Illumination and Shading
Illumination models arc also
frequently called lighting models or shading models. For example, some shading models
invoke an illumination model for every pixel in the image, whereas others
invoke an illumination model for only some pixels, and shade the remaining
pixels by interpolation. Consequently, many of the illumination and shading
models traditionally used in computer graphics include a multitude of kludges,
"hacks," and simplifications that have no firm grounding in theory,
but that work well in practice.
Modeling refraction, reflection, and
shadows requires additional computation that is very similar to, and often is
integrated with, hidden surface elimination. Indeed, these effects occur
because some of the “hidden surfaces” are not really hidden at all
16.1 ILLUMINATION MODELS
16.1.1 Ambient Light
An illumination model can be expressed
by an illumination equation in variables associated with the point on the
object being shaded. The illumination equation that expresses this simple model
is
I = ki ,
Where I is the resulting intensity and the
coefficient ki the object intrinsic intensity.
It depend on the position of the
point being shaded, we can evaluate it once for each object. The process of
evaluating the illumination equation at one or more points on an object is
often referred to as lighting the object.
Now imagine, instead of
self-luminosity, that there is a diffuse, non directional source of light, the
product of multiple reflections of light from the many surfaces present in the
environment. This is known as ambient
light. If we assume that ambient light impinges equally on all surfaces from
all directions, then our illumination equation becomes
I = Iaka
Ia is the intensity of the
ambient light, assumed to be constant for all objects. The amount of ambient
light reflected from an object's surface is determined by ka the
ambient rejection coefficient, which ranges from 0 to 1. The ambient—ref1ection
coefficient is a material property. Like some of the other properties, the
ambient-reliection coefficient is an empirical convenience and does not
correspond directly to any physical property of real materials.
16.1.2 Diffuse Reflection:
Although objects illuminated by
ambient light are more or less brightly lit in direct proportion to the ambient
intensity, they are still uniformly illuminated across their surfaces. Now
consider illuminating an object by a pain: light source, whose rays emanate
uniformly in all directions from a single point. The object’s brightness varies
from one part to another, depending on the direction of and distance to the
light source.
Lambertian reflection:
Dull, matte surfaces, such as chalk, exhibit
diffuse reflection, also known as Lambertian reflection. These surfaces appear
equally bright from all viewing angles because they reflect light with equal
intensity in all directories.
For a given surface,
the brightness depends only on the angle 6 between the direction L to the light
source and ' the surface normal N of
Fig16.1
Light-source attenuation:
If the projections of
two parallel surfaces of identical material, lit from the eye. overlap in an
image, Eq. (16.5) will not distinguish where one surface leaves off and the other begins, no
matter how different are their distances from the light source. To do this, we introduce a
light—source attenuation factor, fm, yielding
Colored lights and surfaces:
Colored lights and surfaces are commonly
treated by writing separate equations for each component of the color model. We
represent an object’s diffuse by one value of Od for each component.
Ex: the triple(odR,odG,odB)
defines an object’s diffuse red,green,blue components in RGB color
system.
Rather than restrict ourselves to a
particular color model, we explicitly indicate those terms in an illumination
equation that are wavelength-dependent by subscripting them with a
. Thus. Eq becomes
16.1.3 Atmospheric Attenuation
To simulate the atmospheric
attenuation from the object to the viewer, many systems provide depth cueing.
In this technique. Which originated with vector graphics hardware, more distant
objects are rendered with lower intensity than are closer ones.
The scale factors determine the blending of
the original intensity with that of a depth-cue color, Idc
. The goal is to modify a previously
computed I
to yield the depth-cued value I’
that is displayed. Given z0, the
0bject’s z coordinate, a scale factor s0 is derived that will be
used to interpolate between I
and ldc
, to determine
1 5.1.4 Specular Reflection
Specular reflection can be observed
on any shiny surface. Illuminate an apple with a bright white light: The
highlight is caused by Specular reflection, whereas the light reflected from
the rest of the apple is the result of diffuse reflection.
Similar as a perfect mirror, light is
reflected only in the direction of reflection R, which is L mirrored about N.
