computer graphics inf4/msc computer graphics lecture 11 texture mapping

Computer Graphics Inf4/MSc

Computer Graphics

Lecture 11

Texture Mapping


The Problem:

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

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Today

• Texture mapping – Texture interpolation– Antialiasing : bilinear interpoation, Mipmaps,

• Common texture coordinates mapping

• Bump mapping

• Environment mapping

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Texture mapping.

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

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Texture mapping.

• Image is ‘pasted’ onto a polygon.• Image is called a Texture map, it’s pixels are often

referred as a Texels and have coordinates (u,v)• Texture coordinates are defined for each vertex of

the polygon and interpolated across the polygon.

v

u

v

u

y

x


Photo-textures

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Computer Graphics Inf4/MSc Finding the texture coords of

arbitrary pixels inside the triangle

y

• Use the barycentric coordinates explained in Lecture 9


Texture Interpolation• Specify a texture coordinate (u,v) at each vertex• Can we just linearly interpolate the values in screen

space?

(0,0) (1,0)

(0,1)

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


• Use a rectangular mesh instead of a triangular mesh or

• Increase the number of polygons

How do we deal with it?

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Today



• Bump mapping


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Aliasing

• Happens when – The camera is zoomed too much into the textured

surface (magnification)– Several texels covering a pixel’s cell (minification)

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Texture Magnification

• Zooming into a surface with a texture• Methods to determine the color of each pixel

– Nearest neighbour – Bilinear interpolation

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

– Nearest neighbour (using the color at the center of the pixel)– Bilinear blending – Mipmapping


Nyquist Limit

• The texture frequency (ft) should be no greater than half the sample frequency (fs)

• ft <= 0.5 fs• Say it is a 2x2 texture :

– Wavelength 2 texels wide– Frequency ft = 1 / 2 – 1 / 2 x 2 <= fs , i.e., – To properly display this texture on a screen, the

frequency must then be at least 2x 1/2, i.e., at least one pixel per texel

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MIP mapMultum In Parvo = Many things in a small place

Produce a texture of multiple resolutionsUse the resolution according to the number of texels in one pixel

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Today



• Bump mapping


Computer Graphics Inf4/MSc Common Texture Coordinate

Mappings

• Orthogonal• Cylindrical• Spherical • Perspective

Projection• Texture

Chart


Demo movie


Texture Mapping & Illumination

• Texture mapping can be used to alter some or all of the constants in the illumination equation: – pixel color, diffuse color, alter the normal, ….

Phong’s Illumination Model

Constant Diffuse Color Diffuse Texture Color Texture used as Label Texture used as Diffuse Color

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Today



• Bump mapping



What's Missing?• What's the difference between a real

brick wall and a photograph of the wall texture-mapped onto a plane?

• What happens if we change the lighting or the camera position?


Bump Mapping• Use textures to alter the surface normal

– Does not change the actual shape of the surface– Just shaded as if it were a different shape

Sphere w/Diffuse Texture Swirly Bump Map Sphere w/Diffuse Texture & Bump Map


Bump Mapping

• Treat the texture as a single-valued height function• Compute the normal from the partial derivatives in

the texture


Another Bump Map Example

Cylinder w/Diffuse Texture Map

Bump Map

Cylinder w/Texture Map & Bump Map


What's Missing?

• There are no bumps on the silhouette of a bump-mapped object


Displacement Mapping

• Use the texture map to actually move the surface point

• The geometry must be displaced before visibility is determined

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Today



• Bump mapping



Environment Maps

• We can simulate reflections by using the direction of the reflected ray to index a spherical texture map at "infinity".

• Assumes that all reflected rays begin from the same point.


Example


Environment Mapping Example

Terminator II

Computer Graphics Inf4/MSc Cubic Mapping

• The map resides on the surfaces of a cube around the object– align the faces of the cube with the

coordinate axes

• To generate the map:• Using methods such as ray tracing

– Or, take 6 photos of a real environment with a camera in the object’s position : much easier


Calculating the reflection vector

• Normal vector of the surface : N• Incident Ray : I• Reflection Ray: R

R = I -2 N ( N . I )

• The texture coordinate is based on the reflection vector

• Assuming the origin of the vector is always in the center of the cube environment map


Indexing Cubic Maps• Assume you have R and the cube’s faces

are aligned with the coordinate axes, and have texture coordinates in [0,1]x[0,1]– How do you decide which face to use?

• The reflection vector coordinate with the largest magnitude

• (0.8, 0.3, 0.2) face in +x direction

– How do you decide which texture coordinates to use?

• Divide by the coordinate with the largest magnitude

• Remapped to a value between 0 and 1.

(0.8,0.3,0.2) ((0.3/0.8 +1)*0.5, ((0.2/0.8 +1)*0.5) = (0.6875, 0.625)


A Sphere Map


Sphere Mapping• To generate the map:

– Take a photograph of a shiny sphere – For synthetic scenes, you can use ray tracing, or

warping a cubic environment map


Indexing Sphere Maps• Given the reflection vector R

• (s,t) on the spherical map

• Problems:– Highly non-uniform sampling

– Highly non-linear mapping

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222 12

2

1 ,

2

1

zyx

yx

RRRm

m

Rt

m

Rs


Non-linear Mapping

• Linear interpolation of texture coordinates picks up the wrong texture pixels– Use small polygons!

Correct Linear


Example


Refractive Environment Mapping

• When simulating effects mapping the refracted environment onto translucent materials such as ice or glass, we must use Refractive Environment Mapping


Snell’s Law

• When light passes through a boundary between two materials of different density (air and water, for example), the light’s direction changes.

• The direction follows Snell’s Law

• We can do environment mapping using the refracted vector T

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Summary



• Bump mapping


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Computer Graphics Inf4/MSc Assignment

• Rendering a head / teapot

• You may use the 3D rendering function of OpenGL, but better marks are given if you do the illumination by yourself

• Extra marks given for – Textures,

– Environment mapping,

– Shadows, mirrors (extra objects)

– Global illumination (ray tracing, etc)

– Make sure the program runs on DICE

computer graphics inf4/msc computer graphics lecture 11 texture mapping

Documents

texture mapping slide

texture magnification

texture sourcewhat

texture methods

common texture coordinates

edge slide

geometry slide

texture coordinate u