CS 445 / 645Introduction to Computer Graphics

Lecture 18Lecture 18

AntialiasingAntialiasing

Lecture 18Lecture 18

AntialiasingAntialiasing

Environment Mapping

Used to model a object that reflects surrounding textures Used to model a object that reflects surrounding textures to the eyeto the eye• Polished sphere reflects walls and ceiling texturesPolished sphere reflects walls and ceiling textures

• Cyborg in Terminator 2 reflects flaming destructionCyborg in Terminator 2 reflects flaming destruction

Texture is distorted fish-eye view of environmentTexture is distorted fish-eye view of environment

Spherical texture mapping creates texture coordinates Spherical texture mapping creates texture coordinates that correctly index into this texture mapthat correctly index into this texture map

Used to model a object that reflects surrounding textures Used to model a object that reflects surrounding textures to the eyeto the eye• Polished sphere reflects walls and ceiling texturesPolished sphere reflects walls and ceiling textures

• Cyborg in Terminator 2 reflects flaming destructionCyborg in Terminator 2 reflects flaming destruction

Texture is distorted fish-eye view of environmentTexture is distorted fish-eye view of environment

Spherical texture mapping creates texture coordinates Spherical texture mapping creates texture coordinates that correctly index into this texture mapthat correctly index into this texture map

Sphere Mapping

Blinn/Newell Lattitude Mapping

Cube Mapping

The q-coordinate

Remember, texture coordinate interpolation is linearRemember, texture coordinate interpolation is linear

Texture coordinates Texture coordinates can contain an can contain an optional q-parameteroptional q-parameter

q scales texture q scales texture coordinates by coordinates by dividing each dividing each coordinate by qcoordinate by q

This captures perspective transformationsThis captures perspective transformations

Remember, texture coordinate interpolation is linearRemember, texture coordinate interpolation is linear

Texture coordinates Texture coordinates can contain an can contain an optional q-parameteroptional q-parameter

q scales texture q scales texture coordinates by coordinates by dividing each dividing each coordinate by qcoordinate by q

This captures perspective transformationsThis captures perspective transformations

Z – into the scene

Imageplane

Multitexturing

Pipelining of multiple texture applications to one Pipelining of multiple texture applications to one polygonpolygon

The results of each texture unit application is The results of each texture unit application is passed to the next texture unit, which adds its passed to the next texture unit, which adds its effectseffects

More bookkeeping is required to pull this offMore bookkeeping is required to pull this off

Pipelining of multiple texture applications to one Pipelining of multiple texture applications to one polygonpolygon

The results of each texture unit application is The results of each texture unit application is passed to the next texture unit, which adds its passed to the next texture unit, which adds its effectseffects

More bookkeeping is required to pull this offMore bookkeeping is required to pull this off

Antialiasing

What is a pixel?

A pixel is not…A pixel is not…

• A boxA box

• A diskA disk

• A teeny tiny little lightA teeny tiny little light

A pixel is a pointA pixel is a point

• It has no dimensionIt has no dimension

• It occupies no areaIt occupies no area

• It cannot be seenIt cannot be seen

• It can have a coordinateIt can have a coordinate

A pixel is not…A pixel is not…

• A boxA box

• A diskA disk

• A teeny tiny little lightA teeny tiny little light

A pixel is a pointA pixel is a point

• It has no dimensionIt has no dimension

• It occupies no areaIt occupies no area

• It cannot be seenIt cannot be seen

• It can have a coordinateIt can have a coordinate

A pixel is more than a point, it is a sample

Samples

Most things in the real world are Most things in the real world are continuouscontinuous

Everything in a computer is Everything in a computer is discretediscrete

The process of mapping a continuous function to a The process of mapping a continuous function to a discrete one is called discrete one is called samplingsampling

The process of mapping a continuous variable to a The process of mapping a continuous variable to a discrete one is called discrete one is called quantizationquantization

Rendering an image requires sampling and Rendering an image requires sampling and quantizationquantization

Most things in the real world are Most things in the real world are continuouscontinuous

Everything in a computer is Everything in a computer is discretediscrete

The process of mapping a continuous function to a The process of mapping a continuous function to a discrete one is called discrete one is called samplingsampling

The process of mapping a continuous variable to a The process of mapping a continuous variable to a discrete one is called discrete one is called quantizationquantization

Rendering an image requires sampling and Rendering an image requires sampling and quantizationquantization

Samples

Samples

Line Segments

We tried to sample a line segment so it would map We tried to sample a line segment so it would map to a 2D raster displayto a 2D raster display

We quantized the pixel values to 0 or 1We quantized the pixel values to 0 or 1

We saw stair steps, or jaggiesWe saw stair steps, or jaggies

We tried to sample a line segment so it would map We tried to sample a line segment so it would map to a 2D raster displayto a 2D raster display

We quantized the pixel values to 0 or 1We quantized the pixel values to 0 or 1

We saw stair steps, or jaggiesWe saw stair steps, or jaggies

Line Segments

Instead, quantize to many shadesInstead, quantize to many shades

But what sampling algorithm is used?But what sampling algorithm is used?

