Shading
For Further Reading
• Angel 7th Ed:
- Chapter 6
2
Why we need shading
• Suppose we build a model of a sphere
using many polygons and color it with
glColor. We get something like
• But we want
3
Shading
• Why does the image of a real sphere look like
• Light-material interactions cause each point to
have a different color or shade
• Need to consider
-
Light sources
Material properties
Location of viewer
Surface orientation
4
Lab – Design Your Own
Shading
• Write a simple function to compute the
light intensity from:
- Light direction
- Normal
- Eye direction
• You’re actually writing a GLSL shader!
But don’t worry, your task is greatly
simplified.
- vec3 type has x, y, z component.
- dot(u, v) produces the dot product of u and v.
5
Scattering
• Light strikes A
- Some scattered
- Some absorbed
• Some of scattered light strikes B
- Some scattered
- Some absorbed
• Some of this scattered
light strikes A
and so on
6
Rendering Equation
• The infinite scattering and absorption of
light can be described by the rendering
equation
- Cannot be solved in general
- Ray tracing is a special case for perfectly
reflecting surfaces
• Rendering equation is global and includes
- Shadows
- Multiple scattering from object to object
7
Global Effects
shadow
multiple reflection
translucent surface
8
Local vs Global Rendering
• Correct shading requires a global
calculation involving all objects and light
sources
- Incompatible with pipeline model which shades
each polygon independently (local rendering)
• However, in computer graphics, especially
real time graphics, we are happy if things
“look right”
- Exist many techniques for approximating global
effects
9
Light-Material Interaction
• Light that strikes an object is partially
absorbed and partially scattered (reflected)
• The amount reflected determines the color
and brightness of the object
- A surface appears red under white light because
the red component of the light is reflected and the
rest is absorbed
• The reflected light is scattered in a manner
that depends on the smoothness and
orientation of the surface
10
Light Sources
General light sources are difficult to work
with because we must integrate light
coming from all points on the source
11
Simple Light Sources
• Point source
- Model with position and color
- Distant source = infinite distance away (parallel)
• Spotlight
- Restrict light from ideal point source
• Ambient light
- Same amount of light everywhere in scene
- Can model contribution of many sources and
reflecting surfaces
12
Surface Types
• The smoother a surface, the more reflected light
is concentrated in the direction a perfect mirror
would reflected the light
• A very rough surface scatters light in all
directions
smooth surface
rough surface
13
Phong Model
• A simple model that can be computed rapidly
• Has three components
- Diffuse
- Specular
- Ambient
• Uses four vectors
- To source
- To viewer
- Normal
- Perfect reflector
14
Ideal Reflector
• Normal is determined by local orientation
• Angle of incidence = angle of relection
• The three vectors must be coplanar
r = 2 (l · n ) n - l
15
Lambertian Surface
• Perfectly diffuse reflector
• Light scattered equally in all directions
• Amount of light reflected is proportional to
the vertical component of incoming light
- reflected light ~cos qi
- cos qi = l · n if vectors normalized
- There are also three coefficients, kr, kb, kg that
show how much of each color component is
reflected
16
Specular Surfaces
• Most surfaces are neither ideal diffusers nor
perfectly specular (ideal refectors)
• Smooth surfaces show specular highlights due
to incoming light being reflected in directions
concentrated close to the direction of a perfect
reflection
specular
highlight
