387 lines
14 KiB
C#
387 lines
14 KiB
C#
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using static UnityEngine.Mathf;
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namespace UnityEngine.Rendering
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{
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/// <summary>
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/// An implementation of Hable's artist-friendly tonemapping curve.
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/// http://filmicworlds.com/blog/filmic-tonemapping-with-piecewise-power-curves/
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/// </summary>
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public class HableCurve
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{
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/// <summary>
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/// Individual curve segment.
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/// </summary>
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public class Segment
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{
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/// <summary>
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/// The offset of the segment on the X axis.
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/// </summary>
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public float offsetX;
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/// <summary>
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/// The offset of the segment on the Y axis.
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/// </summary>
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public float offsetY;
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/// <summary>
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/// The scale of the segment on the X axis.
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/// </summary>
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public float scaleX;
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/// <summary>
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/// The scale of the segment on the Y axis.
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/// </summary>
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public float scaleY;
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/// <summary>
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/// <c>ln(A)</c> constant in the power curve <c>y = e^(ln(A) + B*ln(x))</c>.
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/// </summary>
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public float lnA;
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/// <summary>
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/// <c>B</c> constant in the power curve <c>y = e^(ln(A) + B*ln(x))</c>.
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/// </summary>
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public float B;
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/// <summary>
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/// Evaluate a point on the curve.
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/// </summary>
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/// <param name="x">The point to evaluate.</param>
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/// <returns>The value of the curve, at the point specified.</returns>
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public float Eval(float x)
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{
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float x0 = (x - offsetX) * scaleX;
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float y0 = 0f;
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// log(0) is undefined but our function should evaluate to 0. There are better ways
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// to handle this, but it's doing it the slow way here for clarity.
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if (x0 > 0)
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y0 = Exp(lnA + B * Log(x0));
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return y0 * scaleY + offsetY;
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}
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}
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struct DirectParams
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{
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internal float x0;
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internal float y0;
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internal float x1;
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internal float y1;
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internal float W;
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internal float overshootX;
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internal float overshootY;
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internal float gamma;
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}
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/// <summary>
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/// The white point.
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/// </summary>
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public float whitePoint { get; private set; }
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/// <summary>
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/// The inverse of the white point.
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/// </summary>
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/// <seealso cref="whitePoint"/>
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public float inverseWhitePoint { get; private set; }
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/// <summary>
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/// The start of the linear section (middle segment of the curve).
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/// </summary>
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public float x0 { get; private set; }
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/// <summary>
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/// The end of the linear section (middle segment of the curve).
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/// </summary>
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public float x1 { get; private set; }
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/// <summary>
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/// The three segments of the curve.
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/// </summary>
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public readonly Segment[] segments = new Segment[3];
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/// <summary>
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/// Creates a new curve.
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/// </summary>
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public HableCurve()
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{
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for (int i = 0; i < 3; i++)
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segments[i] = new Segment();
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uniforms = new Uniforms(this);
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}
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/// <summary>
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/// Evaluates a point on the curve.
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/// </summary>
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/// <param name="x">The x-coordinate at which to evaluate the curve.</param>
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/// <returns>The y-coordinate (value) of the curve at the specified x-coordinate.</returns>
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public float Eval(float x)
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{
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float normX = x * inverseWhitePoint;
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int index = (normX < x0) ? 0 : ((normX < x1) ? 1 : 2);
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var segment = segments[index];
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float ret = segment.Eval(normX);
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return ret;
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}
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/// <summary>
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/// Initializes the curve.
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/// </summary>
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/// <param name="toeStrength">The strength of the transition between the curve's toe and the curve's mid-section. A value of 0 results in no transition and a value of 1 results in a very hard transition.</param>
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/// <param name="toeLength">The length of the curve's toe. Higher values result in longer toes and therefore contain more of the dynamic range.</param>
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/// <param name="shoulderStrength">The strength of the transition between the curve's midsection and the curve's shoulder. A value of 0 results in no transition and a value of 1 results in a very hard transition.</param>
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/// <param name="shoulderLength">The amount of f-stops to add to the dynamic range of the curve. This is how much of the highlights that the curve takes into account.</param>
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/// <param name="shoulderAngle">How much overshoot to add to the curve's shoulder.</param>
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/// <param name="gamma">A gamma correction to the entire curve.</param>
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public void Init(float toeStrength, float toeLength, float shoulderStrength, float shoulderLength, float shoulderAngle, float gamma)
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{
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var dstParams = new DirectParams();
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// This is not actually the display gamma. It's just a UI space to avoid having to
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// enter small numbers for the input.
