CS计算机代考程序代写 Excel 3D Object Representation

3D Object Representation

1

Lighting and Rasterization –
Shading

2

Intended Learning Outcomes

 Classify different types of light sources
 Understand the image formation process
 Mathematically model three types of reflection and

understand their properties
 Understand three rendering methods and compare their

pros and cons
 Able to program lighting and shading using OpenGL

3

Lighting and Shading Models

 Calculate intensity and colour of light that we should see
at a given point of a scene

 Ultimate aim : Photorealism

 Lighting /Illumination models
 models lighting from light sources and the

environment

 Shading models
 models how lights are processed (reflected, absorbed,

refracted etc) by the objects and the atmosphere

4

Light sources
 Ambient source

 models background light
 Point source

 for small nearby light sources
 Distributed source

 for large nearby light sources
 models by a collection of point sources

 Lighting direction
 (e.g. sun) – for distant light sources

5

Point Source Distributed Source

6

 Realistic lighting is higher order and complicated

2nd order reflection

2nd order light source

1st order reflection + 2nd order reflection

7

Shading
 When light is incident on an object

 part is reflected
 part is absorbed
 part is refracted

8

Object properties

 Opaque object only reflect and absorb light
 Transparent object only refract and absorb light
 Semi-transparent object reflect, refract and absorb light

 The amount of light reflected depends on material.

 Shiny material : reflect most of the light
 Dull material : absorb most of the light

 Let restrict discussion to opaque object at present

9

Types of Reflection

 Ambient reflection
 Average signal from the background
 Non-directional

 Diffuse reflection
 Rough, dull, matte surfaces
 scatter light equally in all directions

 Specular reflection
 Smooth, shiny, mirror like surfaces
 reflect light more in one direction

10

Ambient reflection

ka ambient reflection coefficent, 0 ≤ ka ≤ 1
Ia incident ambient light

 Can be interpreted as the average value of diffuse
reflection from numerous light sources in the
background

aaambdiff IkI =

11

 Consider a point light source or lighting direction

 Lambertian surfaces : Reflections from the surface are
scattered with equal intensity in all directions,
independent of the viewing direction

Diffuse Reflection

incident light

Diffuse (Lambertian)
Surface (Rough, dull
e.g. wood)

12

 Amount of incident light received by the surface is
proportional to the projected area of the surface in the
lighting direction

13

kd diffuse reflection coefficient, 0 ≤ kd ≤ 1
Il Incident light intensity
N unit normal of the surface
L unit light direction vector

 N·L models the projected area

)(, LN ⋅= lddiffl IkI

14

Incident
light from
light source
with intensity
Il

Unit normal vector N

Surface with
area A

θ

Acosθθ

Unit
lighting
direction
vector L

The total amount of light received
by the surface with area A is
proportional to Acosθ = A (N•L)

15

Specular reflection

 Consider a point light source or lighting direction.
 Ideal specular surface = perfect mirror: light is only

reflected in the direction of R
 Non-ideal reflector: some light are scattered around R

Specular
Surface (Shiny e.g. mirror, gold
silver, glass)

Incident light

L Incident light direction

16

W(θ) specular reflection coefficent, 0 ≤ W(θ) ≤ 1
sometimes W(θ) is assumed to be a constant ks

N bisects L and R (incident angle = reflection angle in a
perfect mirror)

R unit specular reflection direction vector

R = (2N·L)N – L

V unit viewing direction vector

cos(φ) = R·V 0 ≤ φ ≤ π/2

ns specular reflection exponent, ns = ∞ for perfect mirror

φθ snlspecl IWI cos)(, =

17

18

R = (2N·L)N – L

19

20

General Model with n light sources with
ambient, diffuse and specular terms

]))(()([
1

sn
iii

n

i
dliaa WkIIkI RVLN ⋅+⋅+= ∑

=

θ

21

Colour model

 Each light source is a vector with Red, Green, Blue
component (IlR, IlG, IlB)

 Calculates each component separately:

]))(()([

]))(()([

]))(()([

1

1

1

sB

sG

sR

n
iiBi

n

i
dBlBiaBaBB

n
iiGi

n

i
dGlGiaGaGG

n
iiRi

n

i
dRlRiaRaRR

WkIIkI

WkIIkI

WkIIkI

RVLN

RVLN

RVLN

⋅+⋅+=

⋅+⋅+=

⋅+⋅+=

∑

∑

∑

=

=

=

θ

θ

θ

22

B

G

R

Note:

Only colours in the
triangle is displayable.

Some naturally occurring
colours outside the triangle
cannot be displayed!

