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Lighting

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diffuse

specular

ambient

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Lighting and

Illumination

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Illumination Models

Illumination 光源(light sources)照明度變化

The transport luminous flux

(i.e., the the rate the rate of the rate of flow the rate of flow of the rate of flow of light energy)

from light sources between

points via direct and indirect paths

Lighting 物體光線的明暗度 via different illumination sources

The process of computing the luminous

intensity reflected from a specified 3-D point

Shading 描影法,明暗法

The process of assigning a colors to

a pixels

Illumination Models光源模形

Simple approximations of light transport

Physical models of light transport

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Depositphotos: City street at night in degradation

https://cn.depositphotos.com/32200741/stock-video-city-street-at-night-in.html

Lightning Particle System for Unity 3D – Procedural Lightning

https://www.digitalruby.com/lightning-for-unity-3d/

夜幕降臨的夜城交通燈。移動交通的顏色模糊

OpenGL does not account this

effect! Needs more advanced

methods in ray tracing etc.

An example of motion blur showing a London busshowing a London bus passing a telephone box in London

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Ray tracing

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Ray tracing

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This recursive ray tracing of a sphere demonstrates the effects of shallow depth of field, area light sources and diffuse inter-reflection.

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Lighting

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Direct Lighting

Indirect Lighting

散射

Glossy (散射) reflection, glossy refraction ,i.e., summarize and average all glossy ray colors

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Direct and Indirect Lighting

Lighting intensity

will be reduced (i.e., 0<=k<1) for each bounce

OpenGL does direct

lighting without considering blocking (堵塞)

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https://www.scratchapixel.com/lessons/3d-basic-rendering/global-illumination-path-tracing

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Radiosity 輻射度演算法 (computer graphics)

In 3D computer graphics, radiosity is an application of the finite element method to solving the rendering equation to solving the rendering equationfor scenes with surfaces that reflect light diffusely to solving the rendering equationfor scenes with surfaces that reflect light diffusely. Unlike rendering to solving the rendering equationfor scenes with surfaces that reflect light diffusely. Unlike rendering methods that use Monte Carlo algorithms to solving the rendering equationfor scenes with surfaces that reflect light diffusely. Unlike rendering methods that use Monte Carlo algorithms(such as path tracing to solving the rendering equationfor scenes with surfaces that reflect light diffusely. Unlike rendering methods that use Monte Carlo algorithms(such as path tracing), which handle all types of light paths, typical radiosity only account for paths (represented by the code "LD*E") which leave a light source and are reflected diffusely some number of times (possibly zero) before hitting the eye. Radiosity is a global illumination to solving the rendering equationfor scenes with surfaces that reflect light diffusely. Unlike rendering methods that use Monte Carlo algorithms(such as path tracing), which handle all types of light paths, typical radiosity only account for paths (represented by the code "LD*E") which leave a light source and are reflected diffusely some number of times (possibly zero) before hitting the eye. Radiosity is a global illumination algorithm in the sense that the illumination arriving on a surface comes not just directly from the light sources, but also from other surfaces reflecting light. Radiosity is viewpoint independent, which increases the calculations involved, but makes them useful for all viewpoints.

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Radiosity is a method of rendering based on an detailed analysis of light reflections off diffuse surfaces. The images that result from a radiosity renderer are characterized by soft gradual shadows. Radiosity is typically used to render images of the interior of buildings, and can achieve extremely photo-realistic results for scenes that are comprised of diffuse reflecting surfaces. i.e., 1) very slow to store all radiosity in the environment, 2) ray tracing is from lighting sources

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Radiosity was perhaps the first rendering algorithm in widespread use which accounted for diffuse indirect lighting.

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Radiosity 輻射度演算法

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Two Components of Illumination

Light Sources (Emitters)

Emission Spectrum (color)

Geometry (position and direction)

Directional Attenuation

Surface Properties (Reflectors)

Reflectance Spectrum (color)

Geometry (position, orientation, and micro-structure)

Absorption

Approximations

Only direct illumination from the emitters to the reflectors

Ignore the geometry of light emitters, and consider only the geometry of reflectors such as OpenGL

散射

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Ambient Light Source

Even though an object in a scene is not directly lit it will still be visible. This is because light is reflected indirectly from nearby objects. A simple hack that is commonly used to model this indirect illumination is to use of an ambient light source. Ambient light has no spatial or directional characteristics. The amount of ambient light incident on each object is a constant for all surfaces in the scene. An ambient light can have a color.

