Shading

For Further Reading

•Angel 7th Ed: Chapter 6

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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

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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

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.

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Scattering

•Light strikes A Some scattered Some absorbed

•Some of scattered light strikes B Some scattered Some absorbed

•Some of this scatteredlight strikes Aand so on

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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

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Global Effects

translucent surface

shadow

multiple reflection

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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

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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

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Light Sources

General light sources are difficult to work with because we must integrate light coming from all points on the source

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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

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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

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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

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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

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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 i

cos i = l · n if vectors normalized

There are also three coefficients, kr, kb, kg that show how much of each color component is reflected

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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

specularhighlight

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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 cos

shininess coef

absorption coef

incoming intensityreflectedintensity

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The Shininess Coefficient

• Values of between 100 and 200 correspond to metals

• Values between 5 and 10 give surface that look like plastic

cos

90-90

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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

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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 theform 1/(a + bd +cd2) tothe diffuse and specular terms•The constant and linear terms soften the effect of the point source

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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

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Material Properties

•Material properties match light source properties

Nine absorption coefficients• kdr, kdg, kdb, ksr, ksg, ksb, kar, kag, kab

Shininess coefficient

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

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•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)

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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 )+ ka Ia

For each color component

we add contributions from

all sources

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Example

Only differences in these teapots are the parametersin the Phong model

Shading in WebGL

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WebGL lighting

• Need Normals

Material properties

Lights

State-based shading functions have been deprecated (glNormal, glMaterial, glLight)

Compute in application or in shaders

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Example: Cube Lighting

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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 )+ ka Ia

For each color component

we add contributions from

all sources

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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

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The Halfway Vector

• h is normalized vector halfway between l and v

h = ( l + v )/ | l + v |

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Using the halfway vector

•Replace (v · r )by (n · h )

• 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

Vertex Shader in HTML (HTML code)

<script id="vertex-shader" type="x-shader/x-vertex">// vertex attributesattribute vec4 vPosition;attribute vec4 vColor;attribute vec4 vNormal;

varying vec4 fColor;

uniform mat4 modelingMatrix;uniform mat4 viewingMatrix;uniform mat4 projectionMatrix;uniform vec4 lightPosition;uniform vec4 materialAmbient;uniform vec4 materialDiffuse;uniform vec4 materialSpecular;uniform 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.

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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

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Normal for Triangle

p0

p1

p2

n

plane n ·(p - p0 ) = 0

n = (p2 - p0 ) ×(p1 - p0 )

normalize n n/ |n|

p

Note that right-hand rule determines outward face

Angel and Shreiner: Interactive Computer Graphics 7E © Addison-Wesley 2015

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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 diffuse0 = vec4(1.0, 0.0, 0.0, 1.0);var ambient0 = vec4(1.0, 0.0, 0.0, 1.0);var specular0 = vec4(1.0, 0.0, 0.0, 1.0);var light0_pos = vec4(1.0, 2.0, 3,0, 1.0);

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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

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Spotlights

•Derive from point source Direction

Cutoff Attenuation Proportional to cos

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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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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;

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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

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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

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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

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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

|n||n||n||n|

nnnnn

4321

4321

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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)

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Gouraud Low polygon count

Gouraud High polygon count

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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