Computer Graphics Inf4/MSc Computer Graphics Lecture 14 Illumination II – Global Models

Computer Graphics Inf4/MSc

Computer Graphics

Lecture 14

Illumination II – Global Models

Computer Graphics Inf4/MSc

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Global Illumination

• Extends the Local Illumination Model to include:– Reflection (one object in another)– Refraction (Snell’s Law)– Transparency (better model)– Shadows (at point, check each light source)– Antialiasing (usually means supersampling)

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Wireframe view of a test scene.

Orthographic view from above

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Test Scene.

High quality rendering of test scene.

Note :

• Mirror and chrome teapot.• Shadows on floor.• Shiny floor.

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Locally illuminated test scene.

Ambient term only

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Locally illuminated test scene.

Phong shading.

Ambient and Diffuse terms only

Notes :

• Highlight on wall from light is in the wrong place; screen space interpolation.• We cannot illuminate the lights with the light sources – wrong side !

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Locally illuminated test scene.

Phong shading.

Ambient, diffuse andSpecular terms.

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Locally illuminated test scene.

Flat shading.

Note : Mach bands.

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Locally illuminated test scene.

Gouraud shading.

Ambient, diffuse andSpecular terms.

Note: artefacts on wall.

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Solution to Gouraud artefacts.

Gouraud shading.

Re-triangulated mesh.

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Comparison.

Flat Gouraud Phong

Coarser mesh

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Use Local illumination.

• No.

• In our test scene, we can’t represent :– Mirror– Chrome teapot.– Shiny floor– Shadows

with local illumination.

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Kajiya’s Rendering Equation.

S BRDF

xdxxIxxxxxxxgxxI ),(.),,(),().,(),(

Viewer is at point x, looking toward point x.

-I(x,x) determines amount of light arriving at x from x- g(x,x) is a geometry term, = 0 when x is occluded, otherwise = attenuation factor 1/r2 (or 1/(s+k))- (x,x) is the amount of light emitted from x to x.- (x,x,x) is the fraction of light reflected and scattered off x to point x

from point x- The integral S is over all such points (x") on all surfaces.

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Global illumination.

• Two methods :

– View dependent methods.

• Calculate the view from the camera with global illumination.

– Recursive ray-tracing.

– View independent methods.

• Solve lighting for the entire scene.

• Radiosity solution.

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View dependent methods.

• Loop round the pixels…..• Good for lighting effects which have a strong

dependence on view location :– Specular highlights.– Reflections from curved surfaces.

• Only a small number of objects need to be considered at the same time.

• Poor when many objects need to be considered – E.g diffuse interactions (eg. colour bleeding).

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View independent methods.

• Loop round the scene…

• Good when many (all) objects need to be considered at same time.– Diffuse inter-reflections.

• Poor when shading has strong dependence on view location.– Specular reflection.

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Recall : Ray casting.

• Involves projecting an imaginary ray from the centre of projection (the viewers eye) through the centre of each pixel into the scene.

• The first object the ray intersects determines the shade.

Scene

Window

Eyepoint

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Whitted’s algorithm.

• Fire off secondary rays from surface that ray intersects.– Towards Light Source(s) : shadow rays. L (shadow feelers)

– In the reflection direction : reflection rays, R

– In a direction dictated by Snell’s Law : transmitted rays, T

N

L

direction)(Viewer VR

T

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Recursive ray tree.

• Reflection and Transmission Rays spawn other rays.– Shadow rays test only for occlusion.

• The complete set of rays is called a Ray Tree.

Viewpoint

1L

2L

3L

1R

2R

3R1T

2T

Light Source ray determines colour of current object.

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Recursive ray tree.

• Reflection and Transmission Rays spawn other rays.– Shadow rays test only for occlusion.

• The complete set of rays is called a Ray Tree.

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Test Scene.

Ray tree depth 1.

Note only ambient shade on mirror and teapot

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Test Scene.

Ray tree depth 2.

Note only ambient shade on reflection of mirror and teapot.

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Test Scene.

Ray tree depth 3.

Note only ambient shade on reflection of mirror in teapot.

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Test Scene.

Ray tree depth 4.

Note ambient shade on reflection of teapot in reflection of mirror in teapot.

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Test Scene.

Ray tree depth 5.

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Test Scene.

Ray tree depth 6.

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Test Scene.

Ray tree depth 7.

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When to stop ?

• Need to know when to stop the recursion.• Can define a fixed depth.• Hall introduced adaptive tree depth control.

– Calculate maximum contribution of a ray to a pixels final value.

– Multiply contribution of ray’s ancestors down the tree.

– Stop when below some threshold, perhaps stack overflow.

– May miss major contribution this way (culled bright pt)

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Adaptive tree depth control.

Viewpoint

1L

1R

1T0.3

0.2

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Adaptive tree depth control.

Viewpoint

1L

2L

3L

1R

2R

3R1T

2T

0.3 * 0.2

0.2 * 0.2

0.3

0.2

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Global vs. Local illumination.

• In both an object hit by a ray, if lit by a light source, is illuminated by a local illumination model, i.e with specular, diffuse & ambient terms.

• Global: a reflected ray, a shadow feeler, and a transmission ray (if appropriate) are also cast into the scene.

• Phong term only reflects light source.– Need to adjust local illumination terms to normalise total light

values.

– Inconsistent if local and global specular terms used together as local term spreads light source, global term does not.

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Increased reflectivityIn

crea

sed

tran

smis

sivi

tyPhong specular

term is held constant

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Incorrect result.

• Effect of not normalising reflection and transmission – light appears to be created.– Reflection & transmission = 100%

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Problems with Ray-tracing.

• A serious problem with Ray tracing is rays are traced from the eye.– Refraction is not physically correct.

• Shadow rays are cast only to light sources– Lights reflected in mirrors do not cast shadows– Shadows of transparent objects don’t exhibit

refraction.– Still need local illumination for diffuse shading.

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Speeding up Ray Tracing

• Ray tracing is slow, not real-time.

• Use appropriate extents for objects.

• Ray tracing is inherently parallel.

• Use item buffers – z-ordered lists, store closest object per pixel.

• Use light buffer – z-ordered list per light ray used for shadowing.

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Recommended Reading

• Foley at al. Chapter 16, sections 16.11, 16.12 and 16.12.5.

• Introductory text Chapter 14 sections 14.6 and 14.7.

• Most graphics texts cover recursive ray tracing.