The amount of ambient light that is reflected by an object is independent of the object's position or orientation. Surface properties are used to determine how much ambient light is reflected.

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Directional Light Sources

All of the rays from a directional light source have a common direction, and no point of origin. It is as if the light source was infinitely far away from the surface that it is illuminating. Sunlight is an example of an infinite light source. ��

The direction from a surface to a light source is important for computing the light reflected from the surface. With a directional light source this direction is a constant for every surface. A directional light source can be colored.

No attenuation with distance.

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Difference between Light source

And point light source

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Point Light Sources

The point light source emits rays in radial directions from its source. A point light source is a fair approximation to a local light source such as a light bulb.

��

The direction of the light to each point on a surface changes when a point light source is used. Thus, a normalized vector to the light emitter must be computed for each point that is illuminated.

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Other Light Sources

Spotlights

Point source whose intensity falls off away from a given direction
Requires a color, a point, a direction, parameters that control the rate of fall off

Area Light Sources

Light source occupies a 2-D area (usually a polygon or disk)
Generates soft shadows

Extended Light Sources

Spherical Light Source
Generates soft shadows

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Hard Shadow and Soft Shadow

Lecture 15

Average color from all different rays

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Spot Light Source

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Spotlights in use at a music performance

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Point, Directional and Spot Light Source

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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

Glossy (散射) reflection, glossy refraction

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i.e,

Ambient : 周圍的, 環境的

Diffuse: 漫射

Specular: 反射的,鏡射

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Lambert's Cosine Law

Ideal diffuse reflectors reflect light according to Lambert's cosine law, (there are sometimes called Lambertian reflectors). Lambert's law states that the reflected energy from a small surface area in a particular direction is proportional to cosine of the angle between that direction and the surface normal. Lambert's law determines how much of the incoming light energy is reflected. Remember that the amount energy that is reflected in any one direction is constant in this model. In other words the reflected intensity is independent of the viewing direction. The intensity does however depend on the light source's orientation relative to the surface, and it is this property that is governed by Lambert's law.

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Glossy (散射) reflection, glossy refraction

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Computing Diffuse Reflection

The angle between the surface normal and the incoming light ray is called the angle of incidence and we can express a intensity of the light in terms of this angle.

The I_light term represents the intensity of the incoming light at the particular wavelength (the wavelength determines the light's color). The k_d term represents the diffuse reflectivity of the surface at that wavelength.

In practice we use vector analysis to compute cosine term indirectly. If both the normal vector and the incoming light vector are normalized (unit length) then diffuse shading can be computed as follows:

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Diffuse Lighting Examples

We need only consider angles from 0 to 90 degrees. Greater angles (where the dot product is negative) are blocked by the surface, and the reflected energy is 0. Below are several examples of a spherical diffuse reflector with a varying lighting angles.

Why do you think spheres are used as examples when shading?

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Diffuse Lighting Examples

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Specular Reflection

A second surface type is called a specular reflector. When we look at a shiny surface, such as polished metal or a glossy car finish, we see a highlight, or bright spot. Where this bright spot appears on the surface is a function of where the surface is seen from. This type of reflectance is view dependent.

At the microscopic level a specular reflecting surface is very smooth, and usually these microscopic surface elements are oriented in the same direction as the surface itself. Specular reflection is merely the mirror reflection of the light source in a surface. Thus it should come as no surprise that it is viewer dependent, since if you stood in front of a mirror and placed your finger over the reflection of a light, you would expect that you could reposition your head to look around your finger and see the light again. An ideal mirror is a purely specular reflector. In order to model specular reflection we need to understand the physics of reflection.

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Non-ideal Reflectors

Snell's law, however, applies only to ideal mirror reflectors. Real materials, other than mirrors and chrome tend to deviate significantly from ideal reflectors. At this point we will introduce an empirical model that is consistent with our experience, at least to a crude approximation.

