[PPT] - Visualisatie BMT Rendering Arjan Kok a.j.f.kok@tue.nl 1 Lecture PowerPoint Presentation

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Visualisatie

BMT

Rendering Arjan Kok a.j.f.kok@tue.nl

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Lecture overview

Color
Rendering
Illumination

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Visualization pipeline

Raw Data Derived Data Abstract Visualization Object Displayable Image Data Enrichment/Enhancement Visualization Mapping Rendering

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Color

The electromagnetic spectrum

visible to humans contains wavelengths ranging from about 400 to 700 nm

Light we see consists of

different intensities of these wavelengths

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Color

The human eye contains three

receptors (cones): for red, green and blue

Color we see is a combination
f these

Response curves

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Color systems

Color system
A way to represent color on a computer
Most used:
RGB
HSV

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RGB-model

3 primary colors: Red, Green and Blue
Color cube:
Color = point in cube
Additive:
C = rR + gG + bB

R G B

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HSV-model

More user oriented: based on

intuitive perception

Hue (0-1 or 0-360°)
Saturation (0-1)
Value (0-1)
Color is point in cone

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Rendering

How do I generate an image of a scene?
Problems:
World is complex (shape, light)
World is 3 dimensional, screen is 2 dimensional

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Subdivide problem

Geometric modeling
How do we define shape of objects?
Projection and hidden surface removal
How do we determine what is visible on screen and what

is not.

Shading
How do we model color, texture and contribution of

light?

Rasterization
Determine pixel values for visible objects

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Graphics pipeline

Geometric model Viewing Camera parameters Light sources, materials Shading Visible surface determination Rasterize Raster display

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Raster graphics

Currently “standard” for computer graphics
Screen is subdivided in grid of “squares”: picture elements
r pixels
Per pixel: n bits information
Resolution: size of grid and number of bits per pixel

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Raster graphics hardware

system bus system memory CPU display processor video controller

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

frame buffer monitor

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Visualization pipeline

Raw Data Derived Data Abstract Visualization Object Displayable Image Data Enrichment/Enhancement Visualization Mapping Rendering

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Graphics pipeline

Geometric model Viewing Camera parameters Light sources, materials Shading Visible surface determination Rasterize Raster display

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Viewing

Given a 3D model, how do we project this model on screen?
Camera model
Eye/view point:
From which point do we look to the scene?
Target point or viewing direction:
Where do we look at?
Viewing angles:
What lens do we use?

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The camera

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Graphics pipeline

Geometric model Viewing Camera parameters Light sources, materials Shading Visible surface determination Rasterize Raster display

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Why illumination

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Illumination

Illumination model
Illumination (and therefore color) of point on surface is

determined by simulation of light in scene

Illumination model is approximation of real light

transport

Shading method
determines for which points illumination is computed
determines how illumination for other points is

computed

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Illumination models

Model(s) needed for
Emission of light
Scattering light at surfaces
Reception on camera
Desired model requirement
Accurate
Efficient to compute

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Point light source

Emits light equally in all directions
Parameters
Intensity IL
Position P (px,py,pz)
Approximation for small light sources

P

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Direction light source

Emits light in one direction
Can be regarded as point light source at infinity
E.g. sun
Parameters
Intensity IL
Direction D (dx,dy,dz)

D

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Surface illumination

When light arrives at surface, it can be
Absorbed
Reflected
Transmitted

reflection transmission absorption

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Reflection model

Total intensity on point reflected in certain direction is

determined by:

Diffusely reflected light
Specularly reflected light
Reflection of ambient light

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Diffuse reflection

Incoming light is reflected equally in all directions
Amount of reflected light depends only on angle of incident

light viewer surface

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Diffuse reflection

Lambert’ law: Reflected energy from a surface is

proportional to the cosine of the angle of direction of incoming light and normal of surface

Id = kdILcos(θ) = kdIL (N•L)
kd is diffuse reflection coefficient

θ viewer surface

N L V

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Specular reflection

Models reflections of shiny surfaces

θ θ

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Specular reflection

Shininess depends on roughness surface
Incident light is reflected unequally in all directions
Reflection strongest near mirror angle

very shiny less shiny

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Specular reflection / Phong

Light intensity observed by viewer depends on angle of

incident light and angle to viewer

Phong model: Is = ksILcosn(α) = ksIL (V•R)n
ks is specular reflection coefficient
n is specular reflection exponent

