implemented full bezier interpolation for keyframes

io/math.cpp

@@ -1,15 +1,54 @@
 #include "math.h"
 
 #include <QtMath>
+#include <QVector>
+
+#include "debug.h"
 
 int lerp(int a, int b, double t) {
-    return qRound(((1.0 - t) * a) + (t * b));
+	return qRound(((1.0 - t) * a) + (t * b));
 }
 
 float float_lerp(float a, float b, float t) {
-    return ((1.0F - t) * a) + (t * b);
+	return ((1.0F - t) * a) + (t * b);
 }
 
 double double_lerp(double a, double b, double t) {
-    return ((1.0 - t) * a) + (t * b);
+	return ((1.0 - t) * a) + (t * b);
+}
+
+double quad_from_t(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 quad_t_from_x(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);
+	// alt: return (a - b - qSqrt(a*x + c*x - 2*b*x + qPow(b, 2) - a*c))/(a - 2*b + c);
+}
+
+double cubic_from_t(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 cubic_t_from_x(double x_target, double a, double b, double c, double d) {
+	double tolerance = 0.0001;
+
+	double lower = 0.0;
+	double upper = 1.0;
+
+	double percent = 0.5;
+	double x = cubic_from_t(a, b, c, d, percent);
+
+	while (qAbs(x_target - x) > tolerance) {
+		if (x_target > x) {
+			lower = percent;
+		} else {
+			upper = percent;
+		}
+
+		percent = (upper + lower) / 2.0;
+		x = cubic_from_t(a, b, c, d, percent);
+	}
+
+	return percent;
 }