17
Modeling Specular Relections
• Phong proposed using a term that
dropped off as the angle between the
viewer and the ideal reflection increased
Ir ~ ks I cosaf
f
shininess coef
reflected
incoming intensity
intensity
absorption coef
18
The Shininess Coefficient
• Values of a between 100 and 200 correspond to
metals
• Values between 5 and 10 give surface that look
like plastic
cosa f
-90
f
90
19
Ambient Light
• Ambient light is the result of multiple
interactions between (large) light sources
and the objects in the environment
• Amount and color depend on both the
color of the light(s) and the material
properties of the object
• Add ka Ia to diffuse and specular terms
reflection coef
intensity of ambient light
20
Distance Terms
• The light from a point source that reaches
a surface is inversely proportional to the
square of the distance between them
• We can add a factor of the
form 1/(a + bd +cd2) to
the diffuse and specular
terms
• The constant and linear terms soften the
effect of the point source
21
Light Sources
• In the Phong Model, we add the results
from each light source
• Each light source has separate diffuse,
specular, and ambient terms to allow for
maximum flexibility even though this form
does not have a physical justification
• Separate red, green and blue components
• Hence, 9 coefficients for each point source
- Idr, Idg, Idb, Isr, Isg, Isb, Iar, Iag, Iab
22
Material Properties
• Material properties match light source
properties
- Nine absorption coefficients
• kdr, kdg, kdb, ksr, ksg, ksb, kar, kag, kab
- Shininess coefficient a
23
Coefficients Simplified
• OpenGL allows maximum flexibility by
giving us:
- 9 coefficients for each light source
• Idr, Idg, Idb, Isr, Isg, Isb, Iar, Iag, Iab
- 9 absorption coefficients
• kdr, kdg, kdb, ksr, ksg, ksb, kar, kag, kab
24
• But those are counter-intuitive. Usually it
is enough to specify:
• 3 coefficients for the light source:
– Ir, Ig, Ib,
– We assume (Idr, Idg, Idb ) = (Isr, Isg, Isb) = (Iar, Iag, Iab)
• 6 coefficients for the material:
– (kdr, kdg, kdb), (ksr, ksg, ksb),
– We assume (kdr, kdg, kdb) = (kar, kag, kab )
– Often, we also have (ksr, ksg, ksb) = (1, 1, 1)
25
Adding up the Components
For each light source and each color component,
the Phong model can be written (without the
distance terms) as
I =kd Id l · n + ks Is (v · r )a + ka Ia
For each color component
we add contributions from
all sources
26
Example
Only differences in
these teapots are
the parameters
in the Phong model
27
Shading in WebGL
WebGL lighting
•
Need
-
-
-
Normals
Material properties
Lights
State-based shading functions have
been deprecated (glNormal, glMaterial,
glLight)
Compute in application or in shaders
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
29
Example: Cube Lighting
Adding up the Components
For each light source and each color component,
the Phong model can be written (without the
distance terms) as
I =kd Id l · n + ks Is (v · r )a + ka Ia
For each color component
we add contributions from
all sources
31
Modified Phong Model
• The specular term in the Phong model is
problematic because it requires the
calculation of a new reflection vector and
view vector for each vertex
• Blinn suggested an approximation using
the halfway vector that is more efficient
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
32
The Halfway Vector
• h is normalized vector halfway between l
and v
h = ( l + v )/ | l + v |
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
33
Using the halfway vector
• Replace (v · r )a by (n · h )b
• b is chosen to match shininess
• Note that halfway angle is half of angle
between r and v if vectors are coplanar
• Resulting model is known as the modified
Phong or Phong-Blinn lighting model
