Jitter ray origin to add noise instead of banding when raymarching

ScriptableRenderPipeline/HDRenderPipeline/HDRP/Camera/HDCamera.cs

         }
 
         // Set up UnityPerView CBuffer.
-        public void SetupGlobalParams(CommandBuffer cmd, float time, float lastTime)
+        public void SetupGlobalParams(CommandBuffer cmd, float time, float lastTime, uint frameCount)
         {
             cmd.SetGlobalMatrix(HDShaderIDs._ViewMatrix,                viewMatrix);
             cmd.SetGlobalMatrix(HDShaderIDs._InvViewMatrix,             viewMatrix.inverse);
             cmd.SetGlobalVector(HDShaderIDs.unity_DeltaTime, new Vector4(dt, 1.0f / dt, sdt, 1.0f / sdt));
             cmd.SetGlobalVector(HDShaderIDs._SinTime,        new Vector4(Mathf.Sin(ct * 0.125f), Mathf.Sin(ct * 0.25f), Mathf.Sin(ct * 0.5f), Mathf.Sin(ct)));
             cmd.SetGlobalVector(HDShaderIDs._CosTime,        new Vector4(Mathf.Cos(ct * 0.125f), Mathf.Cos(ct * 0.25f), Mathf.Cos(ct * 0.5f), Mathf.Cos(ct)));
+            cmd.SetGlobalInt(HDShaderIDs._FrameCount,        (int)frameCount);
         }
 
         public void SetupGlobalStereoParams(CommandBuffer cmd)

ScriptableRenderPipeline/HDRenderPipeline/HDRP/HDRenderPipeline.cs

                 ssReflection.PushShaderParameters(cmd);
 
                 // Set up UnityPerView CBuffer.
-                hdCamera.SetupGlobalParams(cmd, m_Time, m_LastTime);
+                hdCamera.SetupGlobalParams(cmd, m_Time, m_LastTime, m_FrameCount);
                 if (m_FrameSettings.enableStereo) hdCamera.SetupGlobalStereoParams(cmd);
 
                 cmd.SetGlobalInt(HDShaderIDs._SSReflectionEnabled, m_FrameSettings.enableSSR ? 1 : 0);
 
                             // Overwrite camera properties set during the shadow pass with the original camera properties.
                             renderContext.SetupCameraProperties(camera, m_FrameSettings.enableStereo);
-                            hdCamera.SetupGlobalParams(cmd, m_Time, m_LastTime);
+                            hdCamera.SetupGlobalParams(cmd, m_Time, m_LastTime, m_FrameCount);
                             if (m_FrameSettings.enableStereo) hdCamera.SetupGlobalStereoParams(cmd);
                         }
 

ScriptableRenderPipeline/HDRenderPipeline/HDRP/HDStringConstants.cs

 
         public static readonly int _UseTileLightList = Shader.PropertyToID("_UseTileLightList");
 
+        public static readonly int _FrameCount     = Shader.PropertyToID("_FrameCount");
         public static readonly int _Time           = Shader.PropertyToID("_Time");
         public static readonly int _LastTime       = Shader.PropertyToID("_LastTime");
         public static readonly int _SinTime        = Shader.PropertyToID("_SinTime");

ScriptableRenderPipeline/HDRenderPipeline/HDRP/Lighting/Reflection/ScreenSpaceTracing.hlsl

 //
 // Use library here, like ScreenSpaceProxyRaycastReflection(...)
 
+// #################################################
+// Notes
+// #################################################
+// Some banding issues can occurs when raymarching the depth buffer.
+//
+// This can be hidden by offsetting the ray origin with a jitter.
+// Combined with a temporal filtering, the banding artifact will be smoothed.
+// This will trade banding for noise.
+// 
+// This happens when we raymarch with a ray direction that is quite different from the view vector.
+// Exemple when raymarching with a direction perpendicular to the view vector:
+// 
+// Depth buffer  far
+//                |
+//                v
+//               near
+//
+//         --------
+//  hit ==>xx
+//         xx
+//           
+//  fail ===>
+//           xx
+//  hit  ===>xx
+//              
+//              xx
 
 
 // #################################################
     }
 }
 #endif
+
+float SampleBayer4(uint2 positionSS)
+{
+    const float4x4 Bayer4 = float4x4(0,  8,  2,  10,
+                                         12, 4,  14, 6,
+                                         3,  11, 1,  9,
+                                         15, 7,  13, 5) / 16;
+
+    return Bayer4[positionSS.x % 4][positionSS.y % 4];
+}
 
 // -------------------------------------------------
 // Algorithms

ScriptableRenderPipeline/HDRenderPipeline/HDRP/Material/Lit/Lit.hlsl

         ScreenSpaceRaymarchInput ssRayInput;
         ZERO_INITIALIZE(ScreenSpaceRaymarchInput, ssRayInput);
 
-        ssRayInput.rayOriginWS = rayOriginWS;
+        ssRayInput.rayOriginWS = rayOriginWS + rayDirWS * SampleBayer4(posInput.positionSS + _FrameCount) * 0.1;
         ssRayInput.rayDirWS = rayDirWS;
 #if DEBUG_DISPLAY
         ssRayInput.debug = debug;

ScriptableRenderPipeline/HDRenderPipeline/HDRP/ShaderVariables.hlsl

     float4 _SinTime;                    // { sin(t/8), sin(t/4), sin(t/2), sin(t) }
     float4 _CosTime;                    // { cos(t/8), cos(t/4), cos(t/2), cos(t) }
     float4 unity_DeltaTime;             // { dt, 1/dt, smoothdt, 1/smoothdt }
+    int _FrameCount;
 
     // Volumetric lighting.
     float4 _AmbientProbeCoeffs[7];      // 3 bands of SH, packed, rescaled and convolved with the phase function