unity 根据AnimationCurve实现计算曲线下面积

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   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; }

 

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