Advanced CG Topics 3 of 8: Ray Tracing...

Computing & Information SciencesKansas State University

CG Basics 5 of 8: OpenGL Primer 2

CIS 636/736: (Introduction to) Computer Graphics

William H. Hsu

Department of Computing and Information Sciences, KSU

KSOL course pages: http://snipurl.com/1y5gc

Course web site: http://www.kddresearch.org/Courses/CIS636

Instructor home page: http://www.cis.ksu.edu/~bhsu

Readings:

All slides from SIGGRAPH 2000 tutorial on OpenGL, Shreiner, Angel, Shreiner: http://www.cs.unm.edu/~angel/SIGGRAPH/

Sections 2.6, 3.1, 20.3 – 20.13, Eberly 2e – see http://snurl.com/1ye72

NeHe tutorials: 6 – 10, http://nehe.gamedev.net

Article: http://www.kuro5hin.org/story/2003/10/28/9853/1617

CIS 736Computer Graphics

Advanced CG Topics 3 of 8:Ray Tracing Topics

Lecture Outline

Four More Short OpenGL Tutorials from SIGGRAPH 2000

Vicki Shreiner: Animation and Depth Buffering Double buffering

Illumination: light positioning, light models, attenuation

Material properties

Animation basics in OpenGL

Vicki Shreiner: Imaging and Raster Primitives

Ed Angel: Texture Mapping

Dave Shreiner: Advanced Topics Display lists and vertex arrays

Accumulation buffer

Stencil buffering

Fragment programs (to be concluded in Tutorial 3)

Ray Tracing

What is it? Why use it? Basics Advanced topics References

Ray-Tracing: Why Use It?

Simulate rays of light Produces natural lighting effects

• Reflection • Depth of Field

• Refraction • Motion Blur

• Soft Shadows • Caustics

Ray-Tracing: Why Use It?

Hard to simulate effects with rasterization techniques (OpenGL) Rasterizers require many passes Ray-tracing easier to implement

Ray-Tracing: Who Uses It?

Entertainment (Movies, Commercials) Games pre-production Simulation

Ray-Tracing: History

Decartes, 1637 A.D. - analysis of rainbow Arthur Appel, 1968 - used for lighting 3D models Turner Whitted, 1980 - “An Improved Illumination Model for

Shaded Display” really kicked everyone off. 1980-now - Lots of research

The Basics

Generating Rays Intersecting Rays with the Scene Lighting Shadowing Reflections

The Basic Idea

Simulate light rays from light source to eye

Reflected ray Incident ray

Eye Light

Surface

“Forward” Ray-Tracing

Trace rays from light Lots of work for little return

LightImagePlane

Object

Light Rays

“Backward” Ray-Tracing

Trace rays from eye instead Do work where it matters

This is what most people mean by “ray tracing”.

ImagePlane

Object

Ray Parametric form

Ray expressed as function of a single parameter (“t”)

<x, y, z> = <xo, yo, zo> + t * <xd, yd, zd>

<x, y, z> = ro + trd

t = 0.0

t = 1.0

t = 2.0

t = 2.5

Generating Rays

Trace a ray for each pixel in the image plane

tan(fovx) * 2

(Looking down from the top)

ImagePlane

Generating Rays

(tan(fovx)* 2) / m

(tan(fovy)* 2) / nEye

ImagePlane

(Looking fromthe side)

Generating Rays

renderImage(){ for each pixel i, j in the image

ray.setStart(0, 0, 0); // r

ray.setDir ((.5 + i) * tan(fovx)* 2 / m, (.5 + j) * tan(fovy)* 2 / n,

1.0); // r

ray.normalize(); image[i][j] = rayTrace(ray); }

Triangle Intersection

Want to know: at what point (p) does ray intersect triangle? Compute lighting, reflected rays, shadowing from that point

d <?, ?, ?>(t = ???)

Step 1 : Intersect with plane( Ax + By + Cz + D = 0 )

Plane normal n = <A, B, C>

p = -(n. ro + D) / (n. rd )

Step 2 : Check against triangle edges

Plug p into (p. Ei + di ) for each edge

if signs are all positive or negative, point is inside triangle!

E0Ei = ViVi+1 x n (plane A, B, C)di = -A.N (plane D)

Triangle Normals

Could use plane normals (flat shading) Better to interpolate from vertices

n = anV0 + bnV1 + cnV2

Find areas

area(V0V1V2)

Finding Intersections

Check all triangles, keep the closest intersection

hitObject(ray) { for each triangle in scene does ray intersect triangle? if(intersected and was closer) save that intersection if(intersected) return intersection point and normal}

Lighting

We’ll use triangles for lights Build complex shapes from triangles

Some lighting terms

Surface

Lighting

Use modified Phong lighting similar to OpenGL simulates rough and shiny surfaces

for each light In = IambientKambient +

IdiffuseKdiffuse (L.N) + IspecularKspecular (R.V)n

Ambient Light

Iambient Simulates the indirect lighting in a scene.

