This post continues the tutorial on volumetric rendering, introducing one of the most used techniques: raymarching.

You can find here all the other posts in this series:

Introduction

Loosely speaking, the standard behaviour of Unity 5’s lighting engine stops the rendering when a ray from the camera hits the surface of an object. There is no built-in mechanism for those rays to penetrate within the surface of an object. To compensate for this, we have have introduced a technique called raymarch. What we have in a fragment shader is the position of the point we are rendering (in world coordinates), and the view direction from the camera. We can manually extends those rays, making them hit custom geometries that exists only within the shader code. The barebone shade that allows us to do this is:

struct v2f { float4 pos : SV_POSITION; // Clip space float3 wPos : TEXCOORD1; // World position }; // Vertex function v2f vert (appdata_full v) { v2f o; o.pos = mul(UNITY_MATRIX_MVP, v.vertex); o.wPos = mul(_Object2World, v.vertex).xyz; return o; } // Fragment function fixed4 frag (v2f i) : SV_Target { float3 worldPosition = i.wPos; float3 viewDirection = normalize(i.wPos - _WorldSpaceCameraPos); return raymarch (worldPosition, viewDirection); } 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 struct v2f { float4 pos : SV_POSITION ; // Clip space float3 wPos : TEXCOORD1 ; // World position } ; // Vertex function v2f vert ( appdata_full v ) { v2f o ; o . pos = mul ( UNITY_MATRIX_MVP , v . vertex ) ; o . wPos = mul ( _Object2World , v . vertex ) . xyz ; return o ; } // Fragment function fixed4 frag ( v2f i ) : SV_Target { float3 worldPosition = i . wPos ; float3 viewDirection = normalize ( i . wPos - _WorldSpaceCameraPos ) ; return raymarch ( worldPosition , viewDirection ) ; }

The rest of this post will provide different implementations for the raymarch function.

Raymarching with Constant Step

The first implementation of raymarching introduced in Volume Rendering used a constant step. Each ray is extended by STEP_SIZE in the view direction, until it hits something. If that’s the case, we draw red pixel, otherwise a white one.

Raymarching with constant step can be implemented with the following code:

fixed4 raymarch (float3 position, float3 direction) { for (int i = 0; i < STEPS; i++) { if ( sphereHit(position) ) return fixed4(1,0,0,1); // Red position += direction * STEP_SIZE; } return fixed4(0,0,0,1); // White } 1 2 3 4 5 6 7 8 9 10 11 12 fixed4 raymarch ( float3 position , float3 direction ) { for ( int i = 0 ; i < STEPS ; i ++ ) { if ( sphereHit ( position ) ) return fixed4 ( 1 , 0 , 0 , 1 ) ; // Red position += direction * STEP_SIZE ; } return fixed4 ( 0 , 0 , 0 , 1 ) ; // White }

As seen already, it renders unsexy, flat geometries:

The post Surface Shading will be dedicated entirely to give threedimensionality to volumetric geometries. Before that, need to focus on a better implementation of the raymarch technique.

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Distance Aided Raymarching

What makes raymarching with constant step very inefficient is the fact that rays advances by the same amount every time, regardless of the geometry that fills the volumetric world. The performance of a shader suffers immensely by adding loops. If we want to use real time volumetric rendering, we need to find better a more efficient solution.

We would like a way of estimating how far a ray can travel without hitting a piece of geometry. In order for this technique to work, we need to be able to estimate the distance from our geometry. In the previous post we have used a function called sphereHit which indicated whether a point was inside a sphere or not:

bool sphereHit (float3 p) { return distance(p,_Centre) < _Radius; } 1 2 3 4 bool sphereHit ( float3 p ) { return distance ( p , _Centre ) < _Radius ; }

We can change it in such a way that instead of a boolean value, it returns a distance:

float sphereDistance (float3 p) { return distance(p,_Centre) - _Radius; } 1 2 3 4 float sphereDistance ( float3 p ) { return distance ( p , _Centre ) - _Radius ; }

This now belongs to a family of functions called signed distance functions. As the name suggests, it provides a measure which can be positive or negative. When positive, we are outside the sphere; when negative we are inside and when zero we are exactly on its surface.

What sphereDistance allows us is to have a conservative estimation of how far our ray can travel without hitting a sphere. Without any proper shading, volumetric rendering is fairly uninteresting. Even if this example might seem trivial with a single sphere, it becomes a valuable technique with more complex geometries. The following image (from Distance Estimated 3D Fractals) show how raymarch works. Each ray travels for as long as its distance from the closest object. In such a way we can dramatically reduce the number of steps required to hit a volume.

This brings us to the the distance-aided implementation of raymarching:

fixed4 raymarch (float3 position, float3 direction) { for (int i = 0; i < STEPS; i++) { float distance = sphereDistance(position); if (distance < MIN_DISTANCE) return i / (float) STEPS; position += distance * direction; } return 0; } 1 2 3 4 5 6 7 8 9 10 11 12 fixed4 raymarch ( float3 position , float3 direction ) { for ( int i = 0 ; i < STEPS ; i ++ ) { float distance = sphereDistance ( position ) ; if ( distance < MIN_DISTANCE ) return i / ( float ) STEPS ; position += distance * direction ; } return 0 ; }

To better understand how it works, we replaced the surface rendering with a colour gradient that indicates how many steps were requires for raymarch to hit a piece of geometry:

It’s immediately obvious that the flat geometry that faces the camera can be identified immediately. The edges, instead, are much trickier. This technique also estimate how close we are to any nearby geometry. We will see in a future instalment, Ambient Occlusion, how this can be helpful to add details to our volume.

Conclusion

This post introduces the de-facto standard technique used for real time raymarching shaders. The rays advances in the volumetric medium according to a conservative estimation of the closest nearby geometry.

The next post will focus on how to use distance functions to create geometrical primitives, and how they can be combined together to create whichever shape you want.

Other Resources

⚠ Part 6 of this series is available for preview on Patreon, as the text needs to be completed. If you are interested in volumetric rendering for non-solid materials (clouds, smoke, …) or transparent ones (water, glass, …) the topic is resumed in detailed in the Atmospheric Volumetric Scattering series!