In general, we expect most of the reflected light to travel in the direction of the ideal ray. However, because of microscopic surface variations we might expect some of the light to be reflected just slightly offset from the ideal reflected ray. As we move farther and farther, in the angular sense, from the reflected ray we expect to see less light reflected.

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Phong Illumination

One function that approximates this fall off is called the Phong Illumination model. This model has no physical basis, yet it is one of the most commonly used illumination models in computer graphics.

The cosine term is maximum when the surface is viewed from the mirror direction and falls off to 0 when viewed at 90 degrees away from it. The scalar n_shiny controls the rate of this fall off.

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Effect of the n_shinycoefficient

The diagram below shows the how the reflectance drops off in a Phong illumination model. For a large value of the n_shiny coefficient, the reflectance decreases rapidly with increasing viewing angle.

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Specular Reflection

Glossiness of surfaces

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Computing Phong Illumination

The V vector is the unit vector in the direction of the viewer and the R vector is the mirror reflectance direction. The vector R can be computed from the incoming light direction and the surface normal:

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Blinn & Torrance Variation

Jim Blinn introduced another approach for computing Phong-like illumination based on the work of Ken Torrance. His illumination function uses the following equation:

In this equation the angle of specular dispersion is computed by how far the surface's normal is from a vector bisecting the incoming light direction and the viewing direction.

On your own you should consider

how this approach and the previous

one differ.

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It is faster than computing by Phong illumination

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Phong Examples

The following spheres illustrate specular reflections as the direction of the light source and the coefficient of shininess is varied.

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Putting it all together Phong Illumination Model�

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https://andyzeng.github.io/basicshading

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OpenGL Reflectance Model

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Emission

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OpenGL �Lighting

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OpenGL �Material

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OpenGL Mathematical Model

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s = (L^+V^)/|L^+V^|

Jim Blinn’s method

shininess

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Steps in OpenGL shading

Enable shading and select model
Specify normals
Specify material properties
Specify lights

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Normals

In OpenGL the normal vector is part of the state
Set by glNormal*()

glNormal3f(x, y, z);
glNormal3fv(p);

Usually we want to set the normal to have unit length so cosine calculations are correct

Length can be affected by transformations
Note the scale does not preserved length
glEnable(GL_NORMALIZE) allows for autonormalization at a performance penalty

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Normal for Triangle

p₁

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p₀

p₂

plane n ·(p - p₀ ) = 0

n = (p₁- p₀) ×(p₂- p₀)

normalize n ← n/ |n|

Note that right-hand rule determines outward face

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Enabling Shading

Shading calculations are enabled by

glEnable(GL_LIGHTING)
Once lighting is enabled, glColor() ignored

Must enable each light source individually

glEnable(GL_LIGHTi) i=0,1…..

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Defining a Point Light Source

For each light source, we can set an RGB for the diffuse, specular, and ambient parts, and the position

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GL float diffuse0[]={1.0, 0.0, 0.0, 1.0};

GL float ambient0[]={1.0, 0.0, 0.0, 1.0};

GL float specular0[]={1.0, 0.0, 0.0, 1.0};

Glfloat light0_pos[]={1.0, 2.0, 3,0, 1.0};

glEnable(GL_LIGHTING);

glEnable(GL_LIGHT0);

glLightv(GL_LIGHT0, GL_POSITION, light0_pos);

glLightv(GL_LIGHT0, GL_AMBIENT, ambient0);

glLightv(GL_LIGHT0, GL_DIFFUSE, diffuse0);

glLightv(GL_LIGHT0, GL_SPECULAR, specular0);

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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 (i.e., point light source)

If w =0.0, we are specifying a parallel source with the given direction vector (i.e. direction light source)

The coefficients in the distance terms are by default a=1.0 (constant terms), b=c=0.0 (linear and quadratic terms). Change by

a= 0.80;

glLightf(GL_LIGHT0, GLCONSTANT_ATTENUATION, a);

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Spotlights

Use glLightv to set

Direction GL_SPOT_DIRECTION

Cutoff GL_SPOT_CUTOFF

Attenuation GL_SPOT_EXPONENT

Proportional to cos^αφ

−θ

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Global Ambient Light

Ambient light depends on color of light sources

A red light in a white room will cause a red ambient term that disappears when the light is turned off

