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INFOMAGR Advanced Graphics Jacco Bikker - November 2018 - February 2019 Lecture 4 - Real - time Ray Tracing Welcome! , = (, ) , + , ,

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SLIDE 1

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𝑻

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INFOMAGR – Advanced Graphics

Jacco Bikker - November 2018 - February 2019

Lecture 4 - β€œReal-time Ray Tracing”

Welcome!

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SLIDE 2

Today’s Agenda:

β–ͺ Introduction β–ͺ Ray Distributions β–ͺ The Top-level BVH β–ͺ Real-time Ray Tracing β–ͺ Assignment 2

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SLIDE 3

Introduction

Advanced Graphics – Real-time Ray Tracing 3

Cost Breakdown for Ray Tracing:

β–ͺ Pixels β–ͺ Primitives β–ͺ Light sources β–ͺ Path segments Mind scalability as well as constant cost. Example: scene consisting of 1k spheres and 4 light sources, diffuse materials, rendered to 1M pixels: 1𝑁 Γ— 5 Γ— 1𝑙 = 5 βˆ™ 109 ray/prim intersections. (multiply by desired framerate for realtime)

Using the BVH:

β–ͺ Pixels β–ͺ N primitives βž” log N deep tree β–ͺ Light sources β–ͺ Path segments Example: scene consisting of 1k spheres and 4 light sources, diffuse materials, rendered to 1M pixels: 1𝑁 Γ— 5 Γ— 10 = 5 βˆ™ 107 ray/(prim or node) intersections. (multiply by desired framerate for realtime)

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SLIDE 4

Introduction

Advanced Graphics – Real-time Ray Tracing 4

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SLIDE 5

Introduction

Advanced Graphics – Real-time Ray Tracing 5

Reality Check

Performance is now OK, but we’re not quite ready to render a game world.

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SLIDE 6

Introduction

Advanced Graphics – Real-time Ray Tracing 6

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SLIDE 7

Today’s Agenda:

β–ͺ Introduction β–ͺ Ray Distributions β–ͺ The Top-level BVH β–ͺ Real-time Ray Tracing β–ͺ Assignment 2

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SLIDE 8

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 8 Cost of ray tracing: Dominated by memory access cost. β–ͺ Ray data β–ͺ Node data β–ͺ Triangle data β–ͺ Material data (incl. textures)

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SLIDE 9

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 9 Primary rays: For a tile of pixels, these are organized in a narrow frustum. All rays share a common

  • rigin.
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SLIDE 10

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 10 Shadow rays: For point lights, shadow rays also tend to travel close together. When traced from the light source, they too have a common

  • rigin.
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SLIDE 11

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 11 Secondary rays: Reflected and refracted rays tend to diverge significantly.

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SLIDE 12

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 12

Coherence

Primary rays and shadow rays for point lights are coherent : β–ͺ they tend to intersect the same primitives; β–ͺ they tend to traverse the same BVH nodes. Our problem: Ray tracing cost is dominated by memory latency. Solution: Amortize cost of fetching data over multiple rays.

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SLIDE 13

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 13

Coherent Ray Tracing*

SIMD: four rays for the price of one.

BVHNode::Traverse( Ray r ) { if (!r.Intersects( bounds )) return; if (isleaf()) { IntersectPrimitives(); } else { pool[left].Traverse( r ); pool[left + 1].Traverse( r ); } }

*: Interactive Rendering with Coherent Ray Tracing, Wald et al., 2001

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SLIDE 14

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 14

Coherent Ray Tracing*

SIMD: four rays for the price of one.

BVHNode::Traverse( Ray4 r4 ) { if (!r4.Intersects( bounds )) return; if (isleaf()) { IntersectPrimitives(); } else { pool[left].Traverse( r4 ); pool[left + 1].Traverse( r4 ); } }

*: Interactive Rendering with Coherent Ray Tracing, Wald et al., 2001

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SLIDE 15

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 15

Coherent Ray Tracing

Ray packet traversal: β–ͺ intersect four rays with a single BVH node; β–ͺ if any ray in the packet intersects the node, we traverse it; β–ͺ if the node is a leaf node, we intersect the four rays with each primitive in the leaf. Masking: β–ͺ We maintain an β€˜active’ mask for disabling rays that do not intersect a node.

