Program Listing for File bezier_curve.hpp

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#pragma once

// TODO: Implement a curve manager.

// INTRODUCTION
// A bezier curve (named after french mathematician PIERRE ETIENNE BEZIER) is a parametric curve
// whose only purpose is to look soft and smooth. Bezier curves are all about elegance!
// Those curves can be used to represent the path of a everything (imagine a camera which is moving along a path for
// example).
//
// Bezier curves are fast, flexible, beautiful and easy to compute. You just pass a bunch of parameter points to
// your code and the final curve will be computed. Because every complex curve can be represented with a
// chain of smaller curves, it is recommended to create a chain of curves. Bezier curves are essential
// in the field of computer graphics and image processing. They can also be used for approximation, interpolation and
// more.
//
// COMPUTING
// There are two ways to generate a bezier curves from a group of [n] points.
// You can either write a code that uses recursion to solve the problem or use Bernstein polynomials.
// This engine uses Bernstein polynomial, because we want to avoid the recursion in de-casteljau algorithm.
//
// Pierre Etienne BEZIER       (September 1, 1910 - November 25, 1999), French mathematician and engineer at RENAULT.
// Paul de CASTELJAU           (November 19, 1930), French mathematician and physicist and engineer ar Citroen.
// Sergei Natanovich BERNSTEIN (March 5, 1880 - October 26, 1968), Russian mathematician.
// Charles HERMITE             (December 24, 1822 - January 14, 1901), French mathematician.

// http://pomax.github.io/bezierinfo/
// http://en.wikipedia.org/wiki/B%C3%A9zier_curve
// http://mathworld.wolfram.com/BezierCurve.html
// http://theagsc.com/community/tutorials/so-whats-the-big-deal-with-horizontal-vertical-bezier-handles-anyway#comment-1351842776
// http://learn.scannerlicker.net/2014/04/16/bezier-curves-and-type-design-a-tutorial/
// https://geom.ivd.kit.edu/downloads/pubs/pub-boehm-prautzsch_2002_preview.pdf
// https://www.clear.rice.edu/comp360/lectures/BezSubd.pdf

#include <glm/glm.hpp>

#include <cmath>
#include <vector>

namespace inexor::vulkan_renderer {

struct BezierInputPoint {
    glm::vec3 pos{0.0f, 0.0f, 0.0f};

    float weight{1.0f};
};

struct BezierOutputPoint : public BezierInputPoint {
    glm::vec3 normal{0.0f, 0.0f, 0.0f};

    glm::vec3 tangent{0.0f, 0.0f, 0.0f};
};

class BezierCurve {
    bool m_curve_generated{false};

    float m_curve_precision{0.0f};

    std::vector<BezierInputPoint> m_input_points;

    std::vector<BezierOutputPoint> m_output_points;

    static uint32_t binomial_coefficient(uint32_t n, uint32_t k);

    static float bernstein_polynomial(uint32_t n, uint32_t k, float curve_precision, float coordinate_value);

    BezierOutputPoint calculate_point_on_curve(float curve_precision);

public:
    void add_input_point(const BezierInputPoint &input_point);

    void add_input_point(const glm::vec3 &position, float weight = 1.0f);

    void calculate_bezier_curve(std::uint32_t curve_segments);

    [[nodiscard]] std::vector<BezierOutputPoint> output_points();

    void clear_output();

    void clear_input();

    void clear();

    [[nodiscard]] bool is_curve_generated() const {
        return m_curve_generated;
    }
};

} // namespace inexor::vulkan_renderer