using System; using System.Collections.Generic; using System.Linq; namespace UnityEngine.Experimental.Rendering.HDPipeline { public class LightUtils { // Physical light unit helper // All light unit are in lumen (Luminous power) // Punctual light (point, spot) are convert to candela (cd = lumens / steradian) // For our isotropic area lights which expect radiance(W / (sr* m^2)) in the shader: // power = Integral{area, Integral{hemisphere, radiance * }}, // power = area * Pi * radiance, // radiance = power / (area * Pi). // We use photometric unit, so radiance is luminance and power is luminous power // Ref: Moving Frostbite to PBR // Also good ref: https://www.radiance-online.org/community/workshops/2004-fribourg/presentations/Wandachowicz_paper.pdf // convert intensity (lumen) to candela public static float ConvertPointLightLumenToCandela(float intensity) { return intensity / (4.0f * Mathf.PI); } // convert intensity (candela) to lumen public static float ConvertPointLightCandelaToLumen(float intensity) { return intensity * (4.0f * Mathf.PI); } // angle is the full angle, not the half angle in radiant // convert intensity (lumen) to candela public static float ConvertSpotLightLumenToCandela(float intensity, float angle, bool exact) { return exact ? intensity / (2.0f * (1.0f - Mathf.Cos(angle / 2.0f)) * Mathf.PI) : intensity / Mathf.PI; } public static float ConvertSpotLightCandelaToLumen(float intensity, float angle, bool exact) { return exact ? intensity * (2.0f * (1.0f - Mathf.Cos(angle / 2.0f)) * Mathf.PI) : intensity * Mathf.PI; } // angleA and angleB are the full opening angle, not half angle // convert intensity (lumen) to candela public static float ConvertFrustrumLightLumenToCandela(float intensity, float angleA, float angleB) { return intensity / (4.0f * Mathf.Asin(Mathf.Sin(angleA / 2.0f) * Mathf.Sin(angleB / 2.0f))); } public static float ConvertFrustrumLightCandelaToLumen(float intensity, float angleA, float angleB) { return intensity * (4.0f * Mathf.Asin(Mathf.Sin(angleA / 2.0f) * Mathf.Sin(angleB / 2.0f))); } // convert intensity (lumen) to nits public static float ConvertSphereLightLumenToLuminance(float intensity, float sphereRadius) { return intensity / ((4.0f * Mathf.PI * sphereRadius * sphereRadius) * Mathf.PI); } // convert intensity (nits) to lumen public static float ConvertSphereLightLuminanceToLumen(float intensity, float sphereRadius) { return intensity * ((4.0f * Mathf.PI * sphereRadius * sphereRadius) * Mathf.PI); } // convert intensity (lumen) to nits public static float ConvertDiscLightLumenToLuminance(float intensity, float discRadius) { return intensity / ((discRadius * discRadius * Mathf.PI) * Mathf.PI); } // convert intensity (nits) to lumen public static float ConvertDiscLightLuminanceToLumen(float intensity, float discRadius) { return intensity * ((discRadius * discRadius * Mathf.PI) * Mathf.PI); } // convert intensity (lumen) to nits public static float ConvertRectLightLumenToLuminance(float intensity, float width, float height) { return intensity / ((width * height) * Mathf.PI); } // convert intensity (nits) to lumen public static float ConvertRectLightLuminanceToLumen(float intensity, float width, float height) { return intensity * ((width * height) * Mathf.PI); } public static float ConvertEvToLuminance(float ev) { return Mathf.Pow(2, ev - 3); } public static float ConvertLuminanceToEv(float luminance) { const float k = 12.5f; return (float)Math.Log((luminance * 100f) / k, 2); } public static float ConvertAreaLightLumenToLuminance(LightTypeExtent areaLightType, float lumen, float width, float height = 0) { switch (areaLightType) { case LightTypeExtent.Line: return LightUtils.CalculateLineLightLumenToLuminance(lumen, width); case LightTypeExtent.Rectangle: return LightUtils.ConvertRectLightLumenToLuminance(lumen, width, height); } return lumen; } public static float ConvertAreaLightLuminanceToLumen(LightTypeExtent areaLightType, float