Thus the viewer can see specularly reflected light from a mirror only when the
angle α in Fig. 16.8 is zero; or is the angle between R and the direction to
the viewpoint V.
The Phong illumination model:
Phong BuiTuong [BUIT75] developed a popular
illumination model for non-perfect reflectors, such as the apple. It assumes
that maximum Specular reflectance occurs when α is zero and falls off sharply
as α
increases. This rapid fall of is approximated by cosn α,
where n is the material’s Specular-reflection exponent.
The amount of incident light
specularly reflected depends on the angle of incidence θ .If W(θ) is the
fraction of specularly reflected light, then Phong’s model is
If
the direction of reflection R, and the viewpoint direction V are
normalized, then cosα= R.V . ln addition, W(θ) is typically set to a constant Ks
the material's
specular-reflection coefficient , which
ranges between 0 and 1. The value of ks is selected experimentally
to produce aesthetically pleasing results.
Calculating the reflection vector:
Calculating R requires mirroring L about N. As
shown in Fig. 16.1 l, this can be accomplished with some simple geometry. Since
N and L are normalized, the projection of L onto N is N cosθ. Note that R =N
cosθ+S, where |S| is sinθ. But, by vector subtraction and congruent triangles,
S is just Ncosθ-L. Therefore, R = 2 Ncosθ-L. Substituting N.L for cosθ and R.V
for cosα yields.
The halfway vector:
An
alternative formulation of Phong's illumination model uses the halfway vector
H, so called because its direction is halfway between the directions of the
light source and the viewer. as shown in Fig. 16.12. H is also known as the
direction of maximum highlights
1 6.1.6 Multiple Light Sources
If there are m light sources, then
the terms for each light source are summed:
The summation harbors a new
possibility for error in that I
can now exceed the maximum displayable pixel
value.
1 6.4 SHADOWS
Visible-surface algorithms determine
which surfaces can be seen from the viewpoint shadow algorithms determine which
surfaces can be "‘seen" from the light source. Thus, Visible-surface
algorithms and shadow algorithms are same.
Note that areas in the shadow of all
point light sources are still illuminated by the ambient light. Although
computing shadows requires computing visibility from the light source, as we
have pointed out, it is also possible to generate “fake" shadows without
performing any visibility tests.
1 6.4.1 Scan-Line- Generation of
Shadows
One of the oldest methods for
generating shadows is to augment a scan-line algorithm to interleave shadow and
visible-surface processing lAPPEL68; BOUK70b]. Using the light source as a
center of projection, the edges of polygons that might potentially cast shadows
are projected onto the polygons intersecting the current scan line. when the
scan crosses one of these shadow edges.
the colors of the image pixels are modified accordingly.
A brute-force implementation of this
algorithm must compute all n(n-l) projections of every polygon on every other
polygon. Bouknight and Kelley instead use a clever preprocessing step in which
all polygons are projected onto a sphere surrounding the light source, with the light source as center
of projection.
While the scan-line algorithm’s regular scan
keeps track of which regular polygon edges are being crossed, a separate,
parallel shadow scan keeps track of which shadowing polygon projection edges
are crossed, and thus which shadowing polygon projections the shadow scan is
currently "in".
1 6.4.2 A Two-Pass Object—Precision
Shadow Algorithm
Atherton, Weller, and Greenberg have
developed an algorithm that performs shadow determination before
visible-surface determination [ATHE78]. They process the object description by
using the same algorithm twice, once for the viewpoint, and once for the light
source.
The lit polygons are transformed back into the
modeling coordinates and are merged with a copy of the original database as
surface-detail polygons, creating a viewpoint-independent merged database,
shown in Fig. 16.29. Note that the implementation illustrated in Fig. 16.28
performs the same transformations on both databases before merging them.
1 6.4.3 Shadow Volumes
Crow [CROW77a] describes how to
generate shadows by creating for each object a shadow volume that the object
blocks from the light source. A shadow volume is defined by the light source
and an object and is bounded by a set of invisible shadow polygons. As shown in
Fig. 16.30, there is one quadrilateral shadow polygon for each silhouette edge
of the object relative to the light source. Three sides of a shadow polygon are
defined by a silhouette edge of the objects and the two lines emanating.