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SLIDE 16

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 16

Coherent Ray Tracing*

SIMD: four rays for the price of one.

BVHNode::Traverse( Ray4 r4, bool4 mask4 ) { bool4 hit4 = r4.Intersects( bounds ) & mask4; if (none( hit4 )) return; if (isleaf()) { IntersectPrimitives(); } else { pool[left].Traverse( r4, hit4 ); pool[left + 1].Traverse( r4, hit4 ); } }

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SLIDE 17

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 17

Coherent Ray Tracing

Results: β–ͺ for coherent packets, memory traffic is reduced; β–ͺ overall performance is improved by ~2.3x. Overhead: β–ͺ if only a single ray requires traversal or intersection, all four rays perform this operation.

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SLIDE 18

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 18

Large Packets*

Cost of memory access can be amortized over more rays by using larger packets. Note that a naΓ―ve approach will lead to significant overhead. We therefore add a frustum test to rapidly reject BVH nodes: If the packet frustum does not intersect the node AABB, we discard the node. The cost of this operation is independent of the number of rays in the packet. Likewise, a node is traversed as soon as we find that a ray intersects it. This is also independent of packet size.

*: Large Ray Packets for Real-time Whitted Ray Tracing, Overbeck et al., 2008

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SLIDE 19

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 19

Large Packets

Algorithm:

  • 1. Early hit test: test first active ray against AABB
  • 2. Early miss test: test AABB against frustum
  • 3. Brute force test: test all rays until a hit is

found. This step yields a new first active ray index.

BVHNode::Traverse( RayPacket rp, int first ) { if (!Intersects( rp[first )) // 1 { if (!Intersects( rp.frustum )) return; // 2 FindFirstActive( rp, ++first ); // 3 } if (first < rp.rayCount) { if (isleaf()) { IntersectPrimitives( rp ); } else { left.Traverse( rp, first ); right.Traverse( rp, first ); } } }

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SLIDE 20

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 20

Large Packets

Details: β–ͺ Constructing the frustum β–ͺ Ray order & overhead β–ͺ First / last β–ͺ Optimizations: recursion, SIMD

BVHNode::Traverse( RayPacket rp, int first ) { if (!Intersects( rp[first )) // 1 { if (!Intersects( rp.frustum )) return; // 2 FindFirstActive( rp, ++first ); // 3 } if (first < rp.rayCount) { if (isleaf()) { IntersectPrimitives( rp ); } else { left.Traverse( rp, first ); right.Traverse( rp, first ); } } }

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SLIDE 21

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 21

Frustum Construction

Method 1, for primary rays: Planes are easily defined using the corner rays: 𝑂1 = (π‘ž0βˆ’πΉ) Γ— (π‘ž1 βˆ’ π‘ž0) , 𝑒1 = 𝑂1 βˆ™ 𝐹 𝑂2 = (π‘ž1βˆ’πΉ) Γ— (π‘ž2 βˆ’ π‘ž1) , 𝑒2 = 𝑂2 βˆ™ 𝐹 𝑂3 = (π‘ž2βˆ’πΉ) Γ— (π‘ž3 βˆ’ π‘ž2) , 𝑒3 = 𝑂3 βˆ™ 𝐹 𝑂4 = (π‘ž3βˆ’πΉ) Γ— (π‘ž0 βˆ’ π‘ž3) , 𝑒4 = 𝑂4 βˆ™ 𝐹 Note: for secondary rays, we will not have a common origin, nor corner rays. π‘ž0 π‘ž1 π‘ž2 𝐹 π‘ž3

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SLIDE 22

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 22

Frustum Construction

Method 2, for shadow rays:

  • 1. Determine dominant axis and direction:

𝐸𝑑 = σ𝑗=0

𝑂

𝐸𝑗 , chose axis ΰ·  𝑙 as the largest component of 𝐸𝑑 , ො 𝑣 and ො 𝑀 are the other axes.

