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Keyframe: Move Bezier code into extra function, parameterise

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Bezier interpolation code is now in a dedicated function and can be
used to either find a Y from a known X or a X from a known Y, with a
given allowed error.
This commit is contained in:
Daniel Jour
2019-12-03 16:56:53 +01:00
parent 65cb3dfde9
commit 79cb8483f3
1 changed files with 39 additions and 33 deletions
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72
src/KeyFrame.cpp
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@@ -39,6 +39,44 @@ namespace {
bool IsPointBeforeX(Point const & p, double const x) {
return p.co.X < x;
}
double InterpolateBezierCurve(Point const & left, Point const & right, bool const needY, double const target, double const allowed_error) {
double const X_diff = right.co.X - left.co.X;
double const Y_diff = right.co.Y - left.co.Y;
Coordinate const p0 = left.co;
Coordinate const p1 = Coordinate(p0.X + left.handle_right.X * X_diff, p0.Y + left.handle_right.Y * Y_diff);
Coordinate const p2 = Coordinate(p0.X + right.handle_left.X * X_diff, p0.Y + right.handle_left.Y * Y_diff);
Coordinate const p3 = right.co;
double t = 0.5;
double t_step = 0.25;
do {
// Bernstein polynoms
double B[4] = {1, 3, 3, 1};
double oneMinTExp = 1;
double tExp = 1;
for (int i = 0; i < 4; ++i, tExp *= t) {
B[i] *= tExp;
}
for (int i = 0; i < 4; ++i, oneMinTExp *= 1 - t) {
B[4 - i - 1] *= oneMinTExp;
}
double const x = p0.X * B[0] + p1.X * B[1] + p2.X * B[2] + p3.X * B[3];
double const y = p0.Y * B[0] + p1.Y * B[1] + p2.Y * B[2] + p3.Y * B[3];
bool const stop = abs(target - (needY ? x : y)) < allowed_error;
bool const move_left = (needY ? x : y) > target;
if (stop) {
return needY ? y : x;
}
if (move_left) {
t -= t_step;
}
else {
t += t_step;
}
t_step /= 2;
} while (true);
}
}
@@ -231,39 +269,7 @@ double Keyframe::GetValue(int64_t index) const {
// BEZIER curve!
assert(candidate->interpolation == BEZIER);
double const X_diff = candidate->co.X - predecessor->co.X;
double const Y_diff = candidate->co.Y - predecessor->co.Y;
Coordinate const p0 = predecessor->co;
Coordinate const p1 = Coordinate(p0.X + predecessor->handle_right.X * X_diff, p0.Y + predecessor->handle_right.Y * Y_diff);
Coordinate const p2 = Coordinate(p0.X + candidate->handle_left.X * X_diff, p0.Y + candidate->handle_left.Y * Y_diff);
Coordinate const p3 = candidate->co;
double t = 0.5;
double t_step = 0.25;
do {
// Bernstein polynoms
double B[4] = {1, 3, 3, 1};
double oneMinTExp = 1;
double tExp = 1;
for (int i = 0; i < 4; ++i, tExp *= t) {
B[i] *= tExp;
}
for (int i = 0; i < 4; ++i, oneMinTExp *= 1 - t) {
B[4 - i - 1] *= oneMinTExp;
}
double const x = p0.X * B[0] + p1.X * B[1] + p2.X * B[2] + p3.X * B[3];
double const y = p0.Y * B[0] + p1.Y * B[1] + p2.Y * B[2] + p3.Y * B[3];
if (abs(index - x) < 0.01) {
return y;
}
if (x > index) {
t -= t_step;
}
else {
t += t_step;
}
t_step /= 2;
} while (true);
return InterpolateBezierCurve(*predecessor, *candidate, true, index, 0.01);
}
// Get the rounded INT value at a specific index