computer graphics environment mapping mirroring.ppt

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Computer Graphics Inf4/MSc

Computer Graphics

Lecture 8

Transparency, Mirroring




2

Today

• Environment Mapping

• Mirroring




Environment Maps

• Simple yet powerful method to generate reflections

• Simulate reflections by using the reflection vector to indexa spherical texture map at "infinity".

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




Environment Mapping Example

Terminator II




Cubic Mapping

• The most popular method

• 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




Examples




Calculating the reflection vector

• Normal vector of the surface : N

• Incident Ray : I

• Reflection Ray: R

• N,I,R all normalizedR = I -2 N ( N . I )

• The texture coordinate is basedon the reflection vector

• Assuming the origin of thevector 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

• (0.3, 0.2, 0.8) face in +zdirection




Indexing Cubic Maps – How do you decide which texture coordinates to use?

• Divide by the coordinate with the largest magnitude

• Now ranging [-1,1]

• Remapped to a value between 0 and 1.

(0.3,0.2,0.8) ((0.3/0.8 +1)*0.5, ((0.2/0.8

+1)*0.5) = (0.6875, 0.625)




A Sphere Map

• A mapping between the reflection vector and a

circular texture

• Prepare an image/texture in which the

environment is mapped onto a sphere




Sphere Mapping

• To generate the map:

– Take a photograph of a shiny sphere

– Mapping a cubic environment map onto a sphere

– For synthetic scenes, you can use ray tracing




Sphere Map

• Compute the reflection vector at the surface of the object

• Find the corresponding texture on the sphere map

• Use the texture to color the surface of the object




Indexing Sphere Maps• Given the reflection vector R (Rx,Ry,Rz)

( Rx,Ry,Rz )

• (u,v) on the spherical map

1,0 vu

2221

2

v,

2

1

2

z y x

y x

R R Rmm

R

m

Ru




Indexing Sphere Maps

• The normal vector is the sum of the

reflection vector and the eye vector

Normalization of the vector gives

If the normal is on a sphere of radius 1, itsx,y coordinates are also location on the

sphere map

Finally converting them to make their range

[0,1]

m

R

m

R

m

R

R R Rm

z y x

z y x

1,,

1222

n

1,,( z y x R R RN

2221

1

2v,

2

1

2

z y x

y x

R R Rm

m

R

m

Ru

m

R

m

R

m

R

R R Rm

z y x

z y x

1,,

1222

n




Non-linear Mapping• Problems:

– Highly non-uniform sampling

– Highly non-linear mapping

• Linear interpolation of texture coordinates picks up the wrong

texture pixels – Do per-pixel sampling or use high resolution polygons

Can only view from one direction

Correct Linear




Refractive Environment Mapping

• When simulating effects

mapping the refracted

environment ontotranslucent 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




Snell’s Law

• i: incoming vector

• t: refraction vector

))((1

,)(

where)(

2

1

r wr wk

r w

n

nr

k wr

ni

nit




19

Today

• Environment Mapping

• Mirroring




Planar Reflections (Flat Mirrors)

• Basic idea: Drawing a scene with mirrors!

– We need to draw all the stuff around the mirror

– We need to draw the stuff in the mirror, reflected,

without drawing over the things around the mirror




Reflecting Objects

• If the mirror passes through the

origin, and is aligned with a

coordinate axis, then just

negate appropriate coordinate• For example, if a reflection

plane has a normal n=(0,1,0)

and passes the origin, the

reflected vertices can beobtained by scaling matrix

S(1,-1,1)

Mirror Wall




Reflecting Objects

• If the reflection plane passes

a point p and has a normal

vector n, you translate and

rotate the coordinate system,negate, and move back to

the original coordinate

system

Mirror Wall Mirror

p

)()()1,1,1()()( 1pnnp

T RS RT




Rendering Reflected First

(Using the depth buffer(Z-buffer))• First pass:

– Render the reflected scene without mirror, depth test on• Second pass:

– Disable the color buffer, and render the mirror polygon

– Now the depth buffer of the mirror region is set to the mirror’ssurface• Third Pass:

– Enable the color buffer again – Render the original scene, without the mirror – Depth buffer stops from writing over things in mirror




Reflection Example

The color buffer after the final pass




Reflected Scene First (issues)

• Objects behind the mirror cause

problems:

– The reflected area outside the

mirror region is just overwritten

by the objects in the front

– unless there is a wall, they will

remain visible

• Doesn’t do:

– Reflections of mirrors in

mirrors (recursive reflections)

– Multiple mirrors in one scene

(that aren’t seen in each other)




We need to use the “Stencil Buffer”

• The stencil buffer acts like a paint stencil - it lets somefragments through but notothers

• It stores multi-bit values

• You specify two things: – The test that controls which

fragments get through – The operations to perform on the

buffer when the test passes or fails



Computer Graphics Inf4/MScStencil Tests

• You give an operation, a

reference value, and a mask

• Operations:

– Always let the fragment

through – Never let the fragment

through

– Logical operations between

the reference value and the

value in the buffer: <, <=, =,

!=, >, >=




Stencil Operations• Specify three different operations

– If the stencil test fails

– If the stencil passes but the depth test fails

– If the stencil passes and the depth test passes

• Operations are: – Keep the current stencil value

– Zero the stencil

– Replace the stencil with the reference value – Increment the stencil

– Decrement the stencil

– Invert the stencil (bitwise)




mirror

Reflection Example




Normal first, reflected area next

• First pass: – Render the scene without the mirror

• For each mirror – Second pass:

• Clear the stencil, disable the write to thecolour buffer, render the mirror, settingthe stencil to 1 if the depth test passes

– Third pass:• Clear the depth buffer with the stencil

active, passing things inside the mirror only

• Reflect the world and draw using thestencil test. Only things seen in the mirror will be drawn

• Combine it with the scene made during thefirst pass

The stencil buffer after the second pass

Rendering the mirrored scene into the stencil

active area




Multiple mirrors

• Can manage multiple mirrors

– Render normal view, then do other

passes for each mirror

• A recursive formulation exists for mirrors that see other mirrors

– After rendering the reflected area

inside the mirror surface, render the

mirrors inside the mirror surface, and

so on




Another approach

• You can reflect the viewpoint aboutthe mirror to see what is seen in themirror

• Add a clipping plane at the plane of

the mirror, remove everything that isrendered on the same side of theviewer

• Render the reflected scene and add itto the original scene

Mirror Wall




Readings

• Foley 16.5-6• Real-time Rendering 2, Chapter 5.7, 6.10

computer graphics environment mapping mirroring.ppt

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