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 /* * Copyright 2018 Google Inc. * * Use of this source code is governed by a BSD-style license that can be * found in the LICENSE file. */ #include "include/core/SkCubicMap.h" #include "include/private/base/SkTPin.h" #include "src/base/SkVx.h" #include #include static float eval_poly(float t, float b) { return b; } template static float eval_poly(float t, float m, float b, Rest... rest) { return eval_poly(t, std::fma(m, t, b), rest...); } static float cubic_solver(float A, float B, float C, float D) { #ifdef SK_DEBUG auto valid = [](float t) { return t >= 0 && t <= 1; }; #endif auto guess_nice_cubic_root = [](float a, float b, float c, float d) { return -d; }; float t = guess_nice_cubic_root(A, B, C, D); int iters = 0; const int MAX_ITERS = 8; for (; iters < MAX_ITERS; ++iters) { SkASSERT(valid(t)); float f = eval_poly(t, A, B, C, D); // f = At^3 + Bt^2 + Ct + D if (std::fabs(f) <= 0.00005f) { break; } float fp = eval_poly(t, 3*A, 2*B, C); // f' = 3At^2 + 2Bt + C float fpp = eval_poly(t, 3*A + 3*A, 2*B); // f'' = 6At + 2B float numer = 2 * fp * f; float denom = std::fma(2 * fp, fp, -(f * fpp)); t -= numer / denom; } SkASSERT(valid(t)); return t; } static inline bool nearly_zero(SkScalar x) { SkASSERT(x >= 0); return x <= 0.0000000001f; } static float compute_t_from_x(float A, float B, float C, float x) { return cubic_solver(A, B, C, -x); } float SkCubicMap::computeYFromX(float x) const { x = SkTPin(x, 0.0f, 1.0f); if (nearly_zero(x) || nearly_zero(1 - x)) { return x; } if (fType == kLine_Type) { return x; } float t; if (fType == kCubeRoot_Type) { t = std::pow(x / fCoeff[0].fX, 1.0f / 3); } else { t = compute_t_from_x(fCoeff[0].fX, fCoeff[1].fX, fCoeff[2].fX, x); } float a = fCoeff[0].fY; float b = fCoeff[1].fY; float c = fCoeff[2].fY; float y = ((a * t + b) * t + c) * t; return y; } static inline bool coeff_nearly_zero(float delta) { return std::fabs(delta) <= 0.0000001f; } SkCubicMap::SkCubicMap(SkPoint p1, SkPoint p2) { // Clamp X values only (we allow Ys outside [0..1]). p1.fX = std::min(std::max(p1.fX, 0.0f), 1.0f); p2.fX = std::min(std::max(p2.fX, 0.0f), 1.0f); auto s1 = skvx::float2::Load(&p1) * 3; auto s2 = skvx::float2::Load(&p2) * 3; (1 + s1 - s2).store(&fCoeff[0]); (s2 - s1 - s1).store(&fCoeff[1]); s1.store(&fCoeff[2]); fType = kSolver_Type; if (SkScalarNearlyEqual(p1.fX, p1.fY) && SkScalarNearlyEqual(p2.fX, p2.fY)) { fType = kLine_Type; } else if (coeff_nearly_zero(fCoeff[1].fX) && coeff_nearly_zero(fCoeff[2].fX)) { fType = kCubeRoot_Type; } } SkPoint SkCubicMap::computeFromT(float t) const { auto a = skvx::float2::Load(&fCoeff[0]); auto b = skvx::float2::Load(&fCoeff[1]); auto c = skvx::float2::Load(&fCoeff[2]); SkPoint result; (((a * t + b) * t + c) * t).store(&result); return result; }