  • 2. Construct a plane 𝑄 orthogonal to ΰ· 

𝑙

  • 3. Calculate intersection coordinates 𝑣, 𝑀 of the rays with P
  • 4. Determine π‘£π‘›π‘—π‘œ, 𝑣𝑛𝑏𝑦 and π‘€π‘›π‘—π‘œ, 𝑀𝑛𝑏𝑦
  • 5. Corner rays are now:

π‘£π‘›π‘—π‘œ, π‘€π‘›π‘—π‘œ 𝑣𝑛𝑏𝑦, π‘€π‘›π‘—π‘œ 𝑣𝑛𝑏𝑦, 𝑀𝑛𝑏𝑦 (π‘£π‘›π‘—π‘œ, 𝑀𝑛𝑏𝑦) Note: this still requires a common origin. ΰ·  𝑙 1 ො 𝑣

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SLIDE 23

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 23

Frustum Construction

Method 3, for generic rays:

  • 1. Construct two planes:

𝑄

𝑔𝑏𝑠, orthogonal to ΰ· 

𝑙, at location 𝑙𝑔𝑏𝑠 which is

  • btained from the scene AABB;

𝑄

π‘œπ‘“π‘π‘ , orthogonal to ΰ· 

𝑙, at location π‘™π‘œπ‘“π‘π‘ , which is obtained from the AABB over the ray origins.

  • 2. Calculate intersection coordinates 𝑣𝑔𝑏𝑠, 𝑀𝑔𝑏𝑠

and π‘£π‘œπ‘“π‘π‘ , π‘€π‘œπ‘“π‘π‘  of the rays with 𝑄

𝑔𝑏𝑠 and 𝑄 π‘œπ‘“π‘π‘  .

  • 3. Determine π‘£π‘›π‘—π‘œ

π‘œπ‘“π‘π‘ , 𝑣𝑛𝑏𝑦 π‘œπ‘“π‘π‘ , π‘€π‘›π‘—π‘œ π‘œπ‘“π‘π‘ , 𝑣𝑛𝑏𝑦 π‘œπ‘“π‘π‘  and π‘£π‘›π‘—π‘œ 𝑔𝑏𝑠, 𝑣𝑛𝑏𝑦 𝑔𝑏𝑠 , π‘€π‘›π‘—π‘œ 𝑔𝑏𝑠, 𝑣𝑛𝑏𝑦 𝑔𝑏𝑠 .

  • 4. Corner rays are now defined as

π‘£π‘›π‘—π‘œ

𝑔𝑏𝑠, π‘€π‘›π‘—π‘œ 𝑔𝑏𝑠 βˆ’ π‘£π‘›π‘—π‘œ π‘œπ‘“π‘π‘ , π‘€π‘›π‘—π‘œ π‘œπ‘“π‘π‘  ,

𝑣𝑛𝑏𝑦

𝑔𝑏𝑠 , π‘€π‘›π‘—π‘œ 𝑔𝑏𝑠 βˆ’ 𝑣𝑛𝑏𝑦 π‘œπ‘“π‘π‘ , π‘€π‘›π‘—π‘œ π‘œπ‘“π‘π‘  ,

𝑣𝑛𝑏𝑦

𝑔𝑏𝑠 , 𝑀𝑛𝑏𝑦 𝑔𝑏𝑠

βˆ’ 𝑣𝑛𝑏𝑦

π‘œπ‘“π‘π‘ , 𝑀𝑛𝑏𝑦 π‘œπ‘“π‘π‘  ,

π‘£π‘›π‘—π‘œ

𝑔𝑏𝑠, 𝑀𝑛𝑏𝑦 𝑔𝑏𝑠

βˆ’ (π‘£π‘›π‘—π‘œ

π‘œπ‘“π‘π‘ , 𝑀𝑛𝑏𝑦 π‘œπ‘“π‘π‘ ).

ΰ·  𝑙 𝑙𝑔𝑏𝑠 π‘™π‘œπ‘“π‘π‘ 

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SLIDE 24

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 24

Ray Order

The order of the rays in a packet is important. We keep track of the first active ray: in this case the green dot. We thus enter the node with 61 rays, while only 12 rays actually intersect the node. Keeping track of the last ray helps somewhat. 7 8 63

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SLIDE 25

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 25

Ray Order

Overhead can be reduced by numbering rays in each quadrant sequentially.

15 16 31 32 63

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SLIDE 26

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 26

Ray Order

Overhead can be reduced by numbering rays in each quadrant sequentially. For the general case, Morton order is optimal.

