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Texture

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Overview

• Introduction• Painted textures• Bump mapping• Environment mapping• Three-dimensional textures• Functional textures• Antialiasing textures• OpenGL details

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Introduction

• Few real objects are smooth• Textures can handle large repetitions

– Brick wall– Stripes

• Textures can handle small scale patterns– A brick’s roughness– Concrete– Wood grain

• Textures are typically two dimensional images of what is being simulated

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Painted Textures

• A mapping of locations on the object into locations in the texture

• The value from the texture replaces the diffuse component in the shading calculations

• If the texture is larger than the object, only part of the texture is used or the texture is shrunk

• If the object is larger than the texture, the texture is repeated across the object or the texture is stretched

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Painted Textures

• If the object location maps between texture locations, a value between them can be interpolated

f1 = fract(u)

f2 = fract(v)

T1 = (1.0 – f1) * texture[trunc(u)][trunc(v)] + f1 * texture[trunc(u)+1][trunc(v)]

T2 = (1.0 – f1) * texture[trunc(u)][trunc(v)+1] + f1 * texture[trunc(u)+1][trunc(v)+1]

result = (1.0 – f2) * T1 + f2 * T2

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Repeating Textures

• A texture can be repeated across an object with the equations:

ux Txxxx

repeatfractu ** min

minmax

vy Tyyyy

repeatfractv ** min

minmax

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Repeating Textures

• A repeated texture must be continuous along its edges to prevent obvious seams

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Painted Texture Problem

• The texture values don’t alter the specular highlights– Specular highlighting may be inconsistent with

the texture appearance

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Bump Mapping

• For a real bump, the surface normal changes when moving across the bump

• A similar appearance can be created if a similar change is made to the surface normal for a plane

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Bump Mapping

• In this case, the texture image is called a bump map

• The bump map is used to alter the surface normal

• The altered surface normal is used for the color calculations

NB = bump(u, v, N)RB = 2 * NB * (NB • V) – VCr = kar + IL * [kdr * L • NB + ks * (RB • V)n]Cg = kag + IL * [kdg * L • NB + ks * (RB • V)n]Cb = kab + IL * [kdb * L • NB + ks * (RB • V)n]

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Bump Mapping

• The bump function is based on the gradient of the bump map– The gradient is a measure of how much the bump map values

change at the chosen location• The modified normal is calculated using the gradients in

two directions (Bu and Bv) and two vectors tangent to the surface in those directions (Su and Sv)

• The parenthesized expression can also be multiplied by a factor to control the appearance of the size of the bumps

u

uv

v

vu

S

SB

S

SBNN

**'

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Bump Mapping Examples

• For the examples, the bump map is based on the product of the sine taken of the two coordinates:

sin(10*u*π/1024)*sin(10*v*π/1024)

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Bump Mapping Examples

• A bump mapped plane using factors of 1.0, 0.5, and 2.0

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Bump Mapping Problem

• Because the surface shape is not changed, “bumps” near the silhouette will not change the silhouette shape

• If a bump mapped object is rotated, bumps will disappear when they reach the object profile

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Displacement Mapping

• In displacement mapping, the object is subdivided into many very small polygons

• The texture values cause the vertices to be displaced in the direction of the surface normal

• In this case, thetexture actuallychanges the object shape

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Environment Mapping

• Environment mapping simulates reflective objects

• An environment map is a rendering of the scene from inside the reflective object

• The environment map is used to determine what would be seen in the reflection direction

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Environment Mapping

• The environment map can either be spherical or cube shaped– Spherical environment maps require a

calculation to convert the direction through the sphere into a two-dimensional matrix location

y

x

R

Ru arctan*

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2

1

2

1 zRv

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Environment Mapping

• A cube shaped environment map renders the scene from the center of the object onto the faces of a cube

• The component of the reflection vector with the largest absolute value determines theface the reflection vectorgoes through

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Environment Mapping

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Environment Mapping

• The location on the correct face is calculated by:

• Where a is the component of the reflection vector shown on the horizontal axis, b is the component shown for the vertical axis, and c is the component for the chosen face

c

cau

2

c

cbv

2

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Three-Dimensional Textures

• It is very difficult if not impossible to create a texture that can be wrapped around any irregularly shaped object without a visible discontinuity

• Where a two-dimensional texture is applied to the surface, an object can be thought to be carved out of a three-dimensional texture

• The storage requirements for a three-dimensional texture are extremely large

• Thus, three-dimensional textures are closely related to functional textures

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Functional Textures

• Instead of using a stored image as a texture, a functional texture uses a calculation based on the texture location

• Because the function will be continuous in every direction, the texture is continuous in every direction

• Instead of requiring space, these functional textures require computation time

• By changing how the texture is calculated, many different textures can be created

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Noise

• The beginning step to many functional textures is a noise function

• True white noise is highly random• For graphics, pseudo random noise that is

repeatable is important– With truly random noise, the

texture would change every time the image is rendered or for every scene of an animation

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Perlin Noise

• Perlin developed a noise function this is used in many Hollywood movies

• This noise function has:– No statistical variance when rotated– No statistical variance when translated– A narrow range of values

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Turbulence

• Typically the second step in functional textures is to build a turbulence function on top of the noise function

• The functional textures are then built on top of the turbulence function

• The turbulence function takes multiple samples of the noise function at many different frequencies

• Different researchers will frequently develop their own turbulence function

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Peachy’s Turbulence Function

float turb(float x, float y, float z, float minFreq,float

maxFreq)

{

float result = 0.0;

for (float freq = minFreq; freq < maxFreq; freq = 2.0*freq)

{

result += fabs( noise(x*freq, y*freq, z*freq ) / freq );

}

return result;