- Specified in OpenGL standard
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
34
Vertex Shader in HTML
(HTML code)
<script id="vertex-shader" type="x-shader/x-vertex">
// vertex attributes
attribute vec4 vPosition;
attribute vec4 vColor;
attribute vec4 vNormal;
varying vec4 fColor;
uniform
uniform
uniform
uniform
uniform
uniform
uniform
uniform
mat4 modelingMatrix;
mat4 viewingMatrix;
mat4 projectionMatrix;
vec4 lightPosition;
vec4 materialAmbient;
vec4 materialDiffuse;
vec4 materialSpecular;
float shininess;
Quick Review of Shader Variable Qualifiers
• Attribute
attribute vec4 vNormal; from application
• varying
– copy vertex attributes and other variables from vertex shaders to fragment
shaders
– values are interpolated by rasterizer
varying vec4 fColor;
• uniform
– shader-constant variable from application
uniform mat4 modelingMatrix;
uniform vec4 lightPosition;
(HTML code)
void main()
{
vec4 L = normalize( lightPosition );
vec4 N = normalize( vNormal );
// Compute terms in the illumination equation
vec4 ambient = materialAmbient;
float Kd = max( dot(L, N), 0.0 );
vec4 diffuse = Kd * materialDiffuse;
fColor = (ambient + diffuse) * vColor;
gl_Position = projectionMatrix * viewingMatrix * modelingMatrix
* vPosition;
}
</script>
Setting Up Normals and Light
(JavaScript code)
function quad(a, b, c, d) {
var t1 = subtract(vertices[b], vertices[a]);
var t2 = subtract(vertices[c], vertices[b]);
var normal = cross(t1, t2);
var normal = vec4(normal);
normal = normalize(normal);
pointsArray.push(vertices[a]);
colorsArray.push(vertexColors[a]);
normalsArray.push(normal);
pointsArray.push(vertices[b]);
colorsArray.push(vertexColors[b]);
normalsArray.push(normal);
...
}
function colorCube() {
quad( 1, 0, 3, 2 ); ... }
(JavaScript code)
window.onload = function init()
{
var canvas = document.getElementById( "gl-canvas" );
...
// Generate pointsArray[], colorsArray[] and normalsArray[] from
// vertices[] and vertexColors[].
colorCube();
// normal array atrribute buffer
var nBuffer = gl.createBuffer();
gl.bindBuffer( gl.ARRAY_BUFFER, nBuffer );
gl.bufferData( gl.ARRAY_BUFFER, flatten(normalsArray), gl.STATIC_DRAW );
var vNormal = gl.getAttribLocation( program, "vNormal" );
gl.vertexAttribPointer( vNormal, 4, gl.FLOAT, false, 0, 0 );
gl.enableVertexAttribArray( vNormal );
(JavaScript code)
// uniform variables in shaders
modelingLoc
= gl.getUniformLocation(program, "modelingMatrix");
viewingLoc
= gl.getUniformLocation(program, "viewingMatrix");
projectionLoc = gl.getUniformLocation(program, "projectionMatrix");
gl.uniform4fv( gl.getUniformLocation(program, "lightPosition"),
flatten(lightPosition) );
gl.uniform4fv( gl.getUniformLocation(program, "materialAmbient"),
flatten(materialAmbient));
gl.uniform4fv( gl.getUniformLocation(program, "materialDiffuse"),
flatten(materialDiffuse) );
gl.uniform4fv( gl.getUniformLocation(program, "materialSpecular"),
flatten(materialSpecular) );
gl.uniform1f( gl.getUniformLocation(program, "shininess"),
materialShininess);
(JavaScript code)
function render() {
modeling = mult(rotate(theta[xAxis], 1, 0, 0),
mult(rotate(theta[yAxis], 0, 1, 0),
rotate(theta[zAxis], 0, 0, 1)));
viewing = lookAt([0,0,-2], [0,0,0], [0,1,0]);
projection = perspective(45, 1.0, 1.0, 3.0);
...
gl.uniformMatrix4fv( modelingLoc,
0, flatten(modeling) );
gl.uniformMatrix4fv( viewingLoc,
0, flatten(viewing) );
gl.uniformMatrix4fv( projectionLoc, 0, flatten(projection) );
gl.drawArrays( gl.TRIANGLES, 0, numVertices );
requestAnimFrame( render );
}
A Quick Summary
• Phong lighting implemented in the vertex
shader (inside the HTML file).
• Added to the WebGL JavaScript code:
– (Per-vertex) normal vectors.
– Light position
– Material properties: ambient, diffuse,
specular, shininess.