θ θ

α L R N V

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Specular reflection / Phong

increasing n increasing ks

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Ambient light

Even though parts of scene are not directly lit by light

sources, they can still be visible

Because of indirect illumination

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Ambient light

“Ambient” light IA is an approach to this indirect

illumination

Ambient light is independent of light sources and viewer

position

Contribution of ambient light I = kaIa
ka is ambient reflection coefficient
Ia is ambient light intensity (constant over scene)

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Total illumination model

Total intensity Itotal at point P seen by viewer is

( )

∑

α + θ + =

i i n s i d i a a total

) ( cos k ) cos( k I I k I

α0 θ0 θ1 α1

( )

∑

⋅ + ⋅ + =

i n i s i d i a a total

) R V ( k ) L N ( k I I k I

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Total illumination model

In previous formula ka, kd dependent on wavelength

(different values for R, G and B)

Often division into color and reflection coefficient of

surface where:

0 ≤ ka, ks, ks ≤ 1 (relative amounts)
Ca is ambient reflected color of surface
Cd is diffuse reflected color of surface
Cs is specular reflected color of surface

( ) ( )

( ) ∑ α + θ + + =

i i n s s i d d i a a a e totaal

cos C k cos C k I I C k I I

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Only emission and ambient

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Including diffuse reflection

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Including specular reflection

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Illumination model

Given model:
Simple
Effective
Not real world
More advanced models possible

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Shading

Illumination model computes illumination for a point on

surface

But how do we compute the illumination for all points on all

(visible) surfaces?

Shading methods:
Flat shading
Gouraud shading
Phong shading

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Normal vectors

For illumination model we need normal vectors for
the cell center
the cell nodes
every pixel in the image

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Normal vectors

Cell normals
Use the cross product
f two cell edges
Node normals
Compute cell normals

for neighbor cells

Average cell normals
2

v 1 v 2 v 1 v n × × = 4 4 n 3 n 2 n 1 n n + + + =

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Flat shading

Determine illumination for one point on cell (e.g. center)
Use this illumination for all points on cell
Disadvantages:
Does not account for changing direction to light source
ver polygon
Does not account for changing direction to eye over

polygon

Discontinuity at polygon boundaries (when curved

surface approximated by polygon mesh

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Flat shading

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Gouraud shading

Based on interpolation of illumination values
Compute illumination for nodes of cell
Algorithm
for all nodes of cell
get node normal
compute node illumination using this normal
for all pixels in projection of polygon
compute pixel illumination by interpolation of node

illuminations

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Gouraud shading

I1 I2 I3 ys IA IB

( )

2 1 A

I I 1 I α + α − =

( )

2 1 B

I I 1 I β + β − =

2 1 s 1

y y y y − − = α

3 1 s 1

y y y y − − = β IP

B A P

I I ) 1 ( I γ + γ − =

B A P A

x x x x − − = γ

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Gouraud shading

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Gouraud shading

Advantages
Interpolation is simple, hardware implementation
Continuous shading
Better results for curved surfaces
Disadvantages
Subtle illumination effects (e.g. highlights) require high

subdivision of surface in very small polygons

Mach banding

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Phong shading

Based on normal interpolation
Compute illumination for each visible point of cell
Algorithm
for each node of cell
get node normal
for each pixel in projection of cell
compute point normal by interpolation of node

normals

compute pixel illumination using interpolated normal

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Phong shading

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Phong shading

Advantages
Much better results for curved surfaces
Nice highlights
No Mach banding
Disadvantages
Computational expensive
Normal interpolation and application of illumination

model for each pixel

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Shading summarized

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Shading

Flat shading
1x application of illumination model per cell
1 color per polygon
Gouraud shading
1x application of illumination model per node
Interpolated colors
Phong shading
1x application of illumination model per pixel
Nice highlights

Increase computation time Increase quality

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