| /* |
| * Copyright 2012 Google LLC |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| |
| #include "src/base/SkBezierCurves.h" |
| |
| #include "include/private/base/SkAssert.h" |
| |
| #include <cstddef> |
| |
| static inline double interpolate(double A, double B, double t) { |
| return A + (B - A) * t; |
| } |
| |
| // Perform subdivision using De Casteljau's algorithm, that is, repeated linear |
| // interpolation between adjacent points. |
| void SkBezierCubic::Subdivide(const double curve[8], double t, |
| double twoCurves[14]) { |
| SkASSERT(0.0 <= t && t <= 1.0); |
| // We split the curve "in" into two curves "alpha" and "beta" |
| const auto in_X = [&curve](size_t n) { return curve[2*n]; }; |
| const auto in_Y = [&curve](size_t n) { return curve[2*n + 1]; }; |
| const auto alpha_X = [&twoCurves](size_t n) -> double& { return twoCurves[2*n]; }; |
| const auto alpha_Y = [&twoCurves](size_t n) -> double& { return twoCurves[2*n + 1]; }; |
| const auto beta_X = [&twoCurves](size_t n) -> double& { return twoCurves[2*n + 6]; }; |
| const auto beta_Y = [&twoCurves](size_t n) -> double& { return twoCurves[2*n + 7]; }; |
| |
| alpha_X(0) = in_X(0); |
| alpha_Y(0) = in_Y(0); |
| |
| beta_X(3) = in_X(3); |
| beta_Y(3) = in_Y(3); |
| |
| double x01 = interpolate(in_X(0), in_X(1), t); |
| double y01 = interpolate(in_Y(0), in_Y(1), t); |
| double x12 = interpolate(in_X(1), in_X(2), t); |
| double y12 = interpolate(in_Y(1), in_Y(2), t); |
| double x23 = interpolate(in_X(2), in_X(3), t); |
| double y23 = interpolate(in_Y(2), in_Y(3), t); |
| |
| alpha_X(1) = x01; |
| alpha_Y(1) = y01; |
| |
| beta_X(2) = x23; |
| beta_Y(2) = y23; |
| |
| alpha_X(2) = interpolate(x01, x12, t); |
| alpha_Y(2) = interpolate(y01, y12, t); |
| |
| beta_X(1) = interpolate(x12, x23, t); |
| beta_Y(1) = interpolate(y12, y23, t); |
| |
| alpha_X(3) /*= beta_X(0) */ = interpolate(alpha_X(2), beta_X(1), t); |
| alpha_Y(3) /*= beta_Y(0) */ = interpolate(alpha_Y(2), beta_Y(1), t); |
| } |
| |
| std::array<double, 4> SkBezierCubic::ConvertToPolynomial(const double curve[8], bool yValues) { |
| const double* offset_curve = yValues ? curve + 1 : curve; |
| const auto P = [&offset_curve](size_t n) { return offset_curve[2*n]; }; |
| // A cubic Bézier curve is interpolated as follows: |
| // c(t) = (1 - t)^3 P_0 + 3t(1 - t)^2 P_1 + 3t^2 (1 - t) P_2 + t^3 P_3 |
| // = (-P_0 + 3P_1 + -3P_2 + P_3) t^3 + (3P_0 - 6P_1 + 3P_2) t^2 + |
| // (-3P_0 + 3P_1) t + P_0 |
| // Where P_N is the Nth point. The second step expands the polynomial and groups |
| // by powers of t. The desired output is a cubic formula, so we just need to |
| // combine the appropriate points to make the coefficients. |
| std::array<double, 4> results; |
| results[0] = -P(0) + 3*P(1) - 3*P(2) + P(3); |
| results[1] = 3*P(0) - 6*P(1) + 3*P(2); |
| results[2] = -3*P(0) + 3*P(1); |
| results[3] = P(0); |
| return results; |
| } |
| |