Technische Universität München Computer Graphics SS 2014 Graphics Effects Rüdiger Westermann Lehrstuhl für Computer Graphik und Visualisierung

Technische Universität München

Computer Graphics

Computer GraphicsSS 2014

Graphics Effects

Rüdiger WestermannLehrstuhl für Computer Graphik und Visualisierung


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Advanced graphics effects

Effects which are not provided natively by the rasterization based graphics pipeline• Scene reflections • Shadows


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Reflections• Note the difference between local illumination

and scene reflection– Local illumination considers the reflection of direct light– Scene reflection considers the reflection of the scene

• Problem: which scene point reflects in an object point


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• Scene reflections using rasterization based pipeline– Rasterization based pipeline projects scene onto the image

plane– Camera position is projection center for all scene parts, ie.

single view projection– To simulate scene reflections, the scene has to be rendered

from multiple views, ie. from each object point that reflects towards the viewer

– Requires many rendering passes,and is too costly in general


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• Planar reflections– Reflect the scene about a planar mirror

• Basic algorithm: flip scene through the mirror and re-render


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• Reflect of scene at the mirror plane requires finding the reflection matrix

• Re-render reflected scene but restrict drawing to the pixels through which the mirror is seen

Mirror

Reflected scene

Wall


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• The reflection matrix– p[3]: point on plane– n[3]: plane normal– d: n·p

– Multiply reflection matrix with modeling matrix

1000

]2[2]2[]2[21]1[]2[2]0[]2[2

]1[2]2[]1[2]1[]1[21]0[]1[2

]0[2]2[]0[2]1[]0[2]0[]0[21

ndnnnnnn

ndnnnnnn

ndnnnnnn


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• Restrict drawing of the flipped scene to the pixels through which the mirror is seen

http://en.wikipedia.org/wiki/File:Mirror.jpg




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• Restricted drawing via the stencil test– Stencil buffer: stores for each pixel a bit-mask – A stencil test can be performed after the depth test

for each fragment

Color buffer

Depth buffer

Stencil buffer


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• Typical use of the stencil buffer/test

stencil = 1

InitializeStencil buffer Render pass 1 Render pass 2

Test: ref = 0;

stencil == ref

Test:ref = 1;

stencil == ref


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Mirror rendering algorithm

A) Initialize modelview matrix, enable depth/stencil testing B) Render mirror to mask all covered pixels in stencil buffer

mask = 1


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C) Multiply modeling matrix with reflection matrix to flip the sceneD) Render scene where pixels have been mask*

*clip everything in front of the mirror plane using a clip-plane


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E) Reset modeling matrix to initial stateF) Render scene where pixels have not been mask

+ =





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• Non planar reflections


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• Environment mapping: – Simulate an infinitely small reflecting sphere in the center of

the scene to be reflected

– Compute (or measure) and store in a texture the incoming light at the sphere for all directions

– At run-time, for a given reflection vector look-up the stored light from the texture and use as fragment color

Θ

(𝜃 ,𝜙)

Spherical coordinates

(𝜃 ,𝜙)

http://www.pauldebevec.com/ReflectionMapping/miller.html

http://3.bp.blogspot.com/-ha0s0bOogfk/T5_RZMBhRqI/AAAAAAAAAVo/N94YzMLig08/s1600/lat_long_lens.jpeg


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• Cube maps– An alternative to environment maps which can be generated

very efficiently using rendering functionality

– Captures the incoming light through 6 faces of a cube centeredat the environment center

– Generated by rendering the scene 6 times from the cube center, with the respective cube face being the viewport


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• See alsohttp://en.wikipedia.org/wiki/Cube_mapping

http://en.wikipedia.org/wiki/Cube_mapping

http://en.wikipedia.org/wiki/Cube_mapping


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• Cube map is stored in 6 2D textures

• Cube map access:– For each fragment compute the reflection vector R– The largest component of R selects the cube face– By dividing the other components through the largest, the 2D

texture coordinate in the selected face is given


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Cube map texture coordinates:• Compute reflection vector

major axis s t ma ---------------------------------------------------------------------------- positive_X negative_X positive_Y negative_Y positive_Z negative_Z

s = ( s/|ma| + 1 ) / 2 and t = ( t/|ma| + 1 ) / 2


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• Cube map examples


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Effects which are not provided natively by the rasterization based graphics pipeline• Scene reflections • Shadows


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• Why shadows?