1 6.4.4 A Two- Pass z-Buffer Shadow Algorithm
Williams [WILLTS] developed a
shadow-generation method based on two passes through a z-buffer algorithm, one
for the viewer and one for the light source. His algorithm, unlike the two-pass
algorithm of Section l6.4.2, determines whether a surface is shadowed by using
image precision calculation.
Whenever a pixel is determined to be
visible, its object-precision coordinates in the observer’s view (.x0,yo,z0)
are transformed into coordinates in the light source’s view (x’0,y’o,z’0).
The transformed coordinates x; and y; are used to select the value zL
in the light source. In analogy to texture mapping, we can think of the light’s
z-buffer as a shadow map.
16.4.5 Global Illumination Shadow
Algorithms
Ray-tracing and radiosity algorithms
have been used to generate some of the most impressive pictures of shadows in
complex environments. Simple ray tracing has been used to model shadows from
point light sources, whereas more advanced versions allow extended light
sources.
16.5 THANSPAFIENCY
Much as surfaces can have specular
and diffuse reflection, those that transmit light can be transparent or
translucent. We can usually see clearly through transparent materials, such as
glass, although in general the rays are refracted (bent). Diffuse transmission
occurs through translucent materials, such as frosted glass. Rays passing
through translucent materials are jumbled by surface or internal
irregularities, and thus objects seen through translucent materials are
blurred.
16.5.1 Nonrefractive Transparency
The simplest approach to modeling
transparency ignores refraction, so light rays are not bent as they pass
through the surface. Thus, whatever is Visible on the line of sight through a
transparent surface is also geometrically located on that line of sight. Although
refraction-less transparency is not realistic.
Two different methods have been
commonly used to approximate the way in which the colors of two objects are
combined when one object is seen through the other. We shall refer to these as
interpolated and filtered transparency.
Interpolated transparency:
Interpolated transparency determines the shade
of a pixel in the intersection of two polygons’ projections by linearly
interpolating the individual shades calculated for the two polygons:
The transmission coefficient kt1
measures the transparency of polygon l, and ranges between 0 and l. When kt1
is 0. the polygon is opaque and transmits no light; when kt1 is l,
the polygon is perfectly transparent and contributes nothing to the intensity
Iλ; The value 1 —kt1 is called the p0lygon’s opacity.
For
a more realistic effect, we can interpolate only the ambient and diffuse
components of polygon l with the full shade of polygon 2, and then add in
polygon l’s specular component.
Another approach, often called
screen-door transparency, literally implements a mesh by rendering only some of
the pixels associated with a transparent object’s projection. The low—order
bits of a pixel’s (x, y) address are used to index into a transparency bit
mask. If the indexed bit is 1, then the pixel is written; otherwise, it is
suppressed, and the next closest polygon at that pixel is visible.
Filtered transparency:
Filtered transparency treats a polygon as a
transparent filter that selectively passes different wavelengths; it can be
modeled by
Where Otλ, is polygon l’s
transparency color. A colored filter may be modeled by choosing a different
value of Otλ for each λ (but soc Section 16.9). In either
interpolated or filtered transparency,
if additional transparent polygons are in front of these polygons, then the
calculation is invoked recursively for polygons in back—to—front order, each
time using the previously computed Iλ, as Iλ2.
Implementing
transparency:
Several visible-surface algorithms can be
readily adapted to incorporate transparency, including scan-line and
list-priority algorithms, In list-priority algorithms, the color of a pixel
about to be covered by a transparent polygon is read back and used in the
illumination model while the polygon is being scan converted.
Most
z—buffer—based systems support screen-door transparency because it allows
transparent objects to be intermingled with opaque objects and to be drawn in
any order. Unfortunately, the z-buffer does not store the information needed to
determine which transparent polygons are in front of the opaque polygon, or
even the polygons‘ relative order.
