0_x) - (a_v1_x - a_v0_x);
    T b_y = 3*(a_p1_y - a_v0_y - a_p0_y) - (a_v1_y - a_v0_y);
    T b_z = 3*(a_p1_z - a_v0_z - a_p0_z) - (a_v1_z - a_v0_z);
    m_b.set_value(b_x,b_y,b_z);
 
    m_c.set_value(a_v0_x,a_v0_y,a_v0_z);
    m_d.set_value(a_p0_x,a_p0_y,a_p0_z);
 
  }
 
protected:
  vec3<T> m_a;
  vec3<T> m_b;
  vec3<T> m_c;
  vec3<T> m_d;
};
 
}
 
#include <vector>
 
namespace tools {
 
template <class VEC3>
class clip {
protected:
  typedef typename VEC3::elem_t T;
public:
  clip():m_cur(0){}
  virtual ~clip() {}
private:
  clip(const clip&):m_cur(0){}
  clip& operator=(const clip&){return *this;}
public:
  void reset() {
    m_data[0].clear();
    m_data[1].clear();
    m_cur = 0;
  }
 
  void add(const VEC3& a_point) {m_data[m_cur].push_back(a_point);}
 
  void execute(const plane<VEC3>& plane) {
    //Clip polygon against plane. This might change the number of
    //vertices in the polygon.
 
    size_t n = m_data[m_cur].size();
    if(!n) return;
 
    // create a loop :
    VEC3 dummy = m_data[m_cur][0];
    m_data[m_cur].push_back(dummy);
 
    const VEC3& planeN = plane.normal();
 
    for(size_t i = 0; i < n; i++) {
      VEC3 v0 = m_data[m_cur][i];
      VEC3 v1 = m_data[m_cur][i+1];
 
      T d0 = plane.distance(v0);
      T d1 = plane.distance(v1);
 
      if (d0 >= 0.0f && d1 < 0.0f) { // exit plane
        VEC3 dir = v1-v0;
        // we know that v0 != v1 since we got here
        dir.normalize();
        T dot = dir.dot(planeN);
        VEC3 newvertex = v0 - dir * (d0/dot);
        out_point(newvertex);
      } else if (d0 < 0.0f && d1 >= 0.0f) { // enter plane
        VEC3 dir = v1-v0;
        // we know that v0 != v1 since we got here
        dir.normalize();
        T dot = dir.dot(planeN);
        VEC3 newvertex = v0 - dir * (d0/dot);
        out_point(newvertex);
        out_point(v1);
      } else if (d0 >= 0.0f && d1 >= 0.0f) { // in plane
        out_point(v1);
      }
    }
    m_data[m_cur].clear();
    m_cur ^= 1;
  }
 
  const std::vector<VEC3>& result() const {return m_data[m_cur];}
 
protected:
  void out_point(const VEC3& a_p) {m_data[m_cur ^ 1].push_back(a_p);}
 
protected:
  std::vector<VEC3> m_data[2];
  unsigned int m_cur;
};
 
}
 
#endif