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SLIDE 27

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 27

Divergent Rays: Partition Traversal

int PartitionRays for ( int i = 0; i < 𝑗𝑏; i++ ) if (ray[idx[i]].IntersectsAABB()) swap( idx[𝑗𝑓++], idx[i] ); return 𝑗𝑓; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

rays ray indices 𝑗𝑏 𝑗𝑓

2 1 3 4 5 6 7 8 9 10 11 12 13 14 15

𝑗𝑓

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SLIDE 28

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 28

Divergent Rays: Partition Traversal

int PartitionRays for ( int i = 0; i < 𝑗𝑏; i++ ) if (ray[idx[i]].IntersectsAABB()) swap( idx[𝑗𝑓++], idx[i] ); return 𝑗𝑓; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

rays ray indices 𝑗𝑏 𝑗𝑓

2 5 3 4 1 6 7 8 9 10 11 12 13 14 15

𝑗𝑓

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SLIDE 29

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 29

Divergent Rays: Partition Traversal

int PartitionRays for ( int i = 0; i < 𝑗𝑏; i++ ) if (ray[idx[i]].IntersectsAABB()) swap( idx[𝑗𝑓++], idx[i] ); return 𝑗𝑓; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

rays ray indices 𝑗𝑏 𝑗𝑓

2 5 6 3 4 1 7 8 9 10 11 12 13 14 15

𝑗𝑓

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SLIDE 30

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 30

Divergent Rays: Partition Traversal

int PartitionRays for ( int i = 0; i < 𝑗𝑏; i++ ) if (ray[idx[i]].IntersectsAABB()) swap( idx[𝑗𝑓++], idx[i] ); return 𝑗𝑓; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

rays ray indices 𝑗𝑏 𝑗𝑓

2 5 6 9 4 1 7 8 3 10 11 12 13 14 15

𝑗𝑓

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SLIDE 31

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 31

Divergent Rays: Partition Traversal

int PartitionRays for ( int i = 0; i < 𝑗𝑏; i++ ) if (ray[idx[i]].IntersectsAABB()) swap( idx[𝑗𝑓++], idx[i] ); return 𝑗𝑓; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

rays ray indices 𝑗𝑏 𝑗𝑓

2 5 6 9 11 1 7 8 3 10 4 12 13 14 15

𝑗𝑓

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SLIDE 32

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 32

Divergent Rays: Partition Traversal Partition traversal gathers active rays in a continuous list. This comes at the price of some overhead: β–ͺ

  • ne layer of indirection (ray indices βž” rays);

β–ͺ swapping of indices. In practice, this method is suitable for ray distributions where large gaps in the ray set are to be expected.

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SLIDE 33

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 33

Optimization: Recursion

The recursion can be replaced by a local stack:

struct Stack { BVHNode* node; int first; }; Stack stack[STACKSIZE]; stack[0].node = GetBVHRoot(); stack[0].first = 0; int stackPtr = 1; while( stackPtr > 0) { BVHNode* node = stack[--stackPtr].node; first = stack[stackPtr].first; ... }

BVHNode::Traverse( RayPacket rp, int first ) { if (!Intersects( rp[first )) // 1 { if (!Intersects( rp.frustum )) return; // 2 FindFirstActive( rp, ++first ); // 3 } if (first < rp.rayCount) { if (isleaf()) { IntersectPrimitives( rp ); } else { left.Traverse( rp, first ); right.Traverse( rp, first ); } } }

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SLIDE 34

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 34

Optimization: SIMD

We can still use SIMD to test four rays at once. β–ͺ The smallest primitive thus becomes the β€˜QuadRay’; β–ͺ a packet of 𝑂 rays consists of 𝑂/4 QuadRays; β–ͺ β€˜first’ points to the first QuadRay that has at least one active ray; β–ͺ FindFirst processes the remaining rays four at a time. Note: for AVX, replace β€˜four’ by β€˜eight’.