Mammen [MAMM89] describes how to
render transparent objects properly in back-to-from order in a z-buffer-based
system through the use of multiple tendering passes and additional memory. First,
all the opaque objects are rendered using a conventional z-buffer. Then,
transparent objects are processed into a separate set of buffers that contain,
for each pixel, a transparency value and a flag bit, in addition to the pixel’s
color and 2 value. Each flag bit is initialized to off and each z value is set
to the closest possible value. Information for flagged pixels is then blended
with that in the original frame butler and z-buffer. A flagged pixel’s
transparency z-value replaces that in the opaque z-buffer and the Hag bit is
reset. This process is repeated to render successively closer objects at each
pixel.
Kay and Greenberg [KAY79b} have
implemented a useful approximation to the increased attenuation that occurs
near the silhouette edges of thin curved surfaces, where light passes through
more material. They define kt in terms of a nonlinear function of
the z component of the surface normal after perspective transformation.
where ktmin and ktmax
are the object’s minimum and maximum transparencies, zN is the
z component of the normalized surface normal at the point for which kt,
is being computed, and m is a power factor (typically 2 or 3). A higher m
models a thinner surface. This new value of kt may be used as kt1
in either.
1 6.5.2 Refractive Transparency
Refractive transparency is
significantly more difficult to model than is non refractive transparency,
because the geometrical and optical lines of sight are different. If refraction
is considered in Fig. 16.35, object A is visible through the transparent object
along the line of sight shown; if refraction is ignored, object B is visible.
The relationship between the angle of incidence θi; and the angle of
refraction θt, is given by Snell’s law.
where niλ, and ntλ
are the indices of refraction of the materials. A material’s index of
refraction is the ratio of the speed of light in a vacuum to the speed of light
in the material. The index of refraction`s wavelength-dependence is evident in
many instances of refraction as dispersion .
Total internal reflection:
When light passes from one medium
into another whose index of refraction
is lower, the angle θt, of the transmitted ray is greater than the
angle θi .If θi
becomes sufficiently large, then θt, exceeds 90° and the ray is
reflected from the interface between the media, rather than being transmitted.
This phenomenon is known as total internal reflection, and the smallest θi,
at which it occurs is called the critical angle.
1 6.10 IMPROVING THE CAMERA MODEL:
We have modeled the image produced by
a pinhole camera: each object, regardless of its position in the environment,
is projected sharply and without distortion in the image. Real cameras (and
eyes) have lenses that introduce a variety of distortion and focusing effects.
Depth of field: Objects appear to be more or less
in focus depending on their distance from the lens, an effect known as depth a
field.
A real lens’s focusing effect causes
light rays that would not pass through the pinhole to strike the lens and to
converge to form the image. These rays see a slightly different view of the
scene, including.
Motion blur. Motion blur is the streaked or
blurred appearance that moving objects have because a camera’s shutter is open
for a finite amount of time.
16.1 1 GLOBAL ILLUMINATION ALGORITHMS
An illumination model computes the
color at a point in terms of light directly emitted by light sources and of
light that reaches the point after reflection from and transmission through its
own and other surfaces. This indirectly reflected and transmitted light is often
called global illumination. In contrast, local illumination is light that comes
directly from the light sources to the point being shaded. They model all an
environments interactions with light sources first in a view—independent stage,
and then compute one or more images for the desired viewpoints using
conventional visible-surface and interpolative shading algorithms.
View—dependent algorithms are well-suited for handling specular phenomena that are
highly dependent on the viewer‘s position, but may perform extra work when
modeling diffuse phenomena that change little over large areas of an image, or
between images made from different viewpoints. On the other hand, view—independent algorithms model
diffuse phenomena efficiently, but require overwhelming amounts of storage to
capture enough information about specular phenomena.
1 6.12 RECURSIVE RAY TRACING
This simple algorithm determined the
color of a pixel at the closest intersection of an eye ray with an object. To
calculate shadows, we fire an additional ray from the point of intersection to
each of the light sources. This is shown for a single light source in Fig.
The above fig which is reproduced
from a paper. The first paper published on ray tracing for computer graphics.
lf one of these shadow rays intersects any object along the way, then the
object is in shadow at that point and the shading algorithm ignores the
contribution of the shadow ray's light source.