Diffuse Light

Idiffuse simulates direct lighting on a rough surface

Viewer independent Paper, rough wood, brick, etc...

Specular Light

Ispecular simulates direct lighting on a smooth surface

Viewer dependent Plastic, metal, polished wood, etc...

Shadow Test

Check against other objects to see if point is shadowed

ShadowingObject

Reflection

Angle of incidence = angle of reflection ( θ I = θ R )

I, R, N lie in the same plane

R = I - 2 (N . I) N

I θ I θ R

Putting It All Together

Recursive ray evaluation

rayTrace(ray) { hitObject(ray, p, n, triangle); color = object color; if(object is light) return(color); else return(lighting(p, n, color));}

Calculating surface color

lighting(point) { color = ambient color; for each light if(hitObject(shadow ray)) color += lightcolor *

dot(shadow ray, n); color += rayTrace(reflection) * pow(dot(reflection, ray), shininess); return(color);}

The main program

main() { triangles = readTriangles(); image = renderImage(triangles); writeImage(image);}

This is A Good Start

Lighting, Shadows, Reflection are enough to make some compelling images

Want better lighting and objects Need more speed

More Quality, More Speed

Better Lighting + Forward Tracing Texture Mapping Modeling Techniques Motion Blur, Depth of Field, Blurry Reflection/Refraction

Distributed Ray-Tracing

Improving Image Quality Acceleration Techniques

Refraction

Keep track of medium (air, glass, etc) Need index of refraction (η ) Need solid objects

I θ I

sin(θ I) η 1

sin(θ T) η 2

=Medium 1(e.g. air)

Medium 2(e.g. water)

Refraction

Improved Light Model

Cook & Torrance Metals have different color at angle Oblique reflections leak around corners Based on a microfacet model

Using “Forward” Ray Tracing

Backward tracing doesn’t handle indirect lighting too well To get caustics, trace forward and store results in texture map.

Using “Forward” Ray Tracing

Texture Mapping

Use texture map to add surface detail Think of it like texturing in OpenGL

Diffuse, Specular colors Shininess value Bump map Transparency value

Texture Mapping

Parametric Surfaces

More expressive than triangle Intersection is probably slower u and v on surface can be used as texture s,t

Constructive Solid Geometry

Union, Subtraction, Intersection of solid objects

Have to keep track of intersections

Hierarchical Transformation

Scene made of parts Each part made of smaller parts Each smaller part has transformation linking it to larger part Transformation can be changing over time - Animation

Distributed Ray Tracing

Average multiple rays instead of just one ray Use for both shadows, reflections, transmission (refraction) Use for motion blur Use for depth of field

One ray is not enough (jaggies) Can use multiple rays per pixel - supersampling Can use a few samples, continue if they’re very different -

adaptive supersampling Texture interpolation & filtering

Acceleration

1280x1024 image with 10 rays/pixel 1000 objects (triangle, CSG, NURBS) 3 levels recursion

39321600000 intersection tests

100000 tests/second -> 109 days!

Must use an acceleration method!

Bounding volumes

Use simple shape for quick test, keep a hierarchy

Space Subdivision

Break your space into pieces Search the structure linearly

Parallel Processing

You can always throw more processors at it.

Really Advanced Stuff

Error analysis Hybrid radiosity/ray-tracing Metropolis Light Transport Memory-Coherent Ray-tracing

References

Introduction to Ray-Tracing, Glassner et al, 1989, 0-12-286160-4

Advanced Animation and Rendering Techniques, Watt & Watt, 1992, 0-201-54412-1

Computer Graphics: Image Synthesis, Joy et al, 1988, 0-8186-8854-4

SIGGRAPH Proceedings (All)

Summary

Four More Short OpenGL Tutorials from SIGGRAPH 2000

Vicki Shreiner: Animation and Depth Buffering Double buffering

Illumination: light positioning, light models, attenuation

Material properties

Animation basics in OpenGL

Vicki Schreiner: Imaging and Raster Primitives

Ed Angel: Texture Mapping in OpenGL

Dave Shreiner: Advanced Topics Display lists and vertex arrays

Stencil buffering, fragment programs (to be continued)

Terminology

Double Buffering

Lighting

Illumination Equation – describes light in scene

Ambient light – catch-all term for whole scene, all lights

Diffuse reflectance – omnidirectional, from matte surfaces

Specular reflectance – unidirectional, for highlights: shiny surfaces

Attenuation – how quickly light drops off as function of distance

Pixel and Fragment Programs (“Pixel Shaders”)

Vertex Shaders

Texture Maps

Other Mappings Discussed in Course

Bump aka displacement – perturb surface normal, calculate lighting

Reflection and transparency

Shadow

Environment

Next: Polygons, OpenGL Tutorial 3

Dave Shreiner: Advanced Topics (concluded)

Advanced Primitives: Cubic Curves, Bicubic Surfaces

Advanced CG Topics 3 of 8: Ray Tracing...

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