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CS 445 / 645: Introductory Computer GraphicsPowerPoint Presentation

CS 445 / 645: Introductory Computer Graphics

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### CS 445 / 645: Introductory Computer Graphics

Light

Fiat Lux

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

Administrivia

- 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 and Shading

- 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…

Applying Illumination

- 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

Applying Illumination

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

Flat Shading

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

Is flat shading realistic for faceted object?

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

Flat Shading 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 the facet

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

Gouraud Shading the facet Does this eliminate the facets?

- 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)

Gouraud Shading the facet

- 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!

Gouraud Shading the facet

- 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 the facet

- 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

Phong Shading the facet

- 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

Perspective Distortion the facet

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 the facet

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 the facet

i

Interpolation dependent on polygon orientationA

Rotate -90oand colorsame point

B

C

B

A

D

D

C

Interpolate betweenAB and BC

Interpolate betweenAB and AD

Problems at Shared Vertices the facet

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

Bad Vertex Averaging the facet

Global Illumination the facet

- 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

The ‘Rendering Equation’ the facet

- 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 ‘Rendering Equation’ the facet

- 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

Recursive Ray Tracing the facet

- 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

Recursive Ray Tracing the facet

- 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

Recursive Ray Tracing the facet

- 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

Recursive Ray Tracing the facet

- 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

Radiosity the facet

- 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

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