Figure 16.52 shows two pictures that
Appel rendered with this algorithm, using a pen plotter. He simulated a
halftone pattern by placing a different size "+" at each pixel in the
grid, depending on the pixel's intensity.
Each
of these reflection and refraction rays may, in turn, recursively spawn shadow,
reflection, and refraction rays, as shown in Fig. 16.54.
16.12.1 Efficiency Considerations for Recursive Ray Tracing
The general efficiency techniques are
even more important here than in visible-surface ray tracing for several
reasons. Object spawns one shadow ray for each other in light sources. Thus,
there are potentially m(2n — 1) shadow rays for each ray tree. To
make matters worse, since rays can come from any direction, traditional
efficiency ploys, such as clipping objects to the view volume and culling
back-facing surfaces relative to the eye, cannot be used in recursive my
tracing. Objects that would otherwise be invisible, including back faces. may
be reflected from or refracted through visible surfaces.
Item buffers:
One way of speeding up ray of tracing is simply ROI to use it at all when
determining those objects directly visible to the eye. Weghorst, Hooper, and
Greenberg describe how to create an item buffer by applying a less costly
visible-surface a algorithm, such as the z—buffer algorithm, to the scene,
using the same viewing specification.
Reflection maps:
Tracing rays can be avoided in other situations, too. Hall shows how to combine
ray tracing with the reflection maps. The basic idea is to do less work for the
secondary rays than for primary rays. Those objects that are not directly
visible in an image are divided into two groups on the basis of an estimation
of their indirect visibility. Hall also points out that reflected and refracted
images are often extremely distorted. Therefore, good results may be achieved
by intersecting the reflection and refraction rays with object definitions less
detailed than those used for the eye rays.
Adaptive tree-depth control: Although ray tracing is often used to depict highly specular
objects, most of an image’s area is usually not filled with such objects.
Consequently, a high recursion level often results in unnecessary processing
for large parts of the picture. Hall introduced the use of adaptive tree-depth control, in which a ray is not cast if its
contribution to the pixel's intensity is estimated to be below some preset
threshold. This is accomplished by approximating a ray’s maximum contribution
by calculating its intensity with the assumption that the ray‘s child rays have
intensities of l. This allows the ray’s contribution to its parent to be
estimated. As the ray tree is built. the maximum contribution of a ray is
multiplied by those of its ancestors to derive the ray’s maximum contribution
to the pixel.
Light buffers:
Haines and Greenberg have introduced the
notion of a light bufer to increase the speed with which shadow rays are
processed. A light buffer is a cube centered about a light source and aligned
with the world-coordinate axes, as shown in Fig. l6.57(a). Each side is tiled
with a regular grid of squares, and each square is associated with a
depth-sorted list of surfaces that can be seen through it from the light. The
lists are Filled by scan convening the objects in the scene onto each face of
the light buffer with the center of projection at the light.
Ray classification: The spatial-partitioning approaches make it possible to determine which
objects lie in a given region of 3D space. Arm and Kirk have extended this
concept to partition rays by the objects that they intersect, a technique
called ray classification. A ray may be specified by its position in 5D my
space, determined by the 3D position of its origin in space and its 2D
direction in spherical coordinates. A point in ray space defines a single ray,
whereas a finite subset of ray space defines a family of rays or beam. Ray
classification adaptively partitions ray space into subsets, each of which is
associated with a list of objects that it contains (i.e., that one of its rays
could intersect). To determine the candidate objects that may be intersected by
any ray, we need only to retrieve the list of objects associated with the
subset of ray space in which the ray resides.
16.12.2 A Better Illumination Model
Hall] has developed a model in which
the specular light expressions are scaled by a wavelength-dependent Fresnel
reflectivity term. An additional term for transmitted local light is added to
take into account the contribution of transmitted light directly emitted by the
light sources, and is also scaled by the Fresnel transmissivity terms. The
global reflected and refracted rays further take into account the transmittance
of the medium through which they travel.
1 6.12.3 Area-Sampling Variations
One of conventional ray tracing’s
biggest drawbacks is that this technique point samples on a regular grid.
