CS 445 / 645 Introduction to Computer Graphics

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CS 445 / 645Introduction to Computer Graphics

• Lecture 15
• Shading

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Lighting Review

• Lighting Models
• Ambient
• Normals dont matter
• Lambert/Diffuse
• Angle between surface normal and light
• Phong/Specular
• Surface normal, light, and viewpoint

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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 points should we use?
• Keep in mind
• Its a fairly expensive calculation
• Several possible answers, each with different
  implications for the visual quality of the result

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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. Why?

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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?

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Is flat shading realistic for faceted object?

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

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Flat Shading

• 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 only for shading
• Think of as a better approximation of the real
  surface that the polygons approximate

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Vertex Normals

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

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Gouraud Shading

• 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
• Does this eliminate the facets?

C3
C2
c1 t1(c2-c1) t3(c1 t2(c3-c1)- c1
t1(c2-c1))
c1 t2(c3-c1)
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Gouraud Shading

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

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Gouraud Shading

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

C1
C4
C3
C2
Discontinuity in rateof color changeoccurs here
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Phong Shading

• Phong shading is not the same as Phong lighting,
  though they are sometimes mixed up
• Phong lighting the empirical model weve 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

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Phong Shading

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

N1
N4
Remember Normals used in diffuse and specular
terms Discontinuity in normals rate of change
is harder to detect
N3
N2
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Shortcomings of Shading

• Polygonal silhouettes remain

Gouraud Phong
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Perspective Distortion
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
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Perspective Distortion
Imageplane
Break up large polygonswith many smaller ones
Z into the scene
Notice that linear interpolation in screen
spacedoes not align with linear interpolation in
world space
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Interpolation dependent on polygon orientation
Rotate -90oand colorsame point
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Problems at Shared Vertices
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
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Bad Vertex Averaging
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Shading Models (Direct lighting)

• Flat Shading
• Compute Phong lighting once for entire polygon
• Gouraud Shading
• Compute Phong lighting at the vertices and
  interpolate lighting values across polygon
• Phong Shading
• Compute averaged vertex normals
• Interpolate normals across polygon and perform
  Phong lighting across polygon

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Global Illumination

• Weve 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

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The Rendering Equation

• 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

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The Rendering Equation

• 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

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Shading Models (Indirect lighting)

• Ray Tracing Radiosity

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Recursive Ray Tracing

• Cast a ray from the viewers eye through each
  pixel
• Compute intersection of this ray with objects
  from scene
• Closest intersecting object determines color

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Recursive Ray Tracing

• 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

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Recursive 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

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Recursive Ray Tracing

• Still producing PhDs 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

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Image Synthesis Class

• Prof. Humphreys is looking for students
• Modeled after Stanford course (lets beat em)
• See http//graphics.stanford.edu/courses/cs348b-c
  ompetition/

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Radiosity

• 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