computer graphics - discrete techniques -

Computer GraphicsComputer Graphics- Discrete Techniques -- Discrete Techniques -

Hanyang University

Jong-Il Park

Division of Electrical and Computer Engineering, Hanyang University

ObjectivesObjectives Buffers and pixel operations Mapping methods

Texture mapping Environmental (reflection) mapping

Variant of texture mapping Bump mapping

Solves flatness problem of texture mapping Blending Anti-aliasing


BufferBufferDefine a buffer by its spatial resolution (n x m)

and its depth (or precision) k, the number of bits/pixel

pixel


OpenGL Frame BufferOpenGL Frame Buffer


OpenGL BuffersOpenGL Buffers Color buffers can be displayed

Front Back Auxiliary Overlay

Depth Accumulation

High resolution buffer Stencil

Holds masks


Writing in BuffersWriting in Buffers Conceptually, we can consider all of memory as a

large two-dimensional array of pixels We read and write rectangular block of pixels

Bit block transfer (bitblt) operations The frame buffer is part of this memory

frame buffer(destination)

writing into frame buffer

sourcememory


The Limits of Geometric ModelingThe Limits of Geometric Modeling

Although graphics cards can render over 10 million polygons per second, that number is insufficient for many phenomena Clouds Grass Terrain Skin


Modeling an OrangeModeling an Orange

Consider the problem of modeling an orange (the fruit) Start with an orange-colored sphere

Too simple Replace sphere with a more complex shape

Does not capture surface characteristics (small dimples) Takes too many polygons to model all the dimples


Modeling an Orange (2)Modeling an Orange (2) Take a picture of a real orange, scan it, and “paste”

onto simple geometric model This process is known as texture mapping

Still might not be sufficient because resulting surface will be smooth Need to change local shape Bump mapping


Three Types of MappingThree Types of Mapping Texture Mapping

Uses images to fill inside of polygons

Environment (reflection mapping) Uses a picture of the environment for texture maps Allows simulation of highly specular surfaces

Bump mapping Emulates altering normal vectors during the rendering

process


Texture MappingTexture Mapping

geometric model texture mapped


Environment Mapping Environment Mapping


Bump MappingBump Mapping


Where does mapping take place?Where does mapping take place? Mapping techniques are implemented at the

end of the rendering pipeline Very efficient because few polygons make it past the

clipper


Is it simple?Is it simple? Although the idea is simple---map an image to a

surface---there are 3 or 4 coordinate systems involved

2D image

3D surface


Coordinate SystemsCoordinate Systems

Parametric coordinates May be used to model curves and surfaces

Texture coordinates Used to identify points in the image to be mapped

Object or World Coordinates Conceptually, where the mapping takes place

Window Coordinates Where the final image is really produced



parametric coordinates

texture coordinatesworld coordinates window coordinates


Mapping FunctionsMapping Functions Basic problem is how to find the maps Consider mapping from texture coordinates to a point

on a surface Appear to need three functions

x = x(s,t)y = y(s,t)z = z(s,t)

But we really want to go the other way

s

t

(x,y,z)


Backward MappingBackward Mapping We really want to go backwards

Given a pixel, we want to know to which point on an object it corresponds

Given a point on an object, we want to know to which point in the texture it corresponds

Need a map of the form s = s(x,y,z)t = t(x,y,z)

Such functions are difficult to find in general


Two-part mappingTwo-part mapping One solution to the mapping problem is to first map

the texture to a simple intermediate surface Example: map to cylinder


Box MappingBox Mapping Easy to use with simple orthographic projection Also used in environment maps


Second MappingSecond Mapping Map from intermediate object to actual object

Normals from intermediate to actual Normals from actual to intermediate Vectors from center of intermediate

intermediateactual


AliasingAliasing Point sampling of the texture can lead to aliasing

errors

point samples in u,v (or x,y,z) space

point samples in texture space

miss blue stripes


Area AveragingArea Averaging

A better but slower option is to use area averaging

Note that preimage of pixel is curved

pixelpreimage


Basic StragegyBasic StragegyThree steps to applying a texture

1. specify the texture read or generate image assign to texture enable texturing

2. assign texture coordinates to vertices Proper mapping function is left to application

3. specify texture parameters wrapping, filtering



s

t

x

y

z

image

geometry display


Based on parametric texture coordinates glTexCoord*() specified at each vertex

s

t1, 1

0, 1

0, 0 1, 0

(s, t) = (0.2, 0.8)

(0.4, 0.2)

(0.8, 0.4)

A

B C

a

bc

Texture Space Object Space

Mapping a TextureMapping a Texture


Typical CodeTypical Code

glBegin(GL_POLYGON);glColor3f(r0, g0, b0); //if no shading usedglNormal3f(u0, v0, w0); // if shading usedglTexCoord2f(s0, t0);glVertex3f(x0, y0, z0);glColor3f(r1, g1, b1);glNormal3f(u1, v1, w1);glTexCoord2f(s1, t1);glVertex3f(x1, y1, z1);

.