Whitted suggested that unweighted area sampling could be accomplished by
replacing each linear eye ray with a pyramid defined by the eye and the four
corners of a pixel. These pyramids would be intersected with the objects in the
environment, and sections of them would be recursively refracted and reflected
by the objects that they intersect.
Cone tracing: Cone tracing is developed by
Amanatides generalizes the linear rays into cones. One cone is fired from the
eye through each pixel, with an angle wide enough to encompass the pixel. The
cone is intersected with objects in its path by calculating approximate
fractional blockage values for a small set of those objects closest to the
cone’s origin. Refraction and reflection cones are determined from the optical
laws of spherical minors and lenses as a function of the surface curvature of
the object intersected and the area of intersection. The effects of scattering
on reflection and refraction are simulated by further broadening the angles of
the new reflection and refraction cones..
Beam tracing:
Beam tracing. Introduced by Heckbert and Hanrahau is an object-precision
algorithm for polygonal environments that traces pyramidal beams, rather than
linear rays. The viewing pyramid’s beam is intersected with each polygon in the
environment, in front-to—back sorted order, relative to the pyramid’s apex. If
a polygon is intersected, and therefore visible, it must be subtracted from the
pyramid using an algorithm. For each visible polygon fragment, two polyhedral
pyramids are spawned, one each for reflection and refection. The algorithm
proceeds recursively, with termination criteria similar to those used in ray
tracing..Beam tracing takes advantage of coherence to provide impressive
speedups over conventional ray tracing at the expense of a more complex
algorithm, limited object geometry, and incorrectly modeled refraction.
Pencil tracing: Shinya, Takahashi, and Naito have
implemented an approach called pencil tracing that solves some of the problems
of cone tracing and beam tracing. A pencil is a bundle of rays consisting of a
central axial ray, surrounded by a set of nearby paraxial rays. Each paraxial
ray is represented by a 4D vector that represents its relationship to the axial
ray. Two dimensions express the paraxial ray’s intersection with a plane
perpendicular to the axial ray; the other two dimensions express the paraxial
ray's direction. In many cases, only an axial ray and solid angle suffice to
represent a pencil. If pencils of sufficiently small solid angle are used, then
reflection and refraction can be approximated well by a linear transformation
expressed as a 4 X 4 matrix. They
have developed error estimation techniques for determining an appropriate solid
angle for a pencil. Conventional rays must be traced where a pencil would
intersect the edge of an Object.
16.12.4 Distributed Ray Tracing
Sampling by casting solid beams
rather than infinitesimal rays. In contrast, distributed ray tracing, developed
by Cook. Porter, and Carpenter, is based on a stochastic approach to super
sampling that trades off the objectionable artifacts of aliasing for the loss
offensive artifacts of noise specular reflection from rough surfaces. The word
distributed in this techniques name refers to the fact that rays are
stochastically by distributed to sample the quantities that produce those
affects. The basic concepts have also been applied to other algorithms besides
ray tracing. Poisson distribution is obtained by displacing by u small random
distance the position of each element of a regularly spaced sample grid. This
technique is called jittering. In sampling the 2D image plans, each sample in a
regular grid is jittered by two uncorrelated random quantities, one each for x
and y, both generated with a sufficiently small variance that the samples do
not overlap (Fig. 16.59). Figure i6.6O shows a minimum-distance Poisson
distribution and a jittered regular distribution.
1 6.1 2.5 Ray Tracing from the Light Sources
One serious problem with ray tracing
is caused by tracing all rays from the eye. Shadow rays are cast only to direct
sources of light that are treated separately by the algorithm. Therefore, the
effects of indirect reflected and refracted light sources, such as mirrors and
lenses, are not reproduced properly: Light rays bouncing off a minor do not
cast shadows, and the shadows of transparent objects do not evidence
refraction, since shadow rays are cast in a straight line toward the light
source. It might seem that we would need only to rt1n a conventional ray tracer
"backward" from the light sources to the eye to achieve these
effects. This concept has been called backward my tracing, to indicate that it
runs in the reverse direction from regular ray tracing, but it is also known as
forward my tracing to stress that it follows the actual path from the lights to
the eye. We call it ray tracing from the light sources to avoid confusion.