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const float kPerceptualGamma = 2.2f;
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// Constraints
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{
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toeLength = Pow(Clamp01(toeLength), kPerceptualGamma);
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toeStrength = Clamp01(toeStrength);
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shoulderAngle = Clamp01(shoulderAngle);
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shoulderStrength = Clamp(shoulderStrength, 1e-5f, 1f - 1e-5f);
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shoulderLength = Max(0f, shoulderLength);
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gamma = Max(1e-5f, gamma);
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}
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// Apply base params
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{
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// Toe goes from 0 to 0.5
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float x0 = toeLength * 0.5f;
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float y0 = (1f - toeStrength) * x0; // Lerp from 0 to x0
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float remainingY = 1f - y0;
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float initialW = x0 + remainingY;
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float y1_offset = (1f - shoulderStrength) * remainingY;
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float x1 = x0 + y1_offset;
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float y1 = y0 + y1_offset;
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// Filmic shoulder strength is in F stops
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float extraW = Pow(2f, shoulderLength) - 1f;
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float W = initialW + extraW;
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dstParams.x0 = x0;
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dstParams.y0 = y0;
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dstParams.x1 = x1;
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dstParams.y1 = y1;
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dstParams.W = W;
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// Bake the linear to gamma space conversion
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dstParams.gamma = gamma;
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}
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dstParams.overshootX = (dstParams.W * 2f) * shoulderAngle * shoulderLength;
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dstParams.overshootY = 0.5f * shoulderAngle * shoulderLength;
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InitSegments(dstParams);
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}
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void InitSegments(DirectParams srcParams)
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{
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var paramsCopy = srcParams;
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whitePoint = srcParams.W;
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inverseWhitePoint = 1f / srcParams.W;
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// normalize params to 1.0 range
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paramsCopy.W = 1f;
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paramsCopy.x0 /= srcParams.W;
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paramsCopy.x1 /= srcParams.W;
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paramsCopy.overshootX = srcParams.overshootX / srcParams.W;
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float toeM = 0f;
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float shoulderM = 0f;
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{
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float m, b;
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AsSlopeIntercept(out m, out b, paramsCopy.x0, paramsCopy.x1, paramsCopy.y0, paramsCopy.y1);
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float g = srcParams.gamma;
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// Base function of linear section plus gamma is
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// y = (mx+b)^g
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//
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// which we can rewrite as
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// y = exp(g*ln(m) + g*ln(x+b/m))
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//
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// and our evaluation function is (skipping the if parts):
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/*
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float x0 = (x - offsetX) * scaleX;
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y0 = exp(m_lnA + m_B*log(x0));
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return y0*scaleY + m_offsetY;
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*/
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var midSegment = segments[1];
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midSegment.offsetX = -(b / m);
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midSegment.offsetY = 0f;
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midSegment.scaleX = 1f;
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midSegment.scaleY = 1f;
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midSegment.lnA = g * Log(m);
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midSegment.B = g;
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toeM = EvalDerivativeLinearGamma(m, b, g, paramsCopy.x0);
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shoulderM = EvalDerivativeLinearGamma(m, b, g, paramsCopy.x1);
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// apply gamma to endpoints
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paramsCopy.y0 = Max(1e-5f, Pow(paramsCopy.y0, paramsCopy.gamma));
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paramsCopy.y1 = Max(1e-5f, Pow(paramsCopy.y1, paramsCopy.gamma));
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paramsCopy.overshootY = Pow(1f + paramsCopy.overshootY, paramsCopy.gamma) - 1f;
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}
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this.x0 = paramsCopy.x0;
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this.x1 = paramsCopy.x1;
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// Toe section
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{
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var toeSegment = segments[0];
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toeSegment.offsetX = 0;
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toeSegment.offsetY = 0f;
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toeSegment.scaleX = 1f;
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toeSegment.scaleY = 1f;
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float lnA, B;
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SolveAB(out lnA, out B, paramsCopy.x0, paramsCopy.y0, toeM);
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toeSegment.lnA = lnA;
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toeSegment.B = B;
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}
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// Shoulder section
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{
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// Use the simple version that is usually too flat
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var shoulderSegment = segments[2];
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float x0 = (1f + paramsCopy.overshootX) - paramsCopy.x1;
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float y0 = (1f + paramsCopy.overshootY) - paramsCopy.y1;
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float lnA, B;
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SolveAB(out lnA, out B, x0, y0, shoulderM);
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shoulderSegment.offsetX = (1f + paramsCopy.overshootX);
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shoulderSegment.offsetY = (1f + paramsCopy.overshootY);
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shoulderSegment.scaleX = -1f;
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shoulderSegment.scaleY = -1f;
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shoulderSegment.lnA = lnA;
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shoulderSegment.B = B;
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}
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// Normalize so that we hit 1.0 at our white point. We wouldn't have do this if we
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// skipped the overshoot part.
