From 023f3eca70e0d477d61307864f308e3bec28f6dc Mon Sep 17 00:00:00 2001 From: itsmattkc Date: Sun, 1 Aug 2021 02:28:37 -0700 Subject: [PATCH] bezier: rework quadratic algorithm Fixes #1695 --- app/common/bezier.cpp | 53 +++++++++++++++++++++++-------------------- app/common/bezier.h | 18 ++++++++++++++- app/node/node.cpp | 42 ++++++++++++---------------------- 3 files changed, 61 insertions(+), 52 deletions(-) diff --git a/app/common/bezier.cpp b/app/common/bezier.cpp index c83273243..af75fbb4b 100644 --- a/app/common/bezier.cpp +++ b/app/common/bezier.cpp @@ -28,7 +28,10 @@ namespace olive { double Bezier::QuadraticXtoT(double x, double a, double b, double c) { - return (a - b + qSqrt(a*x + c*x - 2*b*x + qPow(b, 2) - a*c))/(a - 2*b + c); + // Clamp to prevent infinite loop + x = clamp(x, a, c); + + return CalculateTFromX(false, x, a, b, c, 0); } double Bezier::QuadraticTtoY(double a, double b, double c, double t) @@ -36,31 +39,12 @@ double Bezier::QuadraticTtoY(double a, double b, double c, double t) return qPow(1.0 - t, 2)*a + 2*(1.0 - t)*t*b + qPow(t, 2)*c; } -double Bezier::CubicXtoT(double x_target, double a, double b, double c, double d) +double Bezier::CubicXtoT(double x, double a, double b, double c, double d) { - const double tolerance = 0.0001; + // Clamp to prevent infinite loop + x = clamp(x, a, d); - // Clamp to prevent deadlocks - x_target = clamp(x_target, a, d); - - double lower = 0.0; - double upper = 1.0; - - double percent = 0.5; - double x = CubicTtoY(a, b, c, d, percent); - - while (qAbs(x_target - x) > tolerance) { - if (x_target > x) { - lower = percent; - } else { - upper = percent; - } - - percent = (upper + lower) * 0.5; - x = CubicTtoY(a, b, c, d, percent); - } - - return percent; + return CalculateTFromX(true, x, a, b, c, d); } double Bezier::CubicTtoY(double a, double b, double c, double d, double t) @@ -68,4 +52,25 @@ double Bezier::CubicTtoY(double a, double b, double c, double d, double t) return qPow(1.0 - t, 3)*a + 3*qPow(1.0 - t, 2)*t*b + 3*(1.0 - t)*qPow(t, 2)*c + qPow(t, 3)*d; } +double Bezier::CalculateTFromX(bool cubic, double x, double a, double b, double c, double d) +{ + double bottom = 0.0; + double top = 1.0; + + while (true) { + double mid = (bottom + top) * 0.5; + double test = cubic ? CubicTtoY(a, b, c, d, mid) : QuadraticTtoY(a, b, c, mid); + + if (qFuzzyCompare(test, x)) { + return mid; + } else if (x > test) { + bottom = mid; + } else { + top = mid; + } + } + + return qSNaN(); +} + } diff --git a/app/common/bezier.h b/app/common/bezier.h index 16f160dc5..16705901f 100644 --- a/app/common/bezier.h +++ b/app/common/bezier.h @@ -21,6 +21,8 @@ #ifndef BEZIER_H #define BEZIER_H +#include + #include "common/define.h" namespace olive { @@ -32,9 +34,23 @@ public: static double QuadraticTtoY(double a, double b, double c, double t); - static double CubicXtoT(double x_target, double a, double b, double c, double d); + static double QuadraticXtoY(double x, const QPointF &a, const QPointF &b, const QPointF &c) + { + return QuadraticTtoY(a.y(), b.y(), c.y(), QuadraticXtoT(x, a.x(), b.x(), c.x())); + } + + static double CubicXtoT(double x, double a, double b, double c, double d); static double CubicTtoY(double a, double b, double c, double d, double t); + + static double CubicXtoY(double x, const QPointF &a, const QPointF &b, const QPointF &c, const QPointF &d) + { + return CubicTtoY(a.y(), b.y(), c.y(), d.y(), CubicXtoT(x, a.x(), b.x(), c.x(), d.x())); + } + +private: + static double CalculateTFromX(bool cubic, double x, double a, double b, double c, double d); + }; } diff --git a/app/node/node.cpp b/app/node/node.cpp index 23f022641..ee85e378f 100644 --- a/app/node/node.cpp +++ b/app/node/node.cpp @@ -607,46 +607,34 @@ QVariant Node::GetSplitValueAtTimeOnTrack(const QString &input, const rational & } if (before->type() == NodeKeyframe::kBezier && after->type() == NodeKeyframe::kBezier) { + // Perform a cubic bezier with two control points - - double t = Bezier::CubicXtoT(time.toDouble(), - before->time().toDouble(), - before->time().toDouble() + before->valid_bezier_control_out().x(), - after->time().toDouble() + after->valid_bezier_control_in().x(), - after->time().toDouble()); - - double y = Bezier::CubicTtoY(before_val, - before_val + before->valid_bezier_control_out().y(), - after_val + after->valid_bezier_control_in().y(), - after_val, - t); - - interpolated = y; + interpolated = Bezier::CubicXtoY(time.toDouble(), + QPointF(before->time().toDouble(), before_val), + QPointF(before->time().toDouble() + before->valid_bezier_control_out().x(), before_val + before->valid_bezier_control_out().y()), + QPointF(after->time().toDouble() + after->valid_bezier_control_in().x(), after_val + after->valid_bezier_control_in().y()), + QPointF(after->time().toDouble(), after_val)); } else if (before->type() == NodeKeyframe::kBezier || after->type() == NodeKeyframe::kBezier) { // Perform a quadratic bezier with only one control point QPointF control_point; - double control_point_time; - double control_point_value; if (before->type() == NodeKeyframe::kBezier) { control_point = before->valid_bezier_control_out(); - control_point_time = before->time().toDouble() + control_point.x(); - control_point_value = before_val + control_point.y(); + control_point.setX(control_point.x() + before->time().toDouble()); + control_point.setY(control_point.y() + before_val); } else { control_point = after->valid_bezier_control_in(); - control_point_time = after->time().toDouble() + control_point.x(); - control_point_value = after_val + control_point.y(); + control_point.setX(control_point.x() + after->time().toDouble()); + control_point.setY(control_point.y() + after_val); } - // Generate T from time values - used to determine bezier progress - double t = Bezier::QuadraticXtoT(time.toDouble(), before->time().toDouble(), control_point_time, after->time().toDouble()); - - // Generate value using T - double y = Bezier::QuadraticTtoY(before_val, control_point_value, after_val, t); - - interpolated = y; + // Interpolate value using quadratic beziers + interpolated = Bezier::QuadraticXtoY(time.toDouble(), + QPointF(before->time().toDouble(), before_val), + control_point, + QPointF(after->time().toDouble(), after_val)); } else { // To have arrived here, the keyframes must both be linear