luminance, float width, float height = 0) { switch (areaLightType) { case LightTypeExtent.Line: return LightUtils.CalculateLineLightLuminanceToLumen(luminance, width); case LightTypeExtent.Rectangle: return LightUtils.ConvertRectLightLuminanceToLumen(luminance, width, height); } return luminance; } public static float ConvertAreaLightLumenToEv(LightTypeExtent areaLightType, float lumen, float width, float height) { float luminance = ConvertAreaLightLumenToLuminance(areaLightType, lumen, width, height); return ConvertLuminanceToEv(luminance); } public static float ConvertAreaLightEvToLumen(LightTypeExtent areaLightType, float ev, float width, float height) { float luminance = ConvertEvToLuminance(ev); return ConvertAreaLightLuminanceToLumen(areaLightType, luminance, width, height); } // convert intensity (lumen) to nits public static float CalculateLineLightLumenToLuminance(float intensity, float lineWidth) { //Line lights expect radiance (W / (sr * m^2)) in the shader. //In the UI, we specify luminous flux (power) in lumens. //First, it needs to be converted to radiometric units (radiant flux, W). //Then we must recall how to compute power from radiance: //radiance = differential_power / (differrential_projected_area * differential_solid_angle), //radiance = differential_power / (differrential_area * differential_solid_angle * ), //power = Integral{area, Integral{hemisphere, radiance * }}. //Unlike tube lights, our line lights have no surface area, so the integral becomes: //power = Integral{length, Integral{sphere, radiance}}. //For an isotropic line light, radiance is constant, therefore: //power = length * (4 * Pi) * radiance, //radiance = power / (length * (4 * Pi)). return intensity / (4.0f * Mathf.PI * lineWidth); } public static float CalculateLineLightLuminanceToLumen(float intensity, float lineWidth) { return intensity * (4.0f * Mathf.PI * lineWidth); } // spotAngle in radiant public static void CalculateAnglesForPyramid(float aspectRatio, float spotAngle, out float angleA, out float angleB) { // Since the smallest angles is = to the fov, and we don't care of the angle order, simply make sure the aspect ratio is > 1 if (aspectRatio < 1.0f) aspectRatio = 1.0f / aspectRatio; angleA = spotAngle; var halfAngle = angleA * 0.5f; // half of the smallest angle var length = Mathf.Tan(halfAngle); // half length of the smallest side of the rectangle length *= aspectRatio; // half length of the bigest side of the rectangle halfAngle = Mathf.Atan(length); // half of the bigest angle angleB = halfAngle * 2.0f; } // TODO: Do a cheaper fitting // Given a correlated color temperature (in Kelvin), estimate the RGB equivalent. Curve fit error is max 0.008. // return color in linear RGB space public static Color CorrelatedColorTemperatureToRGB(float temperature) { float r, g, b; // Temperature must fall between 1000 and 40000 degrees // The fitting require to divide kelvin by 1000 (allow more precision) float kelvin = Mathf.Clamp(temperature, 1000.0f, 40000.0f) / 1000.0f; float kelvin2 = kelvin * kelvin; // Using 6570 as a pivot is an approximation, pivot point for red is around 6580 and for blue and green around 6560. // Calculate each color in turn (Note, clamp is not really necessary as all value belongs to [0..1] but can help for extremum). // Red r = kelvin < 6.570f ? 1.0f : Mathf.Clamp((1.35651f + 0.216422f * kelvin + 0.000633715f * kelvin2) / (-3.24223f + 0.918711f * kelvin), 0.0f, 1.0f); // Green g = kelvin < 6.570f ? Mathf.Clamp((-399.809f + 414.271f * kelvin + 111.543f * kelvin2) / (2779.24f + 164.143f * kelvin + 84.7356f * kelvin2), 0.0f, 1.0f) : Mathf.Clamp((1370.38f + 734.616f * kelvin + 0.689955f * kelvin2) / (-4625.69f + 1699.87f * kelvin), 0.0f, 1.0f); //Blue b = kelvin > 6.570f ? 1.0f : Mathf.Clamp((348.963f - 523.53f * kelvin + 183.62f * kelvin2) / (2848.82f - 214.52f * kelvin + 78.8614f * kelvin2), 0.0f, 1.0f); return new Color(r, g, b, 1.0f); } } }