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 /* * 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 "include/private/base/SkSpan_impl.h" #include struct SkPoint; /** * 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 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 ConvertToPolynomial(const double curve[8], bool yValues); static SkSpan IntersectWithHorizontalLine( SkSpan controlPoints, float yIntercept, float intersectionStorage[3]); static SkSpan Intersect( double AX, double BX, double CX, double DX, double AY, double BY, double CY, double DY, float toIntersect, float intersectionsStorage[3]); }; class SkBezierQuad { public: static SkSpan IntersectWithHorizontalLine( SkSpan controlPoints, float yIntercept, float intersectionStorage[2]); /** * Given * AY*t^2 -2*BY*t + CY = 0 and AX*t^2 - 2*BX*t + CX = 0, * * Find the t where AY*t^2 - 2*BY*t + CY - y = 0, then return AX*t^2 + - 2*BX*t + CX * where t is on [0, 1]. * * - y - is the height of the line which intersects the quadratic. * - intersectionStorage - is the array to hold the return data pointed to in the span. * * Returns a span with the intersections of yIntercept, and the quadratic formed by A, B, * and C. */ static SkSpan Intersect( double AX, double BX, double CX, double AY, double BY, double CY, double yIntercept, float intersectionStorage[2]); }; #endif // SkBezierCurves_DEFINED