Introduction to 3D GraphicsIntroduction to 3D Graphics

Lecture 1: Illusions and the Lecture 1: Illusions and the Fine Art of ApproximationFine Art of Approximation

Anthony SteedAnthony Steed

University College LondonUniversity College London

OutlineOutline

About the CourseAbout the Course Anatomy of an IllusionAnatomy of an Illusion

– EnvironmentEnvironment– Light transport and interactionLight transport and interaction– Reception at the eyeReception at the eye

The Painter’s Method The Painter’s Method – Ray-castingRay-casting– ApproximationsApproximations

OutlineOutline

About the CourseAbout the Course Anatomy of an IllusionAnatomy of an Illusion

– EnvironmentEnvironment– Light transport and interactionLight transport and interaction– Reception at the eyeReception at the eye

The Painter’s Method The Painter’s Method – Ray-castingRay-casting– ApproximationsApproximations

EnvironmentEnvironment

A description of a space consisting of A description of a space consisting of objectsobjects

Objects have Objects have description description and and statestate Description consists of Description consists of behaviourbehaviour, ,

geometry geometry and and appearanceappearance Geometry must be described relative to Geometry must be described relative to

a a co-ordinate frameco-ordinate frame State defines the object at a particular State defines the object at a particular

moment in timemoment in time

Radiometry - Radiometry - How does light How does light propagate in the real world?propagate in the real world?

700nm 400nm

pure light

spectral distribution

white light

Life and Death of a PhotonLife and Death of a Photon

EmissionEmission

ReflectionReflection

AbsorptionAbsorption

Lighting is a Global Lighting is a Global ProblemProblem

That is, if you consider any point in That is, if you consider any point in the environment, it receives light the environment, it receives light from all aroundfrom all around

Surfaces are Rarely Surfaces are Rarely MirrorsMirrors

Specular surfaceSpecular surface

Diffuse SurfaceDiffuse Surface

Some Simplifying Some Simplifying AssumptionsAssumptions

Wavelength independenceWavelength independence– No fluorescenceNo fluorescence

Time invarianceTime invariance– No phosphorescenceNo phosphorescence

Light transport in a vacuumLight transport in a vacuum– No participating mediaNo participating media

Objects are isotropicObjects are isotropic– Reflectance characteristics are Reflectance characteristics are

constant over the surfaceconstant over the surface

Photometry - Photometry - How do we see How do we see light?light?

Physiology of Eye Physiology of Eye ResponseResponse

6 million cones in the fovea6 million cones in the fovea– cones sense red green or blue lightcones sense red green or blue light– colour perception region is very smallcolour perception region is very small

120 million rods over the whole 120 million rods over the whole eyeeye– peripheral visionperipheral vision– motion sensitivemotion sensitive

Colour ResponseColour Response

ConesCones A = “Red”A = “Red” B = “Green”B = “Green” C = “Blue”C = “Blue”

Assumption for Real-Time Assumption for Real-Time GraphicsGraphics

Ignore “real” spectral distributionsIgnore “real” spectral distributions Instead calculate at three Instead calculate at three

wavelengths, Red, Green and Blue wavelengths, Red, Green and Blue that monitors providethat monitors provide

Obviously this is a gross Obviously this is a gross approximationapproximation– Really should find the spectrum for each Really should find the spectrum for each

point calculate the closest RGB valuepoint calculate the closest RGB value

RGB Colour ModelRGB Colour Model

WHITE

MAGENTA (1,0,1)RED (1,0,0)

BLACK

GREEN (0,1,0) CYAN (0,1,1)

BLUE (0,0,1)

YELLOW (1,1,0)

Colour MatchingColour Matching

How much R,G,B do you need to make a particular “pure” colour?

OutlineOutline

About the CourseAbout the Course Anatomy of an IllusionAnatomy of an Illusion

– EnvironmentEnvironment– Light transport and interactionLight transport and interaction– Reception at the eyeReception at the eye

The Painter’s Method The Painter’s Method – Ray-castingRay-casting– ApproximationsApproximations

Painting Through a Painting Through a WindowWindow

COPView Window (showing pixels)

COP = Centre of Projection

Major Concepts of Major Concepts of GraphicsGraphics

Separation of Scene Specification, Viewing and Rendering

– Scene is modelled independent of any view

– Views are unconstrained

– There are many possible rendering methods given a scene and a view

Major Concepts of Major Concepts of GraphicsGraphics

View volume

– The extent of the pixels on the screen and the COP define a pyramid

– Clipping is the process of removing anything from the scene that is not the view volume

Major Concepts of Major Concepts of GraphicsGraphics

Aliasing Aliasing – Pixels are square and only Pixels are square and only sample sample the the

actual lightactual light

Combating AliasingCombating Aliasing

Send several rays through each pixelSend several rays through each pixel– Stochastic sampleStochastic sample– Regular sample (full-screen anti-aliasing)Regular sample (full-screen anti-aliasing)

Stochastic sample is “correct” since it Stochastic sample is “correct” since it removes regularityremoves regularity

But only regular sample is easy with But only regular sample is easy with the rendering pipelinethe rendering pipeline

Major Concepts of Major Concepts of GraphicsGraphics

Perspective ProjectionPerspective Projection– Image size depends on distanceImage size depends on distance

COP

Major Concepts of Major Concepts of GraphicsGraphics

LightingLighting– Ray-casting is the simple partRay-casting is the simple part– Determining the colour of the pixel is Determining the colour of the pixel is

hard for all the reasons described hard for all the reasons described earlierearlier

– Theoretically we have to calculate all Theoretically we have to calculate all incoming lightincoming light

– In practice we will consider only In practice we will consider only local local illuminationillumination - light received directly - light received directly from light sourcesfrom light sources

SummarySummary

Taken a brief look at the general Taken a brief look at the general problem of doing visual simulationproblem of doing visual simulation

Reviewed the limits of human responseReviewed the limits of human response Given an over-view of the simulation Given an over-view of the simulation

process and the concepts ofprocess and the concepts of– Scene, view, renderingScene, view, rendering– AliasingAliasing– ProjectionProjection– LightingLighting

Future WorkFuture Work

To DevelopTo Develop– Mathematics of scene descriptionMathematics of scene description– Geometric descriptionsGeometric descriptions– Lighting modelsLighting models– Move from ray-cast to forward Move from ray-cast to forward

projectionprojection Stages in the graphics pipelineStages in the graphics pipeline