OpenGL allows a global ambient term that is often helpful

glLightModelfv(GL_LIGHT_MODEL_AMBIENT, global_ambient)

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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 are also part of the OpenGL state and match the terms in the Phong model

Set by glMaterialv()

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GLfloat ambient[] = {0.2, 0.2, 0.2, 1.0};

GLfloat diffuse[] = {1.0, 0.8, 0.0, 1.0};

GLfloat specular[] = {1.0, 1.0, 1.0, 1.0};

GLfloat shine = 100.0

glMaterialf(GL_FRONT, GL_AMBIENT, ambient);

glMaterialf(GL_FRONT, GL_DIFFUSE, diffuse);

glMaterialf(GL_FRONT, GL_SPECULAR, specular);

glMaterialf(GL_FRONT, GL_SHININESS, shine);

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Light Material Tutorial

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Controlling a Light’s Position

Modelview matrix affects a light’s position

Different effects based on when position is specified

eye coordinates
world coordinates
model coordinates

Push and pop matrices to uniquely control a light’s position

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As mentioned previously, a light’s position is transformed by the current ModelView matrix when it is specified. As such, depending on when you specify the light’s position, and what’s in the ModelView matrix, you can obtain different lighting affects.

In general, there are three coordinate systems where you can specify a light’s position/direction

1) Eye coordinates - which is represented by an identity matrix in the ModelView. In this case, when the light’s position/direction is specified, it remains fixed to the imaging plane. As such, regardless of how the objects are manipulated, the highlights remain in the same location relative to the eye.

2) World Coordinates - when only the viewing transformation is in the ModelView matrix. In this case, a light’s position/direction appears fixed in the scene, as if the light were on a lamppost.

3) Model Coordinates - any combination of viewing and modeling transformations is in the ModelView matrix. This method allows arbitrary, and even animated, position of a light using modeling transformations.

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Light Position Tutorial

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Front and Back Faces

The default is shade only front faces which works correct for convex objects
If we set two sided lighting, OpenGL will shaded both sides of a surface
Each side can have its own properties which are set by using GL_FRONT, GL_BACK, or GL_FRONT_AND_BACK in glMaterialf

back faces not visible

back faces visible

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Emissive Term

We can simulate a light source in OpenGL by giving a material an emissive component
This color is unaffected by any sources or transformations

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GLfloat emission[] = 0.0, 0.3, 0.3, 1.0);

glMaterialf(GL_FRONT, GL_EMISSION, emission);

Emission

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Transparency

Material properties are specified as RGBA values
The A value can be used to make the surface translucent
The default is that all surfaces are opaque regardless of A
Later we will enable blending and use this feature

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Transparent Image overlay(Alpha blending)

Medical Volume Rendering

https://learnopencv.com/alpha-blending-using-opencv-cpp-python/

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Efficiency

Because material properties are part of the state, if we change materials for many surfaces, we can affect performance
We can make the code cleaner by defining a material structure and setting all materials during initialization

We can then select a material by a pointer

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typedef struct materialStruct {

GLfloat ambient[4];

GLfloat diffuse[4];

GLfloat specular[4];

GLfloat shineness;

} MaterialStruct;

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Polygonal Shading

Shading calculations are done for each vertex

Vertex colors become vertex shades

By default, vertex colors are interpolated across the polygon

glShadeModel(GL_SMOOTH);

If we use glShadeModel(GL_FLAT); the color at the first vertex will determine the color of the whole polygon

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GL_FLAT

GL_SMOOTH

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Normals and OpenGL

You must supply per-vertex normal vectors if you enable lighting computations

A common oversight - all surfaces are black and may be invisible

Before specifying each vertex, specify a color and a normal vector:

glColor4f(r, g, b, a) defines a color, with many variants

glNormal3f(x, y, z) defines a normal, with many variants

Chapters 2, 4 and 5 of the OpenGL programming guide have many examples

glBegin(GL_QUADS);

glColor3f(1,1,1);

glNormal3f(0,0,1);

glVertex3f(1,1,0);

glColor3f(1,1,1);

glNormal3f(0,0,1);

glVertex3f(-1,1,0);

glColor3f(1,1,1);

glNormal3f(0,0,1);

glVertex3f(-1,-1,0);

glColor3f(1,1,1);

glNormal3f(0,0,1);

glVertex3f(1,-1,0);

glEnd();