This method creates new problem.
Since an insufficient number of rays ever would strike the image plane, let alone
pass through the focusing lens or pinhole. Instead, ray tracing from the light
sources can be used to supplement the lighting information obtained by regular
ray tracing. Heckbert and Hanrahan suggest an elaboration of their proposed
beam-tracing shadow method (Section 16.12.3) to accomplish this. If a light’s
beam tree is traced recursively; successive levels of the tree below the first
level represent indirectly illuminated polygon fragments. Adding these to the
database as surface—detail polygons allows indirect specular illumination to be
modeled. Arvo has implemented a ray tracer that uses a preprocessing step in
which rays from each light source are sent into the environment. Each ray is
assigned an initial quota of energy, some of which is deposited at each
intersection it makes with a diffusely reflecting object. He compensates for
the relative sparseness of ray intersections by mapping each surface tm a
regular rectangular grid of counters that accumulate the deposited energy. Each
ray’s contribution is bilinearly partitioned among the four counters that bound
the grid box in which the ray hits. A conventional ray—tracing pass is then
made, in which the first pass‘s interpolated contributions at each intersection
are used, along with the intensities of the visible light sources, to compute
the diffuse reflection. Unfortunately, if a light ray strikes an object on the
invisible side of a silhouette edge as seen from the eye, the ray can affect
the shading on the visible side. Note that both these approaches to ray tracing
from the light sources use purely specular reflectivity geometry to propagate
rays in both directions.
16.14 THE RENDERING PIPELINE
16.14.1 Local Illumination Pipelines
Z-buffer and Gouraud shading: Perhaps the most straight forward
modification to the pipeline occurs in a system that uses the z-buffer
visible-surface algorithm to render Gouraud shaded polygons. The Z-buffer
algorithm has the advantage that primitives may be presented to it in any
order. Therefore, as before, primitives are obtained by traversing the
database, and are transformed by the modeling transformation into the WC
system.
Primitives may have associated
surface normals that were specified when the model was built. The normals
defined with the objects may represent the true surface geometry, or may
specify user-defined surface blending effects, rather than just being the
averages of the normals of shared faces in the polygonal mesh approximation.
Our next step is to cull primitives
that fall entirely outside of the window and to perform back-face culling. This
trivial-reject phase is typically performed now because we want to eliminate
unneeded processing in the lighting step that follows. By using Gouraud
shading, the illumination equation is evaluated at each vertex, to preserve the
correct angle and distance from each light to the surface. If vertex normals
were not provided with the object, they may be computed immediately before
lighting the vertices. Culling and lighting are often performed in a lighting
coordinate system that is a rigid body transformation of WC .
Next objects are transformed to NPC
by the viewing transformation. and clipped to the view volume. Division by W is
performed, and objects ate mapped to the viewport. At this point, the clipped
primitive is submitted to the z—buffer algorithm, which performs rasterization,
interleaving scan conversion with the interpolation needed to compute the z
value and color-intensity values for each pixel. If a pixel is determined to be
visible, its color-intensity values may be further modified by depth cueing. Although
this pipeline may seem straightforward, there are many new issues that must be
dealt with to provide an efficient and correct implementation.
Z-buffer and Phong shading: This
simple pipeline must be modified to Phong shading, as shown in Fig. Because
Phong shading interpolates surface normals, rather than intensities, the
vertices cannot be lit early in the pipeline. Instead, each object must be
clipped, transformed by the viewing transformation, and passed to the z-buffer
algorithm. Finally, lighting is performed with the interpolated surface normals
that are derived during scan conversion. Thus, each point and its normals must
be back mapped into a coordinate system that is isometric to WC to evaluate the
illumination equation.
List-priority algorithm and Phong
shading: When a
list-priority algorithm is used, the primitives obtained from traversal and
processed by the modeling transformation are inserted in a separate database,
such as a BSP tree, as part of preliminary visible-surface determination. The
application program and the graphics package may each keep separate databases.
