INFOMAGR – Advanced Graphics Jacco Bikker - November 2018 - February 2019 Lecture 4 - “Real - time Ray Tracing” Welcome! 𝑱 𝒚, 𝒚 ′ = 𝒉(𝒚, 𝒚 ′ ) 𝝑 𝒚, 𝒚 ′ + න 𝝇 𝒚, 𝒚 ′ , 𝒚 ′′ 𝑱 𝒚 ′ , 𝒚 ′′ 𝒆𝒚′′ 𝑻
Today’s Agenda: ▪ Introduction ▪ Ray Distributions ▪ The Top-level BVH ▪ Real-time Ray Tracing ▪ Assignment 2
Advanced Graphics – Real-time Ray Tracing 3 Introduction Cost Breakdown for Ray Tracing: Using the BVH: ▪ Pixels ▪ Pixels ▪ Primitives ▪ N primitives ➔ log N deep tree ▪ Light sources ▪ Light sources ▪ Path segments ▪ Path segments Mind scalability as well as constant cost. Example: scene consisting of 1k spheres and Example: scene consisting of 1k spheres and 4 light sources, diffuse materials, rendered 4 light sources, diffuse materials, rendered to 1M pixels: to 1M pixels: 1𝑁 × 5 × 1𝑙 = 5 ∙ 10 9 ray/prim 1𝑁 × 5 × 10 = 5 ∙ 10 7 ray/(prim or node) intersections. intersections. (multiply by desired framerate for realtime) (multiply by desired framerate for realtime)
Advanced Graphics – Real-time Ray Tracing 4 Introduction
Advanced Graphics – Real-time Ray Tracing 5 Introduction Reality Check Performance is now OK, but we’re not quite ready to render a game world.
Advanced Graphics – Real-time Ray Tracing 6 Introduction
Today’s Agenda: ▪ Introduction ▪ Ray Distributions ▪ The Top-level BVH ▪ Real-time Ray Tracing ▪ Assignment 2
Advanced Graphics – Real-time Ray Tracing 8 Ray Distributions Cost of ray tracing: Dominated by memory access cost. ▪ Ray data ▪ Node data ▪ Triangle data ▪ Material data (incl. textures)
Advanced Graphics – Real-time Ray Tracing 9 Ray Distributions Primary rays: For a tile of pixels, these are organized in a narrow frustum. All rays share a common origin.
Advanced Graphics – Real-time Ray Tracing 10 Ray Distributions Shadow rays: For point lights, shadow rays also tend to travel close together. When traced from the light source, they too have a common origin.
Advanced Graphics – Real-time Ray Tracing 11 Ray Distributions Secondary rays: Reflected and refracted rays tend to diverge significantly.
Advanced Graphics – Real-time Ray Tracing 12 Ray Distributions Coherence Primary rays and shadow rays for point lights are coherent : ▪ they tend to intersect the same primitives; ▪ 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.
Advanced Graphics – Real-time Ray Tracing 13 Ray Distributions 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
Advanced Graphics – Real-time Ray Tracing 14 Ray Distributions 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
Advanced Graphics – Real-time Ray Tracing 15 Ray Distributions Coherent Ray Tracing Ray packet traversal: ▪ intersect four rays with a single BVH node; ▪ if any ray in the packet intersects the node, we traverse it; ▪ if the node is a leaf node, we intersect the four rays with each primitive in the leaf. Masking: ▪ We maintain an ‘active’ mask for disabling rays that do not intersect a node.
Advanced Graphics – Real-time Ray Tracing 16 Ray Distributions 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 ); } }
Advanced Graphics – Real-time Ray Tracing 17 Ray Distributions Coherent Ray Tracing Results: ▪ for coherent packets, memory traffic is reduced; ▪ overall performance is improved by ~2.3x. Overhead: ▪ if only a single ray requires traversal or intersection, all four rays perform this operation.