}

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Peachy’s Turbulence Results

• These samples have frequency ranges of [1.0, 4.0], [1.0, 16.0], and [1.0, 256.0]

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Perlin’s Turbulence Functionfloat turb(float x, float y, float z, float minFreq, float maxFreq){

float result = 0.0;x = x + 123.456;for (float freq = minFreq; freq < maxFreq; freq = 2.0*freq){

result += fabs( noise(x, y, z ) ) / freq;x *= 2.0;y *= 2.0;z *= 2.0;

}// return the result adjusted so the mean is 0.0return result-0.3;

}

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Perlin’s Turbulence Results

• These samples have frequency ranges of [1.0, 4.0], [1.0, 16.0], and [1.0, 256.0]

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Marble Texture

• The Perlin/Ebert marble function uses a turbulence value to determine a color for the location

void marble(float x, float y, float z, float color[3]){

float value = x + 3.0 * turb(x, y, z, minFreq, maxFreq);marbleColor( sin(π * value), color );

}

• There are variations in how the marbleColor function is implemented– Linear interpolation between a light and dark color– Spline based interpolation between a light and dark

color

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Linear Interpolation Marble Examples

• These samples have frequency ranges of [1.0, 4.0], [1.0, 16.0], and [1.0, 256.0]

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Spline Interpolation Marble Examples

• These samples have frequency ranges of [1.0, 4.0], [1.0, 16.0], and [1.0, 256.0]

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Spline Interpolation Marble Examples

• These samples have a frequency range of [1.0, 256.0] and have no multiplier and multipliers of 3 and 7

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Cosine Textures

• Based on summations of cosine curves

• Parameters in the equation provide control on result

• The two dimensional equation is:

N

iyGyyi

N

ixGxxi

AyC

AxCyxf

ii

ii

10

10

*cos**

*cos*),(

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Cosine Texture Parameters

• The value of N controls the number of cosine terms– Typically between 4 and 7

• The constants ΦGx ΦGy are global phase shifts that move the pattern

• The Ci terms change the amplitude of the various cosine components

• The A0 terms shift the pattern but are related to the Ci terms

• The ωx1 and ωy1 determine the number of times the pattern repeats

• The xi and yi

are phase values that are interdependent

with the base periods of x and y

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Number of Cosines

• These examples show the results of using 1, 4, and 7 cosines

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Global Phase Shift

• These examples with x global phase shifts of 0 and 150 show that the global phase shift moves the pattern

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Cosine Amplitude Ratio

• These examples show cosine amplitude ratios of 0.3535, 0.7070, and 1.414

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Cosine Offset

• These examples show cosine offset values of 0.5, 1.0, and 1.5

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Base Periods

• The first example has the same base period (256) for x and y, while the second has an x base period of 256 and a y base period of 512

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Base Period Ratio

• These examples have base period ratios of 1.5, 2.0, and 2.5

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Phase Shift Amplitude

• These examples have phase shift amplitudes of 0, π/4, π/2, and π

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Cosine Texture Results

• A cloud-like texture is possible with 4 cosine components, an x global offset of 200, a cosine amplitude ratio of 0.5, a phase shift amplitude of π/2, a cosine offset of 0.75, an x base period of 655, a y base period of 325, and a base period ratio of 1.7

• A bark-like texture is possible with 4 cosine components, a cosine amplitude ratio of 0.707, a cosine offset of 1.0, an x base period of 256, a y base period of 1216, and a base period ratio of 1.7

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Antialiasing Textures

• The frequency of an entity and the rate at which it is sampled can cause visible artifacts

• In this example, it appears that there are multiple textures used

• Aliasing causes these visible artifacts

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Aliasing Corrections

• Aliasing artifacts can be reduced by altering the sampling method

• Common techniques include– Supersampling– Supersampling with jittering– Inverse mapping

• Though the techniques are discussed relative to textures, they apply to other antialiasing applications

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Supersampling

• Multiple evenly spaced samples are taken from the texture for each location

• An average or weighted average is taken of these samples to produce the final result

• One weighted average uses 9 samples and the filter (weighting): 1 2 1

2 4 2

1 2 1

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Supersampling With Jittering

• Instead of taking evenly spaced samples, the sample locations are each shifted by a random amount

• This helps to disturb a regular sampling frequency

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Supersampling Examples

• Supersampling

• Supersampling with jittering

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Inverse Mapping

• The area of the pixel is projected back onto the object

• That object area is projected back into the texture

• Integrating or averaging the values in this area of the texture gives the final texture result to be used

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Inverse Mapping Example

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OpenGL Texture

• The steps to using texture in OpenGL are:– Create or load the texture into OpenGL– Enable texturing– Specify how the texture is to be used– Specify texture coordinates for polygon vertices or surface

corners

• OpenGL allows the programmer to specify if texture is to be added before or after the specular highlight

• OpenGL allows textures of varying resolutions to deal with aliasing problems

• OpenGL also has support for environment mapping

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Texture Coordinates

• The texture coordinates influence how the texture is applied

• Texture coordinates are in the range [0.0, 1.0]• If OpenGL is told to repeat the texture, values

outside of this range cause multiple copies of the texture to be used

• If OpenGL is told to clamp the coordinates, any values below the range will be set to 0.0 and any above the range will be set to 1.0

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Texture Coordinates

• In the first example, texture coordinates are in the range [0.0, 1.0]

• In the second example, texture coordinates are in the range [0.0, 0.5]

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Texture Coordinates

• By picking appropriate texture coordinates, two adjacent planes can be textured seamlessly

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Bézier Surface Texturing

• Bézier surfaces can be textured if points are also supplied for the four corner control points

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Specular Highlights

• OpenGL can include the specular component before texturing

• OpenGL can include the specular component after texturing