光照探针(LightProbe) 与 球谐(Spherical Harmonics)

Game Dev, Graphics

需求：可以手动自定义，并且随Prefab保存的LightProbe

球谐函数 (Spherical Harmonics)

正经定义：
球谐函数是拉普拉斯方程的球坐标系形式解的角度部分

自分白话解释：
球谐函数 - 使用少量系数定义一个球面的整个表面：输入一个方向(球面上一点)，输出该方向的颜色

Unity中使用的是二阶球谐函数 SphericalHarmonicsL2，保存为9个系数(27个float)，使用时转换为7个Vector4提供给Shader(参考buitin shaders中的ShadeSH9)

Unity的实现参考的是 Stupid Spherical Harmonics (SH) Tricks

官方文档中关于光照探针的技术信息： Light Probes: Technical information

关于SH一篇非常好的文章： Benoît Mayaux (Patapom), Spherical Harmonics

还有企鹅学院的两篇：
(Unity Shader球谐光照解析)[https://gameinstitute.qq.com/community/detail/124147]
(球谐光照（spherical harmonic lighting）解析)[https://gameinstitute.qq.com/community/detail/123183]

自动布置LightProbe

将需要LightProbe的位置赋值给 LightProbeGroup.probePositions

官方例子：Placing probes using scripting

Unity中手动计算SH

SphericalHarmonicsL2提供两个方法

  • 添加环境光(AddAmbientLight)
  • 添加平行光(AddDirectionalLight)

Unity官方文档提供了一个例子：[LightProbes.bakedProbes(Unity文档)]https://docs.unity3d.com/ScriptReference/LightProbes-bakedProbes.html

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using UnityEngine;
using UnityEngine.Rendering;

public class ExampleClass : MonoBehaviour
{
    public Color m_Ambient;
    public Light[] m_Lights;

    // On start add the contribution of the ambient light and all lights
    // assigned to the lights array to all baked probes.
    void Start()
    {
        SphericalHarmonicsL2[] bakedProbes = LightmapSettings.lightProbes.bakedProbes;
        Vector3[] probePositions = LightmapSettings.lightProbes.positions;
        int probeCount = LightmapSettings.lightProbes.count;

        // Clear all probes
        for (int i = 0; i < probeCount; i++)
            bakedProbes[i].Clear();

        // Add ambient light to all probes
        for (int i = 0; i < probeCount; i++)
            bakedProbes[i].AddAmbientLight(m_Ambient);

        // Add directional and point lights' contribution to all probes
        foreach (Light l in m_Lights)
        {
            if (l.type == LightType.Directional)
            {
                for (int i = 0; i < probeCount; i++)
                    bakedProbes[i].AddDirectionalLight(-l.transform.forward, l.color, l.intensity);
            }
            else if (l.type == LightType.Point)
            {
                for (int i = 0; i < probeCount; i++)
                    SHAddPointLight(probePositions[i], l.transform.position, l.range, l.color, l.intensity, ref bakedProbes[i]);
            }
        }
        LightmapSettings.lightProbes.bakedProbes = bakedProbes;
    }

    void SHAddPointLight(Vector3 probePosition, Vector3 position, float range, Color color, float intensity, ref SphericalHarmonicsL2 sh)
    {
        // From the point of view of an SH probe, point light looks no different than a directional light,
        // just attenuated and coming from the right direction.
        Vector3 probeToLight = position - probePosition;
        float attenuation = 1.0F / (1.0F + 25.0F * probeToLight.sqrMagnitude / (range * range));
        sh.AddDirectionalLight(probeToLight.normalized, color, intensity * attenuation);
    }
}

在已有LightProbe烘焙的环境中的指定位置获取LightProbe

使用方法LightProbes.GetInterpolatedProbe

LightProbe的SH差值


Unity官方在GDC 2012上的说明, Light Probe Interpolation Using Tetrahedral Tessellations

Unity中烘焙时计算四面体网络(TetrahedronGrid)并保存，运行时根据对象在某个四面体中的位置，利用这个四面体相关的几个SH插值出一个新的SH

更多阅读:
Spherical Harmonics Interpolation, Computation of Laplacians and Gauge Theory

将SH系数注入Renderer

Unity官方的Keijiro Takahashi 写的 LightProbeUtility

注意系数的组合方式在之后的版本中有变化，正确的组合如下

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// Constant + Linear
for (var i = 0; i < 3; i++)
    properties.SetVector(_idSHA[i], new Vector4(
        sh[i, 3], sh[i, 1], sh[i, 2], sh[i, 0] - sh[i, 6] 
    ));

// Quadratic polynomials
for (var i = 0; i < 3; i++)
    properties.SetVector(_idSHB[i], new Vector4(
        sh[i, 4], sh[i, 5], sh[i, 6] * 3, sh[i, 7]
    ));

// Final quadratic polynomial
properties.SetVector(_idSHC, new Vector4(
    sh[0, 8], sh[1, 8], sh[2, 8], 1
));

UnityCG.cginc中相关的代码

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// normal should be normalized, w=1.0
half3 SHEvalLinearL0L1 (half4 normal)
{
    half3 x;

    // Linear (L1) + constant (L0) polynomial terms
    x.r = dot(unity_SHAr,normal);
    x.g = dot(unity_SHAg,normal);
    x.b = dot(unity_SHAb,normal);

    return x;
}

// normal should be normalized, w=1.0
half3 SHEvalLinearL2 (half4 normal)
{
    half3 x1, x2;
    // 4 of the quadratic (L2) polynomials
    half4 vB = normal.xyzz * normal.yzzx;
    x1.r = dot(unity_SHBr,vB);
    x1.g = dot(unity_SHBg,vB);
    x1.b = dot(unity_SHBb,vB);

    // Final (5th) quadratic (L2) polynomial
    half vC = normal.x*normal.x - normal.y*normal.y;
    x2 = unity_SHC.rgb * vC;

    return x1 + x2;
}

// normal should be normalized, w=1.0
// output in active color space
half3 ShadeSH9 (half4 normal)
{
    // Linear + constant polynomial terms
    half3 res = SHEvalLinearL0L1 (normal);

    // Quadratic polynomials
    res += SHEvalLinearL2 (normal);

#   ifdef UNITY_COLORSPACE_GAMMA
        res = LinearToGammaSpace (res);
#   endif

    return res;
}
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