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Lecture 15 - Bits & Pieces Welcome! , = (, ) - - PowerPoint PPT Presentation

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INFOMAGR Advanced Graphics Jacco Bikker - November 2019 - February 2020 Lecture 15 - Bits & Pieces Welcome! , = (, ) , + , , ,

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SLIDE 1

𝑱 π’š, π’šβ€² = 𝒉(π’š, π’šβ€²) 𝝑 π’š, π’šβ€² + ΰΆ±

𝑻

𝝇 π’š, π’šβ€², π’šβ€²β€² 𝑱 π’šβ€², π’šβ€²β€² π’†π’šβ€²β€²

INFOMAGR – Advanced Graphics

Jacco Bikker - November 2019 - February 2020

Lecture 15 - β€œBits & Pieces”

Welcome!

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SLIDE 2

Today’s Agenda:

β–ͺ On Offsetting Shadows and Reflections β–ͺ Consistent Normal Interpolation β–ͺ Packing Normals β–ͺ Spatial Splits in BVHs β–ͺ Research Directions

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SLIDE 3

You have been told…

…To offset your shadow rays by β€˜epsilon times R or L’. β–ͺ How should be chose epsilon? β–ͺ Is epsilon the same everywhere? β–ͺ Is this always sufficient?

Offsets

Advanced Graphics – Bits & Pieces 3 p πœ•π‘ πœ•π‘— 𝑂

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SLIDE 4

You have been told…

Geek solution: use fixed point numbers. This time: epsilon = 1.

Offsets

Advanced Graphics – Bits & Pieces 4 p πœ•π‘ πœ•π‘— 𝑂

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SLIDE 5

SafeOrigin

When R (or L) is almost parallel to the surface, the epsilon offset fails. Alternative: 𝑃 += cos πœ„3 𝑓 𝑆 + 1 βˆ’ cos πœ„3 𝑓 𝑂

Offsets

Advanced Graphics – Bits & Pieces 5 p πœ•π‘ πœ•π‘— 𝑂

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SLIDE 6

SafeOrigin

When R (or L) is almost parallel to the surface, the epsilon offset fails. Alternative: 𝑃 += cos πœ„3 βˆ™ 𝑆 + 1 βˆ’ cos πœ„3 βˆ™ 𝑂

Offsets

Advanced Graphics – Bits & Pieces 6 p πœ•π‘ πœ•π‘— 𝑂

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SLIDE 7

Second Opinion

Ray Tracing Gems, chapter 6: A Fast and Robust Method for Avoiding Self-Intersection. Carsten WΓ€chter and Nikolaus Binder, 2019.

Offsets

Advanced Graphics – Bits & Pieces 7

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SLIDE 8

Today’s Agenda:

β–ͺ On Offsetting Shadows and Reflections β–ͺ Consistent Normal Interpolation β–ͺ Packing Normals β–ͺ Spatial Splits in BVHs β–ͺ Research Directions

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SLIDE 9

The Problem

Vertex normal: the average of the normals of all polygons connected to the vertex. Generating / updating vertex normals in O(N): β–ͺ set each vertex normal to (0,0,0); β–ͺ loop over polygons; β–ͺ add normal of each polygon to each polygon vertex; β–ͺ normalize all vertex normals.

Normals

Advanced Graphics – Bits & Pieces 9

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SLIDE 10

The Problem

Vertex normal: the average of the normals of all polygons connected to the vertex. Using vertex normals: β–ͺ MΓΆller-Trumbore yields β€˜u,v’ coordinates: these are barycentric coordinates; β–ͺ calculate π‘₯ = 1 – (𝑣 + 𝑀); β–ͺ now 𝑂𝑗 = π‘₯ βˆ— 𝑂0 + 𝑣 βˆ— 𝑂1 + 𝑀 βˆ— 𝑂2. Mind the side! Advanced Graphics – Bits & Pieces 10

Normals

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SLIDE 11

The Problem

Vertex normal: the average of the normals of all polygons connected to the vertex. For grazing directions, the reflection may go into the surface. Now what? β–ͺ Use geometric normal instead of interpolated normal? β–ͺ Clamp dot between R and N to 0? β–ͺ Just return black? Advanced Graphics – Bits & Pieces 11

