libcruft-util/bezier.hpp

86 lines
2.3 KiB
C++

/*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* Copyright 2015-2016 Danny Robson <danny@nerdcruft.net>
*/
#ifndef __UTIL_BEZIER_HPP
#define __UTIL_BEZIER_HPP
#include "point.hpp"
#include "region.hpp"
#include <ostream>
namespace util {
struct sdot_t {
float distance;
float dot;
};
template <size_t N>
class bezier {
public:
using value_type = point2f::value_type;
bezier (const util::point2f (&)[N+1]);
point2f eval (float t) const;
// Calculate the expanded polynomial coeffecients in terms of t
std::array<vector2f,N+1>
coeffs (void) const;
size_t intersections (point2f from, point2f to) const;
util::vector2f tangent (float t) const;
// 1st derivative w.r.t. t
util::vector2f d1 (float t) const noexcept;
// 2nd derivative w.r.t. t
util::vector2f d2 (float t) const noexcept;
float closest (point2f) const noexcept;
sdot_t sdot (point2f) const noexcept;
float sdistance2 (point2f) const noexcept;
float sdistance (point2f) const noexcept;
float distance2 (point2f) const noexcept;
float distance (point2f) const noexcept;
region2f region (void) const;
point2f& operator[] (size_t idx);
const point2f& operator[] (size_t idx) const;
const point2f* begin (void) const;
const point2f* end (void) const;
const point2f* cbegin (void) const;
const point2f* cend (void) const;
private:
// HACK: allow easy access to component-wise arithmetic using
// vector2f rather than point2f in the implementation.
union {
point2f m_points[N+1];
vector2f m_coeffs[N+1];
};
};
template <size_t N>
std::ostream& operator<< (std::ostream&, const bezier<N>&);
}
#endif