Computer Graphics Inf4/MSc Computer Graphics Lecture 9 Antialiasing, Texture Mapping

Computer Graphics Inf4/MSc

Computer Graphics

Lecture 9

Antialiasing, Texture Mapping


2

Today

• Texture mapping– Common texture coordinates mapping– Texture coordinates

• Antialiasing

• Antialiasing-textures


Texture Mapping : Why needed?

• We don't want to represent all this detail with colour / geometry


4

Texture mapping.

• Method of improving surface appearance by adding details on surface.

• Done at the rasterization stage


Photo-textures


Interpolating the uv coordinates

Again, we use baricentric Coordinates

u= α u1 + β u2 + γ u3

v = α v1 + β v2 + γ v3

Or scan conversion

u3 v3

u2 v2

u1 v1

Computer Graphics Inf4/MScWhat will the textured triangle

look like?

Computer Graphics Inf4/MSc Interpolation - What Goes

Wrong?

texture source what we get| what we want

• Linear interpolation in screen space:


Why does it happen?

• Uniform steps on the image plane does not correspond to uniform steps along the edge


How do we deal with it?• Use hyperbolic interpolation

– (u,v) cannot be linearly interpolated, but 1/w and (u/w, v/w) can

– w is the last component after the canonical view transformation

– A w is computed for every 3D point

10100

200

02

0

002

z

y

x

nf

fn

nf

nfbt

bt

bt

nlr

lr

lr

n

w

wz

wy

wx

p

p

p

Computer Graphics Inf4/MScTexture Mapping Examples

• Linear interpolation vs. Hyperbolic interpolation• Two triangles per square

Computer Graphics Inf4/MScIn what case hyperbolic interpolation

is essential? 1. ?

2. ?

Computer Graphics Inf4/MSc Common Texture Coordinate

Mappings• Orthogonal• Cylindrical• Spherical

Computer Graphics Inf4/MScTexture Mapping & Illumination

Texture mapping can be used to alter some or all of the constants in the illumination equation:

– pixel color, diffuse color


15

Today

• Texture mapping• Common texture coordinates mapping• Texture coordinates

• Antialiasing

• Antialiasing textures


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Anti-aliasing • Aliasing: distortion artifacts produced when representing a

high-resolution signal at a lower resolution.• Anti-aliasing : techniques to remove aliasing

Aliased polygons(jagged edges)

Anti-aliased polygons


Nyquist Limit

• The signal frequency (fsignal) should be no greater than half the sample frequency (fsample)

• fsignal < 0.5 fsample • In the top, fsignal = 0.8 fsample -> cannot reconstruct the original signal• In the bottom fsignal =0.5 fsample -> the original signal can be reconstructed

by slightly increasing the sampling rate


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Each pixel is subdivided (sub-sampled) into n regions, and each sub-pixel has a color;Compute the average color value

Screen-based Anti-aliasing

weight:

color sample:),,(

y)(x,at color pixel:),(

),,(),(1

i

n

ii

w

yxi

yx

yxiwyx

c

p

cp


Accumulation Buffer (A-Buffer)• Use a buffer that has the same resolution as

the original image• To obtain a 2x2 sampling of a scene, 4

images are made by shifting the buffer horizontally/vertically for half a pixel

• The results are accumulated and the final results are obtained by averaging

• Various sampling schemes are available

Pixel center

Subsampled point


Different Sampling Schemes



Accumulation Buffer (A-Buffer)• The lighting computation is usually done

only once per vertex• Not doing the lighting computation at each

sample point• The A-buffer’s focus is on the edge anti-

aliasing • Also useful for rendering transparent

objects, motion blur (will be covered later in the course)

Edges

Computer Graphics Inf4/MSc Stochastic Sampling• A scene can be produced of objects that are

arbitrarily small• A regular pattern of sampling will always

exhibit some sort of aliasing• By irregular sampling, the higher frequencies

appear in the image as noise rather than aliases• Humans are more sensitive to aliases than noise


Stochastic SamplingOne approach to solve this is to randomly sample over the pixelsJittering : subdivide into n regions of equal size and randomly sample inside each regionCompute the colour at the sample and averageCan precompute a table and recycle it or simply jitter on the fly


Comparison


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Today

• Texture mapping• Common texture coordinates mapping• Texture coordinates

• Antialiasing

• Antialiasing textures


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Aliasing of texturesHappens when the camera is zoomed too much into the textured surface (magnification)Several texels (pixels of the texture) covering a pixel’s cell (minification)


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Texture Magnification • Zooming too much into a surface with a texture • One texel covering many pixels


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Bilinear Interpolation

• Mapping the pixel centre to the uv coordinates• Computing the pixel colour by interpolating

the surrounding texel values


Bilinear Interpolation - 2• For (pu, pv), compute its (u,v) coordinates

by barycentric coordinates• u = pu – (int)pu, v = pv - (int)pv • xl = pu, xr = pu +1, yb = pv, yt = pv +1,

– (pu, pv) : the pixel centre mapped into the texture space

– b(pu,pv) : the colour at point pu, pv

– t(x,y) : the texel colour at (x,y)

– u = pu – (int)pu, v = pv - (int)pv


Texture MinificationWhich texture will cause more aliasing when mapped onto the

floor?


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Texture Minification• Many texels covering a pixel’s cell• Results in aliasing (remember Nyquist limit)• The artifacts are even more noticeable when the

surface moves • Solution

• Mipmapping


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MIP mapMultum In Parvo = Many things in a small place

Produce a texture of multiple resolutionsSwitch the resolution according to the number of texels in one pixel Select a level that the ratio of the texture and the pixel is 1:1


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Selecting the resolution in Mipmap

Map the pixel corners to the texture space Find the resolution that roughly covers the mapped quadrilateral

Apply a bilinear interpolation in that resolution, Or find the two surrounding resolutions and apply a trilinear

interpolation (also along the resolution axis)


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Texture Minification • Multiple textures in a single pixel• Solution:

• Nearest neighbour Bilinear blending Mipmapping


Readings

• Chapter 5.1-2 of Real-Time Rendering Second edition – http://books.google.co.uk/books?id=mOKEfBT

w4x0C&printsec=frontcover&source=gbs_v2_summary_r&cad=0#v=onepage&q=&f=false

• “Hyperbolic Interpolation” IEEE Computer Graphics and Applications, vol12, no.4, 89-94, 1992

Documents

Computer Graphics Inf4/MSc Computer Graphics Lecture 9 Antialiasing, Texture Mapping