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CS 445 / 645: Introductory Computer Graphics

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CS 445 / 645: Introductory Computer Graphics

Light

- Learn more about Paul Debevec’s research
- http://www.debevec.org/FiatLux/h

- Assignment 3 Due
- Sunday, October 21st at Midnight

- Midterm Exam
- Tuesday, October 23rd
- See web page for reading material
- More review info in class after break

- Lighting Models
- Ambient
- Normals don’t matter

- Lambert/Diffuse
- Angle between surface normal and light

- Phong/Specular
- Surface normal, light, and viewpoint

- Ambient
- Shading Models…

- We now have an illumination model for a point on a surface
- Assuming that our surface is defined as a mesh of polygonal facets, which pointsshould we use?
- Keep in mind:
- It’s a fairly expensive calculation
- Several possible answers, each with different implications for the visual quality of the result

- With polygonal/triangular models:
- Each facet has a constant surface normal
- If the light is directional, the diffuse reflectance is constant across the facet

- The simplest approach, flat shading, calculates illumination at a single point for each polygon:
- If an object really is faceted, is this accurate?

- For specular reflectance, direction to eye varies across the facet

- No:
- For point sources, the direction to light varies across the facet

- We can refine it a bit by evaluating the Phong lighting model at each pixel of each polygon, but the result is still clearly faceted:
- To get smoother-looking surfaceswe introduce vertex normals at eachvertex
- Usually different from facet normal
- Used onlyfor shading
- Think of as a better approximation of therealsurface that the polygons approximate

- Vertex normals may be
- Provided with the model
- Computed from first principles
- Approximated by averaging the normals of the facets that share the vertex

- This is the most common approach
- Perform Phong lighting at the vertices
- Linearly interpolate the resulting colors over faces
- Along edges
- Along scanlines

C1

c1 + t1(c2-c1)

- This is what OpenGL does

C3

C2

c1 + t1(c2-c1) + t3(c1 + t2(c3-c1)- c1 + t1(c2-c1))

c1 + t2(c3-c1)

- Artifacts
- Often appears dull, chalky
- Lacks accurate specular component
- If included, will be averaged over entire polygon

C1

C3

C2

Can’t shade that effect!

- Artifacts
- Mach Banding
- Artifact at discontinuities in intensity or intensity slope

- Mach Banding

C1

C4

C3

C2

Discontinuity in rateof color changeoccurs here

- Phong shading is not the same as Phong lighting, though they are sometimes mixed up
- Phong lighting: the empirical model we’ve been discussing to calculate illumination at a point on a surface
- Phong shading: linearly interpolating the surface normal across the facet, applying the Phong lighting model at every pixel
- Same input as Gouraud shading
- Usually very smooth-looking results:
- But, considerably more expensive

- Linearly interpolate the vertex normals
- Compute lighting equations at each pixel
- Can use specular component

N1

Remember: Normals used in

diffuse and specular terms

Discontinuity in normal’s rate of

change is harder to detect

N4

N3

N2

- Polygonal silhouettes remain

Gouraud Phong

Imageplane

Break up large polygonswith many smaller ones

i

i

i

i

i

i

u

u

u

u

u

u

Z – into the scene

Notice that linear interpolation in screen spacedoes not align with linear interpolation in world space

Perspective Distortion

Break up large polygonswith many smaller ones

Imageplane

Z – into the scene

Notice that linear interpolation in screen spacedoes not align with linear interpolation in world space

i

i

A

Rotate -90oand colorsame point

B

C

B

A

D

D

C

Interpolate betweenAB and BC

Interpolate betweenAB and AD

Vertex B is shared by the two rectangles on the right, but not by the one on the left

C

H

D

The first portion of the scanlineis interpolated between DE and ACThe second portion of the scanlineis interpolated between BC and GHA large discontinuity could arise

B

G

F

E

A

- We’ve glossed over how light really works
- And we will continue to do so…
- One step better
- Global Illumination
- The notion that a point is illuminated by more than light from local lights; it is illuminated by all the emitters and reflectors in the global scene

- Jim Kajiya (Current head of Microsoft Research) developed this in 1986
- I(x, x’) is the total intensity from point x’ to x
- G(x, x’) = 0 when x/x’ are occluded and 1/d2 otherwise (d = distance between x and x’)
- e(x, x’) is the intensity emitted by x’ to x
- r(x, x’,x’’) is the intensity of light reflected from x’’ to x through x’
- S is all points on all surfaces

- The light that hits x from x’ is the direct illumination from x’ and all the light reflected by x’ from all x’’
- To implement:
- Must handle recursion effectively
- Must support diffuse and specular light
- Must model object shadowing

- Cast a ray from the viewer’s eye through each pixel
- Compute intersection of this ray with objects from scene
- Closest intersecting object determines color

- Cast a ray from intersected object to light sources and determine shadow/lighting conditions
- Also spawn secondary rays
- Reflection rays and refraction rays
- Use surface normal as guide (angle of incidence equals angle of reflection)
- If another object is hit, determine the light it illuminates by recursing through ray tracing

- Stop recursing when:
- ray fails to intersect an object
- user-specified maximum depth is reached
- system runs out of memory

- Common numerical accuracy error
- Spawn secondary ray from intersection point
- Secondary ray intersects another polygon on same object

- Still producing PhD’s after all these years
- Many opportunities to improve efficiency and accuracy of ray tracing
- Reduce the number of rays cast
- Accurately capture shadows caused by non-lights (ray tracing from the light source)
- Expensive to recompute as eyepoint changes

- Ray tracing models specular reflection and refractive transparency, but still uses an ambient term to account for other lighting effects
- Radiosity is the rate at which energy is emitted or reflected by a surface
- By conserving light energy in a volume, these radiosity effects can be traced