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More Normals and OpenGL

Specifying fewer colors and normals

OpenGL uses the notion of a current color and a current normal

The current normal is applied to all vertices up to the next normal definition

glBegin(GL_QUADS);

glColor3f(1,1,1);

glNormal3f(0,0,1);

glVertex3f(1,1,0);

glVertex3f(-1,1,0);

glVertex3f(-1,-1,0);

glVertex3f(1,-1,0);

glEnd();

Normalizing normals

Normal vectors must be unit vectors for lighting to work correctly (they must be normalized)
By default, vectors are not normalized for you
Causes problems with scaling transformations, but OK for translations and rotations
glEnable(GL_NORMALIZE) or glEnable(GL_RESCALE_NORMAL) will fix it for you, but they are expensive and slow rendering

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OpenGL: Local Shading Models

Local shading models provide a way to determine the intensity and color of a point on a surface

The models are local because they don’t consider other objects at all

We use them because they are fast and simple to compute

They do not require knowledge of the entire scene, only the current piece of surface

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OpenGL: Approximations for Speed

The viewer direction, V, and the light direction, L, depend on the surface position being considered, x

Distant light approximation:

Assume L is constant for all x

Good approximation if light is distant, such as sun

Distant viewer approximation

Assume V is constant for all x

Rarely good, but only affects specularities

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OpenGL Model

Allows emission, E: Light being emitted by surface

Allows separate light intensity for diffuse and specular

Ambient light can be associated with light sources

Allows spotlights that have intensity that depends on outgoing light direction

Allows attenuation of light intensity with distance

Can specify coefficients in multiple ways

Too many variables and commands to present in class

The OpenGL programming guide goes through it all

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OpenGL Commands (1)

glMaterial{if}(face, parameter, value)

Changes one of the coefficients for the front or back side of a face (or both sides)

glLight{if}(light, property, value)

Changes one of the properties of a light (intensities, positions, directions, etc)

There are 8 lights: GL_LIGHT0, GL_LIGHT1, …

glLightModel{if}(property, value)

Changes one of the global light model properties (global ambient light, for instance)

glEnable(GL_LIGHT0) enables GL_LIGHT0

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OpenGL Commands (2)

glColorMaterial(face, mode)

Causes a material property, such as diffuse reflectance coefficient, to track the current glColor()

Speeds things up, and makes coding easier

glEnable(GL_LIGHTING) turns on lighting

Don’t use specular intensity if you don’t have to

It’s expensive - turn it off by giving 0,0,0 as specular color of light

Don’t forget normals

Many other things to control appearance

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Where do we Illuminate?

To this point we have discussed how to compute an illumination model at a point on a surface. But, at which points on the surface is the illumination model applied? Where and how often it is applied has a noticeable effect on the result.

Illuminating can be a costly process involving the computation of and normalizing of vectors to multiple light sources and the viewer.

For models defined by collections of polygonal facets or triangles:

Each facet has a common surface normal
If the light is directional then the diffuse contribution is constant across the facet
If the eye is infinitely far away and the light is directional then the specular contribution is constant across the facet.

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Phong Illumination Model

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Ray Tracing

Ray-casting: one ray from center of projection through each pixel in image plane

Illumination

Phong (local as before)
Shadow rays
Specular reflection
Specular transmission

(3) and (4) are recursive

https://en.wikipedia.org/wiki/Ray_tracing_(graphics)

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Ray-tracing

https://courses.cs.washington.edu/courses/cse457/10sp/projects/trace/

With source code

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Refraction

Index of refraction is relative speed of light

Snell’s law

η_l = index of refraction for upper material

η_t = index of refraction for lower material

[U = θ]

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Ray tracing� Example

Saito, Saturn Ring

Trace Secondary Shadow Ray(s) to all light(s)

Color = Visible ? Illumination Model : 0 ;

Note: return 0 (i.e. black color)

if it is in shadow

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https://graphics.stanford.edu/courses/cs148-10-summer/docs/2006--degreve--reflection_refraction.pdf

https://en.wikipedia.org/wiki/Snell%27s_law

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