Rendering: Reality. Eye acts as pinhole camera. Photons from light hit objects

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1 Basic Ray Tracing

2 Rendering: Reality Eye acts as pinhole camera Photons from light hit objects

3 Rendering: Reality Eye acts as pinhole camera Photons from light hit objects

4 Rendering: Reality Eye acts as pinhole camera Photons from light hit objects Bounce everywhere Extremely few hit eye, form image

5 Rendering: Reality Useful abstraction: virtual image plane

6 Rendering: Reality Pros photorealistic embarrassingly parallel? Cons SLOW for all but extremely trivial scenes

7 Rendering: Ray Tracing Reverse of reality shoot rays through image plane see what they hit

8 Rendering: Ray Tracing Reverse of reality shoot rays through image plane see what they hit reflections? shadows?

9 Rendering: Ray Tracing Reverse of reality shoot rays through image plane see what they hit reflections? shadows? shoot secondary rays

10 Rendering: Ray Tracing Reverse of reality shoot rays through image plane see what they hit reflections? shadows? shoot secondary rays Embarrassingly parallel

11 Ray Tracing is Slow Very true in the past; still true today But real-time ray tracing is coming [Nvidia OptiX]

12 Why Slow? What is the time complexity?

13 Why Slow? What is the time complexity? Naïve algorithm: O(NR) R: number of rays N: number of objects

14 Why Slow? What is the time complexity? Naïve algorithm: O(NR) R: number of rays N: number of objects But rays can be cast in parallel each ray O(N) even faster with good culling

15 Why Slow? Despite being parallel: 1. poor cache coherence nearby rays can hit different geometry

16 Why Slow? Despite being parallel: 1. poor cache coherence nearby rays can hit different geometry 2. unpredictable must shade pixels whose rays hit object may require tracing rays recursively

17 Basic Algorithm For each pixel: shoot ray from camera through pixel find first object it hits if it hit something shade that pixel

18 Basic Algorithm For each pixel: shoot ray from camera through pixel find first object it hits if it hit something shade that pixel maybe shoot secondary rays

19 Shoot Rays From Camera Ray has origin and direction

20 Shoot Rays From Camera Ray has origin and direction Points on ray are the positive span

21 Shoot Rays From Camera Ray has origin and direction Points on ray are the positive span (why positive?)

22 Shoot Rays From Camera How to pick ray? obviously origin is eye

23 Shoot Rays From Camera How to pick ray? obviously origin is eye pick direction to pierce center of pixel

24 Shoot Rays From Camera How to pick ray? obviously origin is eye pick direction to pierce center of pixel

25 Shoot Rays From Camera How to pick ray? obviously origin is eye pick direction to pierce center of pixel Antialiasing: multiple rays/pixel

26 Find First Object Hit By Ray Collision detection: find all values of t where ray hits object boundary Take smallest positive value of t

27 Find First Object Hit By Ray Collision detection: find all values of t where ray hits object boundary Take smallest positive value of t

28 Ray-Plane Collision Detection Plane specified by: point on plane plane normal

29 Ray-Plane Collision Detection Plane specified by: point on plane plane normal

30 Ray-Plane Collision Detection Plane specified by: point on plane plane normal (what if t < 0?)

31 Ray-Plane Collision Detection Plane specified by: point on plane plane normal (what if t < 0?) (what if denominator = 0?)

32 Ray-Triangle Collision Detection First, intersect with triangle s plane Next: is P inside or outside the triangle?

33 Ray-Triangle Collision Detection Normal:

34 Ray-Triangle Collision Detection Normal: Idea: if P inside, must be left of line AB

35 Ray-Triangle Collision Detection Normal: Idea: if P inside, must be left of line AB

36 Ray-Triangle Collision Detection Normal: Idea: if P inside, must be on correct side of lines

37 Ray-Sphere Collision Detection Sphere specified by center radius

38 Ray-Sphere Collision Detection Sphere specified by center radius

39 Ray-Sphere Collision Detection Sphere specified by center radius key idea: can square both sides

40 Ray-Sphere Collision Detection Sphere specified by center radius Quadratic equation!

41 Zero, One, or Two Roots

42 Ray-Box Collision Detection Challenge: ray could hit any of six sides Could do lots of ray-plane and point-inrectangle checks

43 What is Shading? Shading: coloring the pixels What does color depend on?

44 What is Shading? Shading: coloring the pixels What does color depend on? object material incoming light angle of viewer

45 Shading Materials Different materials can behave very differently opaque vs translucent vs transparent shiny vs dull

46 Shading Materials Different materials can behave very differently opaque vs translucent vs transparent shiny vs dull We classify different responses to light into types

47 Emissive Lighting Light generated within material

48 Diffuse Reflection Light comes in, bounces out randomly

49 Diffuse Reflection Light comes in, bounces out randomly Typical for rough unpolished materials View angle doesn t matter

50 Specular Reflection Light reflects perfectly Typical for smooth, polished surfaces

51 General Opaque Materials Lie on diffuse-specular spectrum

52 General Opaque Materials Lie on diffuse-specular spectrum Pure diffuse: Lambertian idealized material common in CV

53 General Opaque Materials Lie on diffuse-specular spectrum Pure diffuse: Lambertian idealized material common in CV Pure specular: mirror

54 What About Translucent? Subsurface Scattering

55 What About Translucent? Subsurface Scattering Refraction

56 What About Translucent? Subsurface Scattering Refraction Structural Color Not today.

57 The Rendering Equation

58 The Rendering Equation

59 The Rendering Equation BRDF Bidirectional Reflectance Distribution Function (encodes material)

60 Why the Cosine Term? Light at angle hits surface more sparsely Lambert s Cosine Law

61 BRDFs Positive and bidirectional: Captured for different materials, stored in libraries

62 BRDFs Positive and bidirectional: Captured for different materials, stored in libraries More complicated versions exist that account for wavelength, subsurface scattering, transmission, etc etc

63 The Rendering Equation Often too slow for graphics approximate!

64 Local Illumination Simplifying assumptions: ignore everything except: eye, light, and object

65 Local Illumination Simplifying assumptions: ignore everything except eye, light, and object basic version: no shadows, reflections, etc

66 Local Illumination Simplifying assumptions: ignore everything except eye, light, and object basic version: no shadows, reflections, etc but can support basic shadows/reflection

67 Local Illumination Simplifying assumptions: ignore everything except eye, light, and object basic version: no shadows, reflections, etc but can support basic shadows/reflection only point lights only simple (diffuse & specular) materials

68 Global Illumination

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