42
Normalization
• Cosine terms in lighting calculations can be
computed using dot product
• Unit length vectors simplify calculation
• Usually we want to set the magnitudes to have
unit length but
- Length can be affected by transformations
- Note that scaling does not preserved length
• GLSL has a normalization function
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
43
Normal for Triangle
n
plane
p2
n ·(p - p0 ) = 0
n = (p2 - p0 ) ×(p1 - p0 )
normalize n  n/ |n|
p
p1
p0
Note that right-hand rule determines outward face
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
44
Specifying a Point Light Source
• For each light source, we can set an RGBA for the
diffuse, specular, and ambient components, and
for the position
var
var
var
var
diffuse0 = vec4(1.0, 0.0, 0.0, 1.0);
ambient0 = vec4(1.0, 0.0, 0.0, 1.0);
specular0 = vec4(1.0, 0.0, 0.0, 1.0);
light0_pos = vec4(1.0, 2.0, 3,0, 1.0);
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
45
Distance and Direction
• The source colors are specified in RGBA
• The position is given in homogeneous
coordinates
- If w =1.0, we are specifying a finite location
- If w =0.0, we are specifying a parallel source
with the given direction vector
• The coefficients in distance terms are usually
quadratic (1/(a+b*d+c*d*d)) where d is the
distance from the point being rendered to the
light source
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
46
Spotlights
• Derive from point source
- Direction
- Cutoff
- Attenuation Proportional to cosaf
-q
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
f
q
47
Moving Light Sources
• Light sources are geometric objects whose
positions or directions are affected by the
model-view matrix
• Depending on where we place the position
(direction) setting function, we can
- Move the light source(s) with the object(s)
- Fix the object(s) and move the light source(s)
- Fix the light source(s) and move the object(s)
- Move the light source(s) and object(s) independently
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48
Material Properties
• Material properties should match the terms in
the light model
• Reflectivities
• w component gives opacity
var materialAmbient = vec4( 1.0, 0.0, 1.0, 1.0 );
var materialDiffuse = vec4( 1.0, 0.8, 0.0, 1.0);
var materialSpecular = vec4( 1.0, 0.8, 0.0, 1.0 );
var materialShininess = 100.0;
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
49
Front and Back Faces
• Every face has a front and back
• For many objects, we never see the back face
so we don’t care how or if it’s rendered
• If it matters, we can handle in shader
back faces not visible
back faces visible
Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015
50
Polygon Normals
• Polygons have a single normal
- Shades at the vertices as computed by the
Phong model can be almost same
- Identical for a distant viewer (default) or if there
is no specular component
• Consider model of sphere
• Want different normals at
each vertex even though
this concept is not quite
correct mathematically
51
Smooth Shading
• We can set a new
normal at each vertex
• Easy for sphere model
- If centered at origin n = p
• Now smooth shading
works
• Note silhouette edge
52
Mesh Shading
• The previous example is not general
because we knew the normal at each
vertex analytically
• For polygonal models, Gouraud proposed
we use the average of normals around a
mesh vertex
n1  n 2  n 3  n 4
n
| n1 |  | n 2 |  | n 3 |  | n 4 |
53
Gouraud and Phong Shading
• Gouraud Shading
- Find average normal at each vertex (vertex normals)
- Apply Phong model at each vertex
- Interpolate vertex shades across each polygon
• Phong shading
- Find vertex normals
- Interpolate vertex normals across edges
- Option 1 (faster, but less accurate):
• Find shades along edges
• Interpolate edge shades across polygons
- Option 2 (slower but more accurate):
• Interpolate normals across polygons
• Find shades (for each pixel)
54
Gouraud
Low polygon count
Gouraud
High polygon count
55
Comparison
• If the polygon mesh approximates surfaces with
a high curvatures, Phong shading may look
smooth while Gouraud shading may show edges
• Phong shading requires much more work than
Gouraud shading
- Usually not available in real time systems
• Both need data structures to represent meshes
so we can obtain vertex normals
56