unity 根据AnimationCurve实现计算曲线下面积

Posted 2020-11-16 liucup

   想使用Animation曲线制作变速移动, 需要 当前曲线下面积/曲线总面积 获取当前移动进度，在网上找到了unity animationCurve的实现代码，修改后做积分可以求得面积代码如下：

public float AreaUnderCurve(AnimationCurve curve, float w, float h)
{
        var areaUnderCurve = 0f;
        var keys = curve.keys;

        for (var i = 0; i < keys.Length - 1; i++)
        {
            // Calculate the 4 cubic Bezier control points from Unity AnimationCurve (a hermite cubic spline) 
            var K1 = keys[i];
            var K2 = keys[i + 1];
            var A = new Vector2(K1.time * w, K1.value * h);
            var D = new Vector2(K2.time * w, K2.value * h);
            var e = (D.x - A.x) / 3.0f;
            var f = h / w;
            var B = A + new Vector2(e, e * f * K1.outTangent);
            var C = D + new Vector2(-e, -e * f * K2.inTangent);

            /*
             * The cubic Bezier curve function looks like this:
             * 
             * f(x) = A(1 - x)^3 + 3B(1 - x)^2 x + 3C(1 - x) x^2 + Dx^3
             * 
             * Where A, B, C and D are the control points and, 
             * for the purpose of evaluating an instance of the Bezier curve, 
             * are constants. 
             * 
             * Multiplying everything out and collecting terms yields the expanded polynomial form:
             * f(x) = (-A + 3B -3C + D)x^3 + (3A - 6B + 3C)x^2 + (-3A + 3B)x + A
             * 
             * If we say:
             * a = -A + 3B - 3C + D
             * b = 3A - 6B + 3C
             * c = -3A + 3B
             * d = A
             * 
             * Then we have the expanded polynomal:
             * f(x) = ax^3 + bx^2 + cx + d
             * 
             * Whos indefinite integral is:
             * a/4 x^4 + b/3 x^3 + c/2 x^2 + dx + E
             * Where E is a new constant introduced by integration.
             * 
             * The indefinite integral of the quadratic Bezier curve is:
             * (-A + 3B - 3C + D)/4 x^4 + (A - 2B + C) x^3 + 3/2 (B - A) x^2 + Ax + E
             */

            float a, b, c, d;
            a = -A.y + 3.0f * B.y - 3.0f * C.y + D.y;
            b = 3.0f * A.y - 6.0f * B.y + 3.0f * C.y;
            c = -3.0f * A.y + 3.0f * B.y;
            d = A.y;

            /* 
             * a, b, c, d, now contain the y component from the Bezier contorl points.
             * In other words - the AnimationCurve Keyframe value * h data!
             * 
             * What about the x component for the Bezier control points - the AnimationCurve
             * time data?  We will need to evaluate the x component when time = 1.
             * because we use curve range 0 - 1
             * 
             * x^4, x^3, X^2, X all equal 1, so we can conveniently drop this coeffiecient.
             * 
             * Lastly, for each segment on the AnimationCurve we get the time difference of the 
             * Keyframes and multiply by w.
             * 
             * Iterate through the segments and add up all the areas for 
             * the total area under the AnimationCurve!
             */

            var t = (K2.time - K1.time) * w;
            var area = ((a / 4.0f) + (b / 3.0f) + (c / 2.0f) + d) * t;
            areaUnderCurve += area;
        }

        return areaUnderCurve;
}