Quattron technology uses
4 primary
Colours RYGB that
extends the displayble
colours

CIE chromaticity diagram
-Represent all possible colours
seeable by humans

23

LG-32UD59-B

https://www.forbes.com/sites/forbes-personal-shopper/2018/05/28/lg-32ud59-b-review-a-decent-4k-monitor-with-excellent-color-reproduction/#4d0a7b3240d3

24

Shading Models /Rendering Models
 Input : Object tessellated into polygons (standard

graphics object)

 Three common ways to shade the polygons:

 Flat Shading
 Gouraud Shading
 Phong Shading

Increasing realism

Increasing computational cost

25

Flat shading

 A single intensity is calculated for the polygon. All points
of the polygon are then displayed with the same intensity
value

 Fast (Adv.)
 Faceted look – ugly!
 Human vision is subject to “Mach band effect” – intensity

discontinuities are accentuated. This amplifies the
edges of the polygons, which is undesirable

26

27

Gouraud shading

 Linearly interpolate intensity values across each
polygon

 Intensities for each polygon are matched with the values
of adjacent polygons along the common edges

 Interpolation eliminates the intensity discontinuities that
occur in flat shading

 Slower (disadv.)
 Smooth out specular highlights (disadv.)

28

 Step 1 : Determine the average unit normal vector at
each polygon vertex

(each Nk is a unit vector,
Nv is a unit vector by def.)

 Step 2 : Apply an illumination model to each vertex to
calculate the vertex intensity

 Step 3 : linearly interpolate the vertex intensities over the
surface of the polygon

∑

∑

=

==
n

k
k

n

k
k

v

1

1

N

N
N

29

30

Linear Interpolation
 Points lying on an edge of the polygon : linearly

interpolate between two endpoints

 interior points of the polygon : linearly interpolate across
the scan line

2
21

41
1

21

24
4 Iyy

yy
I

yy
yy

I
−
−

+
−
−

=

5
45

4
4

45

5 I
xx
xx

I
xx
xx

I ppp −
−

+
−
−

=

31

Phong shading

 Similar to Gouraud shading, but interpolates normal
vectors instead.

 Captures specular highlights
 Highest realism
 Slowest (disadv.)

32

 Step 1 : determine the average unit normal vector at
each polygon vertex

 Step 2 : linearly interpolate the vertex normals over the
surface of the polygon

 Step 3 : apply an illumination model to calculate pixel
intensities of each surface point

2
21

1
1

21

2 NNN
yy
yy

yy
yy

−
−

+
−
−

=

33

Incremental form

 Linear interpolation equation is expressed in incremental
form to save computation:

one scan line down

21

12
1)( yy

II
IyI

−
−

+=

21

12)()1(
yy
II

yIyI
−
−

+=−

34

OpenGL Functions : Lighting
glEnable (GL_LIGHTING); // activate lighting routines

glLight* (lightName, lightProperty, propertyValue);

GLfloat light1PosType [ ] = {2.0, 0.0, 3.0, 1.0}; // point
// source; the last entry is 1.0

GLfloat light2PosType [ ] = {0.0, 1.0, 0.0, 0.0}; // light
// direction; the last entry is 0.0

glLightfv (GL_LIGHT1, GL_POSITION, light1PosType); // v
for vector

glEnable (GL_LIGHT1);

glLightfv (GL_LIGHT2, GL_POSITION, light2PosType);
glEnable (GL_LIGHT2);

35

Light source colour

 (R, G, B, A) A stands for alpha value

GLfloat blackColor [ ] = {0.0, 0.0, 0.0, 1.0};
GLfloat whiteColor [ ] = {1.0, 1.0, 1.0, 1.0};

glLightfv (GL_LIGHT3, GL_AMBIENT, blackColor);
glLightfv (GL_LIGHT3, GL_DIFFUSE, whiteColor);
glLightfv (GL_LIGHT3, GL_SPECULAR, whiteColor);

36

Surface Property

glMaterial* (surfFace, surfProperty, propertyValue);

diffuseCoeff [ ] = {0.2, 0.4, 0.9, 1.0}; // kdR = 0.2, kdG = 0.4, kdB = 0.9
specularCoeff [ ] = {1.0, 1.0, 1.0, 1.0}; // WR(θ) = 1.0, …

glMaterialfv (GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE,
diffuseCoeff );

glMaterialfv (GL_FRONT_AND_BACK, GL_SPECULAR, specularCoeff);
glMaterialf (GL_FRONT_AND_BACK, GL_SHININESS, 25.0 ); // ns = 25

37

Surface Rendering

 FLAT and Gouraud Shading
glShadeModel (surfRenderingMethod);

surfRenderingMethod = GL_FLAT Flat shading
= GL_SMOOTH Gouraud

 Calculating normals
glNormal3* (Nx, Ny, Nz);

38

 Gouraud shade a triangle

glEnable (GL_NORMALIZE); // convert all normal vectors to unit vector
glLightModeli (GL_LIGHT_MODEL_LOCAL_VIEWER, GL_TRUE);

// set correct V for specular calculations

glBegin (GL_TRIANGLES);
glNormal3fv (normalVector1); // normal vector at vertex1 calculated

// by average unit normal vector
glVertex3fv (vertex1);
glNormal3fv (normalVector2);
glVertex3fv (vertex2);
glNormal3fv (normalVector3);
glVertex3fv (vertex3);

glEnd ( );

39

References

 Text: Ch. 17.1-17.3 for lighting and shading equations
 Text: Ch. 19.3 – 19.4 for CIE chromaticity diagram and

RGB model
 Text: Ch. 17.10 for different shading method
 Text: Ch. 