What is Computer Graphics and What is Computer Graphics and Image Processing?Image Processing?

All visual computer output depends on computer graphics and image processing.

3D computer graphics is used in visualisation, simulation, CAD and entertainment.

Course StructureCourse Structure

Rendering: producing a ‘realistic’ image from a scene description

Modelling: defining scene objects mathematically.

Animation: controlling the evolution of objects over time.

Lectures: Rendering (4), Modelling (5), Animation (1)

Seminars:Guest Postgrads (2)Honours Groups (6)

Aims of RenderingAims of Rendering

Criteria for Rendering:Speed: Some applications (e.g. flight simulation) require

interactive (> 10 Hz) rendering updates.

Aesthetics: A subjective value attached by the viewer to the image. Difficult to measure.

Visual Realism: An image that captures the effects of light interacting with objects (‘photorealism’).

Information: How effectively the image conveys the required information.

These criteria are often in conflict.

Ray TracingRay Tracing

A powerful alternative to polygon scan-conversion techniques.

Given a set of 3D objects, shoot a ray from the eye through the centre of every pixel and see what it hits.

Enables: reflection, shadows, refraction, transparency.

Ray Tracing ExampleRay Tracing Example

From the Computer Animated Short Film “Tin Toy” (© Pixar)

Ray Tracing AlgorithmRay Tracing Algorithm

Select an eye point and a screen plane

FOR every pixel in the screen plane [num. pixels depends on image resolution]

determine the ray from the eye through the pixel’s centre

FOR every object in the scene [num. objects depends on scene size]

IF the object is intersected by the ray THEN

IF the intersection is the closest (so far) to the eye THEN

record the intersection point and object

ENDIF

ENDIF

ENDFOR

set pixel’s colour to that of the object at the closest intersection point

ENDFOR

Intersection of a ray with a sphereIntersection of a ray with a sphere

Sphere Ray (parametric):

Sphere (implicit):

Trick: substitute a parametric ray equation into an implicit sphere equation.

Derivation:

Result: real – two intersections, imaginary – no intersection, – one intersection

Cylinder, cone, torus are treated similarly

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a

bs

a

bs

acb

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Intersection of a ray with a polygonIntersection of a ray with a polygon

Plane: Ray: Plane: Derivation:

Does fall inside the polygon (check by clipping against its edges.

Box, polygon, polyhedron are treated as a set of bounded planes.

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ND

NOds

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Other implicit objects suited to Ray Other implicit objects suited to Ray TracingTracing

Quadrics: or Useful quadrics are the ellipsoid (sphere is a special

case), infinite cylinder and infinite cone. Various hyperbloids and parabloids are also defined by

these equations but they tend to be less useful.

Superquadrics:

Super-ellipsoids are the only ones used in practice. acts as a ‘pointiness’ parameter: more pointy,

more rounded (closer to a box), is octahedral.

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kczbyax nnn )()()(

n 2n2n1n

Ray Tracing: shadingRay Tracing: shading

Once , the intersection point of ray with the closest object has been found it is possible to:1. Find the object’s surface

normal at

2. Shoot rays from to all light sources

3. Calculate the diffuse and specular lighting at . Along with ambient illumination this gives the colour of the object at .

iP i

N iP

iP

iP

iP

Ray Tracing: shadowsRay Tracing: shadows

If an object blocks the ray from the intersection point to a light source then it is casting a shadow over that point.

Also need to watch out for self-shadowing.

Recursive Ray Tracing: reflectionRecursive Ray Tracing: reflection

By spawning secondary (recursive) rays from a point of intersection reflection, transparency and refraction can be simulated.

A new ray aligned with the angle of reflection enables perfect (mirror) reflection.

Each new ray provides a scaled (distance attenuated) contribution to the pixel colour.

Recursive Ray Tracing: refractionRecursive Ray Tracing: refraction

Objects can be totally or partially transparent This allows objects behind

the current one to be seen through it.

Light rays which intersect transparent objects can have their contribution scaled.

Transparent objects can have refractive indices Bending the rays as they pass

through the objects.

Supporting transparency and reflection requires that a ray be split into two parts.

Sampling in Ray TracingSampling in Ray Tracing

Single Point Shoot a single ray through the pixel’s centre. Prone to aliasing

problems.

Super-sampling for anti-aliasing Shoot multiple rays through the pixel and average the results. Can use a regular grid, random, jittered or Poisson disc

distribution of rays.

Adaptive super-sampling Shoot a few rays through the pixel, check the variance of the

resulting values. If sufficiently similar then stop. Otherwise, shoot some more rays.

Trade-off the objectionable artefacts of aliasing for the less objectionable artefacts of noise.

Distributed Ray TracingDistributed Ray Tracing

Super-sampling (and anti-aliasing) is only one reason for taking multiple samples per pixel. Many effects can be achieved by distributing multiple ray samples

over some range. Called distributed ray tracing. The term distributed refers to the

stochastic distribution of rays.

Examples of distributed ray tracing:1. Distribute the rays from a light source over an area. Allows area

light sources and produces soft shadows with penumbrae.

2. Distribute the camera position over an area. Allows simulation of a camera with a finite aperture lens and produces depth of field effects.

3. Distribute the samples in time. Produces motion blur effects on moving objects.

4. Distribute reflected rays over a range of directions. Can simulate imperfect specular reflection.

Distributed Ray Tracing: area lightsDistributed Ray Tracing: area lights

Light rays coming from an area light source are distributed.

If some are blocked then the point is in a penumbrae.

If all are blocked then the point is in umbrae.

Allows area light sources, in addition to point and directional light.

Improving EfficiencyImproving Efficiency

Ray tracing (especially when distributed or recursive) is computationally costly. Naively, require a minimum of

intersection tests.

A small proportion of objects are intersected by a given ray. So, quickly identifying non-intersected objects is important.

Speedups: Intersect bounding boxes or spheres first. Only need to test the full

object if the bounding sphere is intersected. Spatial subdivision. Group objects into cells. If a ray does not pass

through a particular cell it cannot intersect the objects belonging to that cell.

Use Visibility pre-processing to cull out all objects and polygons invisible along a particular viewing direction.

numobjectsresolution

Exercise: Recursive Ray TracingExercise: Recursive Ray Tracing

Assuming all objects are perfect reflectors and have ambient, diffuse and specular (Phong model) lighting, show all rays and vectors needed to calculate the shading at P.

Solution: Recursive Ray TracingSolution: Recursive Ray Tracing

[A] Primary Intersection [B] Secondary Intersection