Here, we see that rendering can require yet another database. Since, in this
case polygons are split, correct shading information must be determined for the
newly created vertices. The rendering database can now be traversed to return
primitives in a correct in back-to-front order. The overhead of building this
database can be applied toward the creation of multiple pictures. Primitives
extracted from the rendering database are clipped and normalized, and are
presented to the remaining stages of the pipeline.
1 5.14.2 Global Illumination
Pipelines
The incorporating global illumination
effect requires information about the geometric relationships between the
object being rendered and the other objects in the world. It is to calculate
needed information from a specific viewpoint in advance of scan conversion and to
Store it in tables. This eliminates the need to access the full db
representation of other objects while processing the current object. In the
case of shadows, preprocessing the
environment to add surface detail polygon shadows is another way to allow the
use of an otherwise conventional pipeline.
Radiosity: The diffuse Radiosity algorithms
offer an interesting example of how to take advantage of the conventional
pipeline to achieve global-illumination effects. These algorithms process
objects and assign to them a set of view-independent vertex intensities. These
objects may then be presented to a modified version of the pipeline for
z-buffer and Gouraud shading, depicted in Fig that eliminates the lighting
stage.
Ray tracing: it is the simplest because those
objects that are visible at each pixel and their illumination are determined
entirely in WC. Once objects have been obtained from the database and
transformed by the modeling transformation, they are loaded into the ray tracer’s
WC database, which is typically implemented using the techniques of Sections
15.10.2 and 16. I2. 1, to support efficient my intersection calculations.
16.14.3 Designing Flexible Renderers
The several design approaches have
been suggested to increase the case with which illumination and shading
algorithms may be implemented and used.
Modularization: A straightforward approach is to
modularize the illumination and shading model in a part of the rendering system
that is often known as its shader. The standard mechanism for passing
parameters to shaders, different shaders can be used in the same system. The
decision to call can be made at runtime based objects. The system performs scan
using a scan-line algorithm, the results are added to linked list of spans. It contains information about a set of values of
endpoints, including their x and z values.
Special languages: In contrast to providing
extensibility at the level of the programming language in which the system is
built, it is possible to design special languages that are better suited to specific
graphics tasks. Cook has designed a special-purpose language in which a shader
is built as a tree expression called a shade
tree. It takes parameters from its
children and produces parameters for its parent. The parameters are the terms
of the illumination equation. Some nodes, such as diffuse, specular, or square root
are built into the language. Others can be defined by the user and dynamically
loaded when needed. All nodes can access information about the lights. A shade
tree thus describes a particular shading process and is associated with one or
more objects through use of a separate modeling language. Different objects may
have different shade trees.
The flexibility of shade trees and
pixel-stream editors may be combined by designing a rendering system that
allows its users to write their own shaders in a special programming language
and to associate them with selected objects. This approach is taken in the
RenderMan Interface. It defines a set of key places in the rendering process at
which user-defined or system-defined shaders can be called.
Visible surface determination is done
with a sub pixel z-buffer whose sub pixel centers are jittered to accomplish
stochastic sampling. The closest micro-polygon covering a sub pixel center is
visible at that sub pixel. To avoid the need to store micro polygon meshes and sub
pixel z and intensity values for the entire image. The image is divided into
rectangular partitions into which each object is sorted by the upper left hand
corner of its extent. The partitions are then processed left to right, top to
bottom. The resulting sub objects or micro polygons are placed in the
partitions that they intersect.
16.14.4 Progressive Refinement:
Instead of attempting to render a final
version of a picture all at once, we can first render the picture coarsely, and
then progressively refine it, to improve it. For eg a first image might have no
antliasing, simpler object models and simpler shading. The user views an image,
idle cycles may be spent improving its quality. If the metric by which to
determine what to do next, then refinement can occur adaptively. Bergman,
Fuchs, Grant, and Spach have developed such a system that uses a variety of
heuristics to determine how it should spend its time. For eg a polygon is
Gouraud-shaded, rather than constant-shaded, only if the range of its vertex
intensities exceeds a threshold. Ray-tracing and radiosity algorithms are both
amenable to- progressive refinement.
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