Instead, quantize to many shadesInstead, quantize to many shades

But what sampling algorithm is used?But what sampling algorithm is used?

Area SamplingShade pixels according to the area covered by thickened Shade pixels according to the area covered by thickened

lineline

This is This is unweightedunweighted area sampling area sampling

A rough approximation formulated by dividing each pixel A rough approximation formulated by dividing each pixel into a finer grid of pixelsinto a finer grid of pixels

Shade pixels according to the area covered by thickened Shade pixels according to the area covered by thickened lineline

This is This is unweightedunweighted area sampling area sampling

A rough approximation formulated by dividing each pixel A rough approximation formulated by dividing each pixel into a finer grid of pixelsinto a finer grid of pixels

Unweighted Area Sampling

Primitive cannot affect intensity of pixel if it does Primitive cannot affect intensity of pixel if it does not intersect the pixelnot intersect the pixel

Equal areas cause equal intensity, regardless of Equal areas cause equal intensity, regardless of distance from pixel center to areadistance from pixel center to area

Primitive cannot affect intensity of pixel if it does Primitive cannot affect intensity of pixel if it does not intersect the pixelnot intersect the pixel

Equal areas cause equal intensity, regardless of Equal areas cause equal intensity, regardless of distance from pixel center to areadistance from pixel center to area

Weighted Area Sampling

Unweighted sampling colors two pixels identically Unweighted sampling colors two pixels identically when the primitive cuts the same area through when the primitive cuts the same area through the two pixelsthe two pixels

Intuitively, pixel cut through the center should be Intuitively, pixel cut through the center should be more heavily weighted than one cut along more heavily weighted than one cut along cornercorner

Unweighted sampling colors two pixels identically Unweighted sampling colors two pixels identically when the primitive cuts the same area through when the primitive cuts the same area through the two pixelsthe two pixels

Intuitively, pixel cut through the center should be Intuitively, pixel cut through the center should be more heavily weighted than one cut along more heavily weighted than one cut along cornercorner

Weighted Area Sampling

Weighting function, W(x,y)Weighting function, W(x,y)

• specifies the contribution of primitive passing through specifies the contribution of primitive passing through the point (x, y) from pixel centerthe point (x, y) from pixel center

Weighting function, W(x,y)Weighting function, W(x,y)

• specifies the contribution of primitive passing through specifies the contribution of primitive passing through the point (x, y) from pixel centerthe point (x, y) from pixel center

x

IntensityW(x,y)

Images

An image is a 2D function An image is a 2D function II(x, y) that specifies (x, y) that specifies intensity for each point (x, y)intensity for each point (x, y)

An image is a 2D function An image is a 2D function II(x, y) that specifies (x, y) that specifies intensity for each point (x, y)intensity for each point (x, y)

Sampling and Image

Our goal is to convert the continuous image to a Our goal is to convert the continuous image to a discrete set of samplesdiscrete set of samples

The graphics system’s display hardware will The graphics system’s display hardware will attempt to reconvert the samples into a attempt to reconvert the samples into a continuous image: continuous image: reconstructionreconstruction

Our goal is to convert the continuous image to a Our goal is to convert the continuous image to a discrete set of samplesdiscrete set of samples

The graphics system’s display hardware will The graphics system’s display hardware will attempt to reconvert the samples into a attempt to reconvert the samples into a continuous image: continuous image: reconstructionreconstruction

Point Sampling an Image

Simplest sampling is on a gridSimplest sampling is on a grid

Sample dependsSample dependssolely on valuesolely on valueat grid pointsat grid points

Simplest sampling is on a gridSimplest sampling is on a grid

Sample dependsSample dependssolely on valuesolely on valueat grid pointsat grid points

Point Sampling

Multiply sample grid by image intensity to obtain a Multiply sample grid by image intensity to obtain a discrete set of points, or samples.discrete set of points, or samples.

Multiply sample grid by image intensity to obtain a Multiply sample grid by image intensity to obtain a discrete set of points, or samples.discrete set of points, or samples.

Sampling Geometry

Some objects missed entirely, others poorly Some objects missed entirely, others poorly sampledsampled

Some objects missed entirely, others poorly Some objects missed entirely, others poorly sampledsampled

Sampling Errors

Fixing Sampling Errors

SupersamplingSupersampling• Take more than one sample for each pixel and combine Take more than one sample for each pixel and combine

themthem

– How many How many samples is samples is enough?enough?

– How do we How do we know no know no features are features are lost?lost?

SupersamplingSupersampling• Take more than one sample for each pixel and combine Take more than one sample for each pixel and combine

themthem

– How many How many samples is samples is enough?enough?

– How do we How do we know no know no features are features are lost?lost?

150x15 to 100x10

200x20 to 100x10

300x30 to 100x10

400x40 to 100x10

Unweighted Area Sampling

Average supersampled pointsAverage supersampled points

All points are weighted equallyAll points are weighted equally

Average supersampled pointsAverage supersampled points

All points are weighted equallyAll points are weighted equally

Weighted Area Sampling

Points in pixel are weighted differentlyPoints in pixel are weighted differently

• Flickering occurs as object movesFlickering occurs as object movesacross displayacross display

Overlapping regions eliminates flickerOverlapping regions eliminates flicker

Points in pixel are weighted differentlyPoints in pixel are weighted differently

• Flickering occurs as object movesFlickering occurs as object movesacross displayacross display

Overlapping regions eliminates flickerOverlapping regions eliminates flicker

How is this done today?Full Screen Antialiasing

Nvidia GeForce2Nvidia GeForce2• OpenGL: render image 400% larger and supersampleOpenGL: render image 400% larger and supersample

• Direct3D: render image 400% - 1600% largerDirect3D: render image 400% - 1600% larger

Nvidia GeForce3Nvidia GeForce3• MultisamplingMultisampling but with fancy overlaps but with fancy overlaps

– Don’t render at higher resolutionDon’t render at higher resolution

– Use one image, but combine values of neighboring pixelsUse one image, but combine values of neighboring pixels

– Beware of recognizable combination artifactsBeware of recognizable combination artifacts

Human perception of patterns is too goodHuman perception of patterns is too good

Nvidia GeForce2Nvidia GeForce2• OpenGL: render image 400% larger and supersampleOpenGL: render image 400% larger and supersample

• Direct3D: render image 400% - 1600% largerDirect3D: render image 400% - 1600% larger

Nvidia GeForce3Nvidia GeForce3• MultisamplingMultisampling but with fancy overlaps but with fancy overlaps

– Don’t render at higher resolutionDon’t render at higher resolution

– Use one image, but combine values of neighboring pixelsUse one image, but combine values of neighboring pixels

– Beware of recognizable combination artifactsBeware of recognizable combination artifacts

Human perception of patterns is too goodHuman perception of patterns is too good

GeForce3

MultisamplingMultisampling

• After each pixel is rendered, write pixel value to two After each pixel is rendered, write pixel value to two different places in frame bufferdifferent places in frame buffer

MultisamplingMultisampling

• After each pixel is rendered, write pixel value to two After each pixel is rendered, write pixel value to two different places in frame bufferdifferent places in frame buffer

GeForce3 - Multisampling

After rendering two copies of entire frameAfter rendering two copies of entire frame

• Shift pixels of Sample #2 left and up by ½ pixelShift pixels of Sample #2 left and up by ½ pixel

• Imagine laying Sample #2 (red) over Sample #1 (black)Imagine laying Sample #2 (red) over Sample #1 (black)

After rendering two copies of entire frameAfter rendering two copies of entire frame

• Shift pixels of Sample #2 left and up by ½ pixelShift pixels of Sample #2 left and up by ½ pixel

• Imagine laying Sample #2 (red) over Sample #1 (black)Imagine laying Sample #2 (red) over Sample #1 (black)

GeForce3 - Multisampling

Resolve the two samples into one image by Resolve the two samples into one image by computing average between each pixel from computing average between each pixel from Sample 1 (black) and the four pixels from Sample 1 (black) and the four pixels from Sample 2 (red) that Sample 2 (red) that are 1/ sqrt(2) pixels are 1/ sqrt(2) pixels awayaway

Resolve the two samples into one image by Resolve the two samples into one image by computing average between each pixel from computing average between each pixel from Sample 1 (black) and the four pixels from Sample 1 (black) and the four pixels from Sample 2 (red) that Sample 2 (red) that are 1/ sqrt(2) pixels are 1/ sqrt(2) pixels awayaway

GeForce3 - Multisampling

No AA MultisamplingNo AA MultisamplingNo AA MultisamplingNo AA Multisampling

GeForce3 - Multisampling

• 4x Supersample Multisampling

ATI Smoothvision

ATI SmoothVisionATI SmoothVision• Programmer selects Programmer selects

samping patternsamping pattern

ATI SmoothVisionATI SmoothVision• Programmer selects Programmer selects

samping patternsamping pattern

3dfx

3dfx Multisampling3dfx Multisampling• 2- or 4-frame shift and average2- or 4-frame shift and average

Tradeoffs?Tradeoffs?

3dfx Multisampling3dfx Multisampling• 2- or 4-frame shift and average2- or 4-frame shift and average

Tradeoffs?Tradeoffs?