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SLIDE 35

Ray Distributions

Advanced Graphics – Real-time Ray Tracing 35

Results

Compared to 2x2 SIMD packet traversal, ranged traversal improves primary and shadow rays by ~3.5x. Note that ray divergence has a large impact on performance. 1 16.85 (100%) 25.11 (100%) 18.44 (100%) 2 11.61 (69%) 18.83 (75%) 12.93 (70%) 3 6.98 (41%) 12.56 (50%) 7.48 (41%) 4 3.85 (23%) 7.71 (31%) 3.87 (21%)

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SLIDE 36

Today’s Agenda:

β–ͺ Introduction β–ͺ Ray Distributions β–ͺ The Top-level BVH β–ͺ Real-time Ray Tracing β–ͺ Assignment 2

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SLIDE 37

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 37

Ray Tracing Animated Scenes

Covered so far: β–ͺ Static geometry: high-quality construction with spatial splits β–ͺ Deformations: BVH refitting (water, waving trees, … ) β–ͺ Structural changes: binned BVH construction Not covered: β–ͺ Rigid motion

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SLIDE 38

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 38

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SLIDE 39

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 39

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SLIDE 40

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 40

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SLIDE 41

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 41

Combining BVHs

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SLIDE 42

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 42

Combining BVHs

Two BVHs can be combined into a single BVH, by simply adding a new root node pointing to the two BVHs. β–ͺ This works regardless of the method used to build each BVH β–ͺ This can be applied repeatedly to combine many BVHs

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SLIDE 43

Advanced Graphics – Real-time Ray Tracing 43

Scene Graph

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SLIDE 44

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 44

Scene Graph

world car wheel wheel wheel wheel turret plane plane car wheel wheel wheel wheel turret buggy wheel wheel wheel wheel dude dude dude

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SLIDE 45

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 45

Scene Graph

If our application uses a scene graph, we can construct a BVH for each scene graph node. The BVH for each node is built using an appropriate construction algorithm: β–ͺ High-quality SBVH for static scenery (offline) β–ͺ Fast binned SAH BVHs for dynamic scenery The extra nodes used to combine these BVHs into a single BVH are known as the Top-level BVH .

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SLIDE 46

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 46

Rigid Motion

Applying rigid motion to a BVH:

  • 1. Refit the top-level BVH
  • 2. Refit the affected BVH
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SLIDE 47

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 47

Rigid Motion

Applying rigid motion to a BVH:

  • 1. Refit the top-level BVH
  • 2. Refit the affected BVH
  • r:
  • 2. Transform the ray, not the node

Rigid motion is achieved by transforming the rays by the inverse transform upon entering the sub-BVH.

(this obviously does not only apply to translation)

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SLIDE 48

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 48

The Top-level BVH - Construction

Input: list of axis aligned bounding boxes for transformed scene graph nodes Algorithm:

  • 1. Find the two elements in the list for which the AABB has the smallest

surface area

  • 2. Create a parent node for these elements
  • 3. Replace the two elements in the list by the parent node
  • 4. Repeat until one element remains in the list.

Note: algorithmic complexity is 𝑃(𝑂3).

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SLIDE 49

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 49

The Top-level BVH – Faster Construction*

Algorithm:

Node A = list.GetFirst(); Node B = list.FindBestMatch( A ); while (list.size() > 1) { Node C = list.FindBestMatch( B ); if (A == C) { list.Remove( A ); list.Remove( B ); A = new Node( A, B ); list.Add( A ); B = list.FindBestMatch( A ); } else A = B, B = C; }

*: Fast Agglomerative Clustering for Rendering, Walter et al., 2008

A B C A B A B

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SLIDE 50

Top-level BVH

Advanced Graphics – Real-time Ray Tracing 50

The Top-level BVH – Traversal

The leafs of the top-level BVH contain the sub-BVHs. When a ray intersects such a leaf, it is transformed by the inverted transform matrix of the sub-BVH. After this, it traverses the sub-BVH. Once the sub-BVH has been traversed, we transform the ray again, this time by the transform matrix of the sub-BVH. For efficiency, we store the inverted matrix with the sub-BVH root.

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SLIDE 51

Today’s Agenda:

β–ͺ Introduction β–ͺ Ray Distributions β–ͺ The Top-level BVH β–ͺ Real-time Ray Tracing β–ͺ Assignment 2

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SLIDE 52
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SLIDE 53

https://sketchfab.com/SEED.EA/collections/pica-pica

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SLIDE 54

https://www.models-resource.com/wii_u/mariokart8/model/10718

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SLIDE 55

INFOMAGR – Advanced Graphics

Jacco Bikker - November 2018 - February 2019

END of β€œReal-time Ray Tracing”

next lecture: β€œSIMD recap”