hermite_tube.h

#pragma once
 
#include <array>
 
#include "bezier_tube.h"
#include "convert_curve.h"
#include "hermite.h"
 
namespace cgv {
namespace math {
 
template<typename T>
struct hermite_tube_node {
    hermite_node<fvec<T, 3>> pos;
    hermite_node<T> rad;
};
 
template<typename T>
class cubic_hermite_tube {
public:
    using vec_type = fvec<T, 3>;
    using matrix_type = fmat<T, 4, 4>;
    using node_type = hermite_tube_node<T>;
    
    // the start node
    node_type n0;
    // the end node
    node_type n1;
 
    template<typename ParamT = float>
    node_type evaluate(ParamT t) const {
        node_type n;
        n.pos = interpolate_cubic_hermite(n0.val, n0.tan, n1.val, n1.tan, t);
        n.rad = interpolate_cubic_hermite(n0.val, n0.tan, n1.val, n1.tan, t);
        return n;
    }
 
    template<typename ParamT = float>
    std::vector<node_type> sample(size_t num_segments) const {
        std::vector<node_type> points;
        points.reserve(num_segments + 1);
        sample_steps_transform<ParamT>(std::back_inserter(points), [this](ParamT t) { return evaluate(t); }, num_segments);
        return points;
    }
 
    std::pair<vec_type, vec_type> approximate_axis_aligned_bounding_box() const {
        std::pair<vec_type, vec_type> box;
        std::array<quadratic_bezier_tube<T>, 2> qtubes = split_to_quadratic_bezier_tubes();
 
        std::pair<vec_type, vec_type> qbox = qtubes[0].axis_aligned_bounding_box();
        box.first = qbox.first;
        box.second = qbox.second;
 
        qbox = qtubes[1].axis_aligned_bounding_box();
        box.first = min(box.first, qbox.first);
        box.second = max(box.second, qbox.second);
 
        return box;
    }
 
    std::array<quadratic_bezier_tube<T>, 2> split_to_quadratic_bezier_tubes() const {
        std::array<vec_type, 5> ps = split_hermite_to_quadratic_beziers(n0.pos, n1.pos);
        std::array<T, 5> rs = split_hermite_to_quadratic_beziers(n0.rad, n1.rad);
 
        std::array<quadratic_bezier_tube<T>, 2> qtubes;
        qtubes[0].n0 = { ps[0], rs[0] };
        qtubes[0].n1 = { ps[1], rs[1] };
        qtubes[0].n2 = { ps[2], rs[2] };
        qtubes[1].n0 = { ps[2], rs[2] };
        qtubes[1].n1 = { ps[3], rs[3] };
        qtubes[1].n2 = { ps[4], rs[4] };
        return qtubes;
    }
};
 
 
} // namespace math
} // namespace cgv