| /* |

| * Copyright 2023 Google LLC |

| * |

| * Use of this source code is governed by a BSD-style license that can be |

| * found in the LICENSE file. |

| */ |

| #ifndef SkBezierCurves_DEFINED |

| #define SkBezierCurves_DEFINED |

| |

| #include <array> |

| |

| /** |

| * Utilities for dealing with cubic Bézier curves. These have a start XY |

| * point, an end XY point, and two control XY points in between. They take |

| * a parameter t which is between 0 and 1 (inclusive) which is used to |

| * interpolate between the start and end points, via a route dictated by |

| * the control points, and return a new XY point. |

| * |

| * We store a Bézier curve as an array of 8 floats or doubles, where |

| * the even indices are the X coordinates, and the odd indices are the Y |

| * coordinates. |

| */ |

| class SkBezierCubic { |

| public: |

| |

| /** |

| * Evaluates the cubic Bézier curve for a given t. It returns an X and Y coordinate |

| * following the formula, which does the interpolation mentioned above. |

| * X(t) = X_0*(1-t)^3 + 3*X_1*t(1-t)^2 + 3*X_2*t^2(1-t) + X_3*t^3 |

| * Y(t) = Y_0*(1-t)^3 + 3*Y_1*t(1-t)^2 + 3*Y_2*t^2(1-t) + Y_3*t^3 |

| * |

| * t is typically in the range [0, 1], but this function will not assert that, |

| * as Bézier curves are well-defined for any real number input. |

| */ |

| static std::array<double, 2> EvalAt(const double curve[8], double t); |

| |

| /** |

| * Splits the provided Bézier curve at the location t, resulting in two |

| * Bézier curves that share a point (the end point from curve 1 |

| * and the start point from curve 2 are the same). |

| * |

| * t must be in the interval [0, 1]. |

| * |

| * The provided twoCurves array will be filled such that indices |

| * 0-7 are the first curve (representing the interval [0, t]), and |

| * indices 6-13 are the second curve (representing [t, 1]). |

| */ |

| static void Subdivide(const double curve[8], double t, |

| double twoCurves[14]); |

| |

| /** |

| * Converts the provided Bézier curve into the the equivalent cubic |

| * f(t) = A*t^3 + B*t^2 + C*t + D |

| * where f(t) will represent Y coordinates over time if yValues is |

| * true and the X coordinates if yValues is false. |

| * |

| * In effect, this turns the control points into an actual line, representing |

| * the x or y values. |

| */ |

| static std::array<double, 4> ConvertToPolynomial(const double curve[8], bool yValues); |

| }; |

| |

| #endif |