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• Shadows and visibility: Remember, the depth-test resolves visibility on a per-fragment basis– z-buffer stores minimum z-value of all fragments

projecting into the same pixel– Testing during fragment processing

• Frustum (perspective) transformation preserves z-ordering

• Incremental z-value update (if fragment is closer to near plane than current one)

– Visibility is with respect to the viewer


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z-buffer algorithm:colorbuffer BackgroundColorz-buffer 1

foreach polygonforeach fragmentx,y // generated by the

rasterizerz = fragmentx,y.depth

if z < z-buffer[x,y] then // depth testz-buffer[x,y] = zcolorbuffer[x,y] = fragmentx,y.color


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• Visibility: which objects can be seen from the view point?• Shadows: which objects can be seen from the light source?

© Bertrand Clerc Designhttp://bertrandclerc.com/interaction/shades-of-vauxhall/

http://bertrandclerc.com/interaction/shades-of-vauxhall/




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• Shadow mapping– Simulates shadows in two rendering passes

(1)Renders the scene from the light source position to determine all fragments which are not in shade, ie. which are seen by the light

(2)Renders the scene from the camera position and tests each generated fragment whether it was seen or not in the first pass- If it was seen in the first pass it receives light,

otherwise it is in shade and its color is darkened- The test simply checks whether in the first pass

there was a fragment closer to the light than the current fragment


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• Shadow mapping – the 1st pass– Since we need the fragments from the first pass to perform

the test in the second pass, these fragments have to be stored

– What we store is the distances of these fragments to the light source, which is simply the content of the deph buffer after the first pass


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• Shadow mapping – the 1st pass:the depth buffer after the first rendering pass is stored in a texture map – the shadow map– In DX this can be realized by a pixel shader that computes the

fragments depth values and writes these values into a texture resource instead of the color buffer

– First, set up the description of the texture, then create that texture, and finally use the texture to setup a render target view

– The so-generated texture can then be made accessible to a pixel shader in the second rendering pass


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• Shadow mapping – the 2nd pass renders from the camera– A pixel shader computes the fragments distances to the light

source– The shader also projects the fragments towards the light source

into the shadow map – the fragments coordinate after projection is used as texture coordinate into the shadow map

LightDepth of fragment

to light source


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• Shadow mapping – the 2nd pass– Finally, the shader compares the fragments depth with the

depth stored in the shadow map and decides whether it is in shade or not

Light

Depth in shadow map

Depth of fragment

to light source


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• Shadow mapping– Requires one additional rendering pass per light source– Can only be used in combination with point light sources– Artefacts can occur due to the resolution of the shadow map

4096x40961024x1024


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Shadow volumes

• Shadow volumes– Relies on a geometric representation of the spatial

region that is shadowed by an object– Shadow polyhedra is generated by projecting the

objects´ shilouette edges (as seen from the light source) onto the shadowed surface and connecting the respective points

– Shadow algorithm now tests whether object points, ie. fragments, are inside or outside a shadow volume


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Shadow volumes

• Shadow volumes


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Shadow volumes

• Shadow volume geometry

Without shadows Shadow volume Final scene


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Shadow volumes

• When is a point in shadow?• Shadow volume algorithm [Crow 1977]

– Intersect the rays from the eye with shadow volume boundaries

– For each ray • Start with counter = 0, and increment/decrement

the counter at every shadow volume front/back face• If ray hits an object and counter == 0, then the

object point is not in shadow


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Shadow volumes

• Algorithm [Heidmann 91]1. Render the unlit scene and clear the stencil buffer2. Loop over all light sources

• Clear stencil buffer, disable depth write and color write but leave depth test enabled

• Render front-facing polygons of the shadow volume and increment the stencil where they pass the depth test

• Render back-facing polygons of the shadow volume and decrement the stencil where they pass the depth test

• Render the lit scene where stencil value = 0 (with additive blending)

• Note: – Stencil value classifies fragments as shadowed or unshadowed

• Shadowed pixels end up with non-zero stencil


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Shadowing object Light

source

Eyeposition

zero

zero

+1

+1+2 +2

+3

Unshadowedobject

+ ---+ +

Shadow Volume Count = +1+1+1-1-1-1 = 0

Illuminated (Behind Shadow Volumes)


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source

Eyeposition

zero

zero

+1

+1+2 +2

+3

Shadowedobject

+ -+ +

Shadow Volume Count = +1+1+1-1 = 2

Shadowed (inside Shadow Volumes)


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source

Eyeposition

zero

zero

+1

+1+2 +2

+3

Unshadowedobject

Shadow Volume Count = 0

Illuminated (before Shadow Volumes)

Documents

Technische Universität München Computer Graphics SS 2014 Graphics Effects Rüdiger Westermann Lehrstuhl für Computer Graphik und Visualisierung