Advanced Graphics – Real-time Ray Tracing 18 Ray Distributions Large Packets* Cost of memory access can be amortized over more rays by using larger packets. Note that a naïve 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
Advanced Graphics – Real-time Ray Tracing 19 Ray Distributions BVHNode::Traverse( RayPacket rp, int first ) Large Packets { if (!Intersects( rp[first )) // 1 Algorithm: { if (!Intersects( rp.frustum )) 1. Early hit test: test first active ray against AABB return; // 2 FindFirstActive( rp, ++first ); // 3 2. Early miss test: test AABB against frustum } 3. Brute force test: test all rays until a hit is if (first < rp.rayCount) found. { This step yields a new first active ray index. if (isleaf()) { IntersectPrimitives( rp ); } else { left.Traverse( rp, first ); right.Traverse( rp, first ); } } }
Advanced Graphics – Real-time Ray Tracing 20 Ray Distributions BVHNode::Traverse( RayPacket rp, int first ) Large Packets { if (!Intersects( rp[first )) // 1 Details: { if (!Intersects( rp.frustum )) return; // 2 ▪ Constructing the frustum FindFirstActive( rp, ++first ); // 3 ▪ Ray order & overhead } if (first < rp.rayCount) ▪ First / last { if (isleaf()) ▪ Optimizations: recursion, SIMD { IntersectPrimitives( rp ); } else { left.Traverse( rp, first ); right.Traverse( rp, first ); } } }
Advanced Graphics – Real-time Ray Tracing 21 Ray Distributions Frustum Construction 𝑞 1 Method 1, for primary rays: 𝑞 0 Planes are easily defined using the corner rays: 𝑂 1 = (𝑞 0 −𝐹) × (𝑞 1 − 𝑞 0 ) , 𝑒 1 = 𝑂 1 ∙ 𝐹 𝐹 𝑂 2 = (𝑞 1 −𝐹) × (𝑞 2 − 𝑞 1 ) , 𝑒 2 = 𝑂 2 ∙ 𝐹 𝑂 3 = (𝑞 2 −𝐹) × (𝑞 3 − 𝑞 2 ) , 𝑒 3 = 𝑂 3 ∙ 𝐹 𝑂 4 = (𝑞 3 −𝐹) × (𝑞 0 − 𝑞 3 ) , 𝑒 4 = 𝑂 4 ∙ 𝐹 𝑞 2 Note: for secondary rays, we will not have a common origin, nor corner rays. 𝑞 3
Advanced Graphics – Real-time Ray Tracing 22 Ray Distributions 1 𝑙 Frustum Construction Method 2, for shadow rays: 1. Determine dominant axis and direction: 𝑂 𝐸 𝑗 , chose axis 𝐸 𝑡 = σ 𝑗=0 𝑙 as the largest component of 𝐸 𝑡 , ො 𝑣 and ො 𝑤 are the other axes. 𝑣 ො 2. Construct a plane 𝑄 orthogonal to 𝑙 3. Calculate intersection coordinates 𝑣, 𝑤 of the rays with P 4. Determine 𝑣 𝑛𝑗𝑜 , 𝑣 𝑛𝑏𝑦 and 𝑤 𝑛𝑗𝑜 , 𝑤 𝑛𝑏𝑦 5. Corner rays are now: 𝑣 𝑛𝑗𝑜 , 𝑤 𝑛𝑗𝑜 𝑣 𝑛𝑏𝑦 , 𝑤 𝑛𝑗𝑜 𝑣 𝑛𝑏𝑦 , 𝑤 𝑛𝑏𝑦 (𝑣 𝑛𝑗𝑜 , 𝑤 𝑛𝑏𝑦 ) Note: this still requires a common origin.
Advanced Graphics – Real-time Ray Tracing 23 Ray Distributions 𝑙 Frustum Construction Method 3, for generic rays: 1. Construct two planes: 𝑔𝑏𝑠 , orthogonal to 𝑄 𝑙 , at location 𝑙 𝑔𝑏𝑠 which is obtained from the scene AABB; 𝑜𝑓𝑏𝑠 , orthogonal to 𝑄 𝑙 , at location 𝑙 𝑜𝑓𝑏𝑠 , which is obtained from the AABB over the ray origins. 2. Calculate intersection coordinates 𝑣 𝑔𝑏𝑠 , 𝑤 𝑔𝑏𝑠 𝑙 𝑜𝑓𝑏𝑠 𝑙 𝑔𝑏𝑠 and 𝑣 𝑜𝑓𝑏𝑠 , 𝑤 𝑜𝑓𝑏𝑠 of the rays with 𝑄 𝑔𝑏𝑠 and 𝑄 𝑜𝑓𝑏𝑠 . 𝑔𝑏𝑠 , 𝑤 𝑛𝑗𝑜 𝑔𝑏𝑠 . 𝑜𝑓𝑏𝑠 and 𝑣 𝑛𝑗𝑜 𝑔𝑏𝑠 , 𝑣 𝑛𝑏𝑦 𝑔𝑏𝑠 , 𝑣 𝑛𝑏𝑦 𝑜𝑓𝑏𝑠 , 𝑣 𝑛𝑏𝑦 𝑜𝑓𝑏𝑠 , 𝑣 𝑛𝑏𝑦 𝑜𝑓𝑏𝑠 , 𝑤 𝑛𝑗𝑜 3. Determine 𝑣 𝑛𝑗𝑜 4. Corner rays are now defined as 𝑔𝑏𝑠 − 𝑣 𝑛𝑗𝑜 𝑜𝑓𝑏𝑠 , 𝑔𝑏𝑠 , 𝑤 𝑛𝑗𝑜 𝑜𝑓𝑏𝑠 , 𝑤 𝑛𝑗𝑜 𝑣 𝑛𝑗𝑜 𝑔𝑏𝑠 , 𝑤 𝑛𝑗𝑜 𝑔𝑏𝑠 − 𝑣 𝑛𝑏𝑦 𝑜𝑓𝑏𝑠 , 𝑜𝑓𝑏𝑠 , 𝑤 𝑛𝑗𝑜 𝑣 𝑛𝑏𝑦 𝑔𝑏𝑠 , 𝑤 𝑛𝑏𝑦 𝑜𝑓𝑏𝑠 , 𝑔𝑏𝑠 𝑜𝑓𝑏𝑠 , 𝑤 𝑛𝑏𝑦 𝑣 𝑛𝑏𝑦 − 𝑣 𝑛𝑏𝑦 𝑔𝑏𝑠 , 𝑤 𝑛𝑏𝑦 𝑔𝑏𝑠 𝑜𝑓𝑏𝑠 , 𝑤 𝑛𝑏𝑦 𝑜𝑓𝑏𝑠 ) . 𝑣 𝑛𝑗𝑜 − (𝑣 𝑛𝑗𝑜
Advanced Graphics – Real-time Ray Tracing 24 Ray Distributions Ray Order 0 7 The order of the rays in a packet is important. 8 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. 63
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