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{
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// Evaluate shoulder at the end of the curve
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float scale = segments[2].Eval(1f);
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float invScale = 1f / scale;
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segments[0].offsetY *= invScale;
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segments[0].scaleY *= invScale;
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segments[1].offsetY *= invScale;
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segments[1].scaleY *= invScale;
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segments[2].offsetY *= invScale;
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segments[2].scaleY *= invScale;
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}
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}
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// Find a function of the form:
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// f(x) = e^(lnA + Bln(x))
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// where
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// f(0) = 0; not really a constraint
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// f(x0) = y0
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// f'(x0) = m
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void SolveAB(out float lnA, out float B, float x0, float y0, float m)
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{
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B = (m * x0) / y0;
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lnA = Log(y0) - B * Log(x0);
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}
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// Convert to y=mx+b
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void AsSlopeIntercept(out float m, out float b, float x0, float x1, float y0, float y1)
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{
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float dy = (y1 - y0);
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float dx = (x1 - x0);
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if (dx == 0)
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m = 1f;
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else
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m = dy / dx;
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b = y0 - x0 * m;
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}
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// f(x) = (mx+b)^g
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// f'(x) = gm(mx+b)^(g-1)
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float EvalDerivativeLinearGamma(float m, float b, float g, float x)
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{
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return g * m * Pow(m * x + b, g - 1f);
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}
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/// <summary>
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/// An utility class to ease the binding of curve parameters to shaders.
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/// </summary>
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public class Uniforms
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{
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HableCurve parent;
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internal Uniforms(HableCurve parent)
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{
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this.parent = parent;
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}
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/// <summary>
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/// Main curve settings, stored as <c>(inverseWhitePoint, x0, x1, 0)</c>.
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/// </summary>
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public Vector4 curve => new Vector4(parent.inverseWhitePoint, parent.x0, parent.x1, 0f);
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/// <summary>
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/// Toe segment settings, stored as <c>(offsetX, offsetY, scaleX, scaleY)</c>.
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/// </summary>
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public Vector4 toeSegmentA => new Vector4(parent.segments[0].offsetX, parent.segments[0].offsetY, parent.segments[0].scaleX, parent.segments[0].scaleY);
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/// <summary>
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/// Toe segment settings, stored as <c>(ln1, B, 0, 0)</c>.
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/// </summary>
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public Vector4 toeSegmentB => new Vector4(parent.segments[0].lnA, parent.segments[0].B, 0f, 0f);
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/// <summary>
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/// Mid segment settings, stored as <c>(offsetX, offsetY, scaleX, scaleY)</c>.
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/// </summary>
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public Vector4 midSegmentA => new Vector4(parent.segments[1].offsetX, parent.segments[1].offsetY, parent.segments[1].scaleX, parent.segments[1].scaleY);
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/// <summary>
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/// Mid segment settings, stored as <c>(ln1, B, 0, 0)</c>.
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/// </summary>
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public Vector4 midSegmentB => new Vector4(parent.segments[1].lnA, parent.segments[1].B, 0f, 0f);
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/// <summary>
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/// Shoulder segment settings, stored as <c>(offsetX, offsetY, scaleX, scaleY)</c>.
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/// </summary>
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public Vector4 shoSegmentA => new Vector4(parent.segments[2].offsetX, parent.segments[2].offsetY, parent.segments[2].scaleX, parent.segments[2].scaleY);
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/// <summary>
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/// Shoulder segment settings, stored as <c>(ln1, B, 0, 0)</c>.
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/// </summary>
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public Vector4 shoSegmentB => new Vector4(parent.segments[2].lnA, parent.segments[2].B, 0f, 0f);
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}
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/// <summary>
|
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/// An instance of the <see cref="Uniforms"/> utility class for this curve.
|
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/// </summary>
|
||
|
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public readonly Uniforms uniforms;
|
||
|
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}
|
||
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}
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