Normals

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SLIDE 12

Advanced Graphics – Bits & Pieces 12

Normals

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SLIDE 13

Advanced Graphics – Bits & Pieces 13

Normals

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SLIDE 14

Consistent Normal Interpolation*

Can we come up with an interpolated normal π‘œπ‘‘ that behaves properly? - Requirements: β–ͺ It is smooth β–ͺ Reflections in π‘œπ‘‘ point away from the surface β–ͺ If all vertex normals are equal to π‘œ, π‘œπ‘‘ = π‘œ β–ͺ If 𝑒𝑝𝑒 𝑗, π‘œ = 1, π‘œπ‘‘ = π‘œπ‘ž It turns out that this is indeed possible. The paper outlines how to calculate, for a given 𝑗, a vector 𝑠 that satisfies the constraints. π‘œπ‘‘ now is simply π‘œπ‘π‘ π‘›π‘π‘šπ‘—π‘¨π‘“ 𝑗 + 𝑠 .

*: Reshetov et al., Consistent Normal Interpolation. ACM Transactions on Graphics, 2010.

Advanced Graphics – Bits & Pieces 14

Normals

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SLIDE 15

Advanced Graphics – Bits & Pieces 15

Normals

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SLIDE 16

Advanced Graphics – Bits & Pieces 16

Normals

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SLIDE 17

Advanced Graphics – Bits & Pieces 17

Normals

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SLIDE 18

Advanced Graphics – Bits & Pieces 18

Normals

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SLIDE 19

Normal Mapping

A normal map can be used to modify normals. Advanced Graphics – Bits & Pieces 19

Normals

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SLIDE 20

Normal Mapping

A normal map can be used to modify normals. This is typically done in tangent space. Problem: the orientation of tangent space matters. We need to align π‘ˆ and 𝐢 with the texture, in other words: it needs to be based on the U and V vectors over the surface. This is non-

  • trivial. For a derivation of the calculation of

T and B, see: learnopengl.com/Advanced-Lighting/Normal-Mapping Advanced Graphics – Bits & Pieces 20

Normals

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SLIDE 21

What if the normal sends you into the surface

Advanced Graphics – Bits & Pieces 21

Normals

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SLIDE 22

What if the normal sends you into the surface

Advanced Graphics – Bits & Pieces 22

Normals

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SLIDE 23

What if the normal sends you into the surface

Microfacet-based Normal Mapping for Robust Monte Carlo Path Tracing. SchΓΌssler et al., 2017.

Advanced Graphics – Bits & Pieces 23

Normals

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SLIDE 24

Today’s Agenda:

β–ͺ On Offsetting Shadows and Reflections β–ͺ Consistent Normal Interpolation β–ͺ Packing Normals β–ͺ Spatial Splits in BVHs β–ͺ Research Directions

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SLIDE 25

Efficiently Storing Normals

A float color pixel contains r, g and b. Wouldn’t it be convenient if the fourth component could store the normal? βž” Can we store a normal accurately in 32 bits? Observation: For a normal, we need two components (plus a sign). βž” Can we store the two components in 16 bits each?

Packing

Advanced Graphics – Bits & Pieces 25

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SLIDE 26

Efficiently Storing Normals

For an extensive study on this topic, see: aras-p.info/texts/CompactNormalStorage.html Bottom line: We can encode a normal in 32-bit, and the precision will be excellent: expect approximately four digits of precision. Pack:

uint PackNormal( float3 N ) { float f = 65535.0f / sqrtf( 8.0f * N.z + 8.0f ); return (uint)(N.x * f + 32767.0f) + ((uint)(N.y * f + 32767.0f) << 16); }

Packing

Advanced Graphics – Bits & Pieces 26

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SLIDE 27

Efficiently Storing Normals

For an extensive study on this topic, see: aras-p.info/texts/CompactNormalStorage.html Bottom line: We can encode a normal in 32-bit, and the precision will be excellent: expect approximately four digits of precision. Unpack:

float3 UnpackNormal( uint p ) { float4 nn = make_float4( (float)(p & 65535) * (2.f / 65535.f), (float)(p >> 16) * (2.f / 65535.f), 0, 0 ); nn += make_float4( -1, -1, 1, -1 ); float l = dot( make_float3( nn.x, nn.y, nn.z ), make_float3( -nn.x, -nn.y, -nn.w ) ); nn.z = l, l = sqrtf( l ), nn.x *= l, nn.y *= l; return make_float3( nn ) * 2.0f + make_float3( 0, 0, -1 ); }

Packing

Advanced Graphics – Bits & Pieces 27

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SLIDE 28

Today’s Agenda:

β–ͺ On Offsetting Shadows and Reflections β–ͺ Consistent Normal Interpolation β–ͺ Packing Normals β–ͺ Spatial Splits in BVHs β–ͺ Research Directions

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SLIDE 29

Splitting

Problematic Large Polygons

Large polygons lead to poor BVHs. (far more common than you’d think) Advanced Graphics – Bits & Pieces 29

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SLIDE 30

Splitting

Problematic Large Polygons

Large polygons lead to poor BVHs. Using the spatial splits in kD-trees, this is far less of an issue: The triangle will simply be assigned to each subspace. Advanced Graphics – Bits & Pieces 30

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SLIDE 31

Splitting

Problematic Large Polygons

Large polygons lead to poor BVHs. Using the spatial splits in kD-trees, this is far less of an issue: The triangle will simply be assigned to each subspace. Solution 1: split large polygons*. Observations:

  • 1. A polygon can safely reside in multiple leafs;
  • 2. The bounds of a leaf do not have to include the

entire polygon.

*: Early Split Clipping for Bounding Volume Hierarchies, Ernst & Greiner, 2007

Advanced Graphics – Bits & Pieces 31

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SLIDE 32

Splitting

Early Split Clipping

Observations:

  • 1. A polygon can safely reside in multiple leafs;
  • 2. The bounds of a leaf do not have to include the

entire polygon.

  • 3. BVH construction only uses primitive bounding

boxes. Algorithm: Prior to BVH construction, we recursively subdivide any polygon with a surface area that exceeds a certain threshold.

Issues:

β–ͺ Threshold parameter β–ͺ Individual polygons are split, regardless of surrounding geometry β–ͺ Primitives may end up multiple times in the same leaf

(some of these issues are resolved in: The Edge Volume Heuristic - Robust Triangle Subdivision for Improved BVH Performance, Dammertz & Keller, 2008)

Advanced Graphics – Bits & Pieces 32

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SLIDE 33

Splitting

Spatial Splits for BVHs

Observation: spatial splits are not limited to kD-trees. But: spatial splits tend to increase the cost of a split. Idea:

  • 1. Determine cost of optimal object partition;
  • 2. Determine cost of optimal spatial split;
  • 3. Apply spatial split if cost is lower than object partition*.

*: Spatial Splits in Bounding Volume Hierarchies, Stich et al., 2009

π·π‘‘π‘žπ‘šπ‘—π‘’ = π΅π‘šπ‘“π‘”π‘’ βˆ— π‘‚π‘šπ‘“π‘”π‘’ + π΅π‘ π‘—π‘•β„Žπ‘’ βˆ— π‘‚π‘ π‘—π‘•β„Žπ‘’ < 𝐡 βˆ— 𝑂 Advanced Graphics – Bits & Pieces 33

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SLIDE 34

Splitting

State of the Art: SBVH

Summary: high quality bounding volume hierarchies can be

  • btained by combining the surface area heuristic and spatial splits.

Compared to a regular SAH BVH, spatial splits improve the BVH by ~25% (see paper for scenes and figures). Advanced Graphics – Bits & Pieces 34

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SLIDE 35

Better BVHs

Advanced Graphics – Bits & Pieces 35

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SLIDE 36

Better BVHs

Advanced Graphics – Bits & Pieces 36

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SLIDE 37

BVH

Bounding Volume Hierarchies – Final Words

Materials: SAH guided spatial split partitioning for fast BVH construction. Ganestam and Doggett, 2016. Fast Parallel Construction of High-Quality Bounding Volume Hierarchies. Karras and Aila, 2013. Efficient Incoherent Ray Traversal on GPUs Through Compressed Wide BVHs. Ylitie et al., 2017. Tree Rotations for Improving Bounding Volume Hierarchies. Kensler, 2008. Improved Two-Level BVHs using Partial Re-Braiding. Benthin et al., 2017. Advanced Graphics – Bits & Pieces 37

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SLIDE 38

Today’s Agenda:

β–ͺ On Offsetting Shadows and Reflections β–ͺ Consistent Normal Interpolation β–ͺ Packing Normals β–ͺ Spatial Splits in BVHs β–ͺ Research Directions

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SLIDE 39

Materials

Future Work

Advanced Graphics – Bits & Pieces 40

Other resources: Implementing the Disney BSDF schuttejoe.github.io/post/disneybsdf Efficient Rendering of Layered Materials using an Atomic Decomposition with Statistical Operators. Belcour, 2018. Eric Heitz’s Research Page: eheitzresearch.wordpress.com/research (all his work is good)

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SLIDE 40

Spectral Rendering

Future Work

Advanced Graphics – Bits & Pieces 41

Other resources: Hero Wavelength Spectral Sampling. Wilie et al., 2014. Physically Meaningful Rendering using Tristimulus Colours. Meng et al., 2015.

  • PBRT. Pharr et al., 2004-2018.

https://www.pbrt.org Mitsuba Renderer. W. Jakob, 2014. https://www.mitsuba-renderer.org

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SLIDE 41

Participating Media

Future Work

Advanced Graphics – Bits & Pieces 42

Other resources: Importance Sampling Techniques for Path Tracing in Participating Media. Kulla and Fajardo, 2014. Area Light Equi-Angular Sampling on ShaderToy: https://ww.shadertoy.com/view/ldXGzS

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SLIDE 42

Light Transport

Future Work

Advanced Graphics – Bits & Pieces 43

Other resources: The Rendering Equation. James T. Kajiya, 1986. Bidirectional Path Tracing. Michal Vlnas, 2018 (student paper). Global Illumination using Photon Maps. Jensen, 1996. Progressive Photon Mapping. Hachisuka et al., 2008. (article on) Vertex Connection and Merging, Georgev et al., 2012. https://schuttejoe.github.io/post/vertexcon nectionandmerging

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SLIDE 43

Primitives

Future Work

Advanced Graphics – Bits & Pieces 44

Other resources: Direct Ray Tracing of Smoothed and Displacement Mapped Triangles. Smits et al., 2000. Direct Ray Tracing of Phong Tessellation. Ogaki and Tokuyoshi, 2011. Two-Level Ray Tracing with Reordering for Highly Complex Scenes. Hanika et al., 2010.

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SLIDE 44

Production

Future Work

Advanced Graphics – Bits & Pieces 45

Other resources: The Iray Light Transport Simulation and Rendering System. Keller et al., 2017. The Design and Evolution of Disney’s Hyperion Renderer. Burley et al., 2018. Manuka: A batch-shading architecture for spectral path tracing in movie production. Fascione et al., 2018. Mitsuba 2: A Retargetable Forward and Inverse Renderer. Nimier-David, 2019.

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SLIDE 45

Production

Future Work

Advanced Graphics – Bits & Pieces 46

Other resources: OptiX: A General Purpose Ray Tracing

  • Engine. Parker et al., 2010.

REAL-TIME RAYTRACING WITH NVIDIA RTX. Stich, 2018. (not a lot of research so far…)

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SLIDE 46

Massive Scenes

Future Work

Advanced Graphics – Bits & Pieces 47

Moana Island scene. Heather Pritchett & Rasmus Tamstorf, 2016. ~15 billion primitives.

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SLIDE 47

Today’s Agenda:

β–ͺ On Offsetting Shadows and Reflections β–ͺ Consistent Normal Interpolation β–ͺ Packing Normals β–ͺ Spatial Splits in BVHs β–ͺ Research Directions

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SLIDE 48

Exam Questions

In path tracing, we can reduce variance by using cosine weighted sampling of the hemisphere, rather than uniform sampling, for diffuse surfaces. a) Why does this reduce variance? b) When using cosine weighted sampling, the result remains unbiased. What does unbiased mean? Advanced Graphics – Bits & Pieces 49

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SLIDE 49

Exam Questions

An exam can be seen as a Monte-Carlo process. Explain why. Advanced Graphics – Bits & Pieces 50

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SLIDE 50

Exam Questions

Advanced Graphics – Bits & Pieces 51 A scene is illuminated by a single double-sided square light souce. Two algorithms are used to sample the light source: the first picks a random point on a random side of the light source, while the second algorithm only picks random points on the side of the light source facing point 𝒒. a) Write down the Monte-Carlo integrator that estimates the illumination on point 𝒒 using the first algorithm. b) Write down the Monte-Carlo integrator that estimates the illumination on point 𝒒 using the second algorithm. Note: both methods should obviously produce the same answer,

  • n averageβ„’.
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SLIDE 51

INFOMAGR – Advanced Graphics

Jacco Bikker - November 2019 – February 2020

END of β€œBits & Pieces”

next lecture: β€œBig Picture”