.glEnd();


Magnification and MinificationMagnification and Minification

Texture PolygonMagnification Minification

PolygonTexture

More than one texel can cover a pixel (minification) ormore than one pixel can cover a texel (magnification)

Can use point sampling (nearest texel) or linear filtering( 2 x 2 filter) to obtain texture values


Environment mappingEnvironment mapping Environmental mapping is way to create the

appearance of highly reflective surfaces without ray tracing which requires global calculations

Examples: The Abyss, Terminator 2 Is a form of texture mapping

Supported by OpenGL and Cg


ExampleExample


Reflecting the EnvironmentReflecting the Environment

V

N

R


Mapping to a sphereMapping to a sphere

V

N

R


Cube MapCube Map


IssuesIssues Must assume environment is very far from object

(equivalent to the difference between near and distant lights)

Object cannot be concave (no self reflections possible)

No reflections between objects Need a reflection map for each object Need a new map if viewer moves


Bump mappingBump mapping


Modeling an OrangeModeling an Orange Consider modeling an orange Texture map a photo of an orange onto a surface

Captures dimples Will not be correct if we move viewer or light We have shades of dimples rather than their correct

orientation Ideally we need to perturb normal across surface of

object and compute a new color at each interior point


Bump Mapping (Blinn)Bump Mapping (Blinn) Consider a smooth surface

n

p


Rougher VersionRougher Version

n’

p

p’


Displacement FunctionDisplacement Function

p’ = p + d(u,v) n

d(u,v) is the bump or displacement function

|d(u,v)| << 1


Approximating the NormalApproximating the Normal

n’ = p’u p’v

≈ n + (∂d/∂u)n pv + (∂d/∂v)n pu

• The vectors n pv and n pu lie in the tangent plane • Hence the normal is displaced in the tangent plane• Must precompute the arrays ∂d/ ∂u and ∂d/ ∂v

• Finally, we perturb the normal during shading


Image ProcessingImage Processing Suppose that we start with a function d(u,v) We can sample it to form an array D=[dij] Then ∂d/ ∂u ≈ dij – di-1,j

and ∂d/ ∂v ≈ dij – di,j-1 Embossing: multipass approach using

accumulation buffer


Eg. Bump mappingEg. Bump mapping


Opacity and TransparencyOpacity and Transparency Opaque surfaces permit no light to pass

through Transparent surfaces permit all light to pass Translucent surfaces pass some light translucency = 1 – opacity ()

opaque surface =1


Physical ModelsPhysical Models Dealing with translucency in a physically

correct manner is difficult due to the complexity of the internal interactions of light and

matter Using a pipeline renderer


Writing ModelWriting Model Use A component of RGBA (or RGB) color to

store opacity During rendering we can expand our writing

model to use RGBA values

destinationcomponent

blend

destination blending factor

source blending factor sourcecomponent

Color Buffer


Blending EquationBlending Equation

We can define source and destination blending factors for each RGBA component

s = [sr, sg, sb, s]

d = [dr, dg, db, d]

Suppose that the source and destination colors are b = [br, bg, bb, b]

c = [cr, cg, cb, c]

Blend as c’ = [br sr+ cr dr, bg sg+ cg dg , bb sb+ cb db , b s+ c d ]


FogFog We can composite with a fixed color and have

the blending factors depend on depth Simulates a fog effect

Blend source color Cs and fog color Cf by

Cs’=f Cs + (1-f) Cf

f is the fog factor Exponential Gaussian Linear (depth cueing)


Fog FunctionsFog Functions


OpenGL Fog FunctionsOpenGL Fog FunctionsGLfloat fcolor[4] = {……}:

glEnable(GL_FOG);glFogf(GL_FOG_MODE, GL_EXP);glFogf(GL_FOG_DENSITY, 0.5);glFOgv(GL_FOG, fcolor);


Line AliasingLine Aliasing Ideal raster line is one pixel wide All line segments, other than vertical and horizontal

segments, partially cover pixels Simple algorithms color only whole pixels Lead to the “jaggies” or aliasing Similar issue for polygons


Anti-AliasingAnti-Aliasing


Area Averaging Area Averaging

Use average area 1+2-12 as blending factor


OpenGL AntialiasingOpenGL Antialiasing Can enable separately for points, lines, or polygons

glEnable(GL_POINT_SMOOTH);glEnable(GL_LINE_SMOOTH);glEnable(GL_POLYGON_SMOOTH);

glEnable(GL_BLEND);glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);


Accumulation BufferAccumulation Buffer Compositing and blending are limited by

resolution of the frame buffer Typically 8 bits per color component

The accumulation buffer is a high resolution buffer (16 or more bits per component) that avoids this problem

Write into it or read from it with a scale factor Slower than direct compositing into the frame

buffer Application: Compositing, Image Filtering (convolution),

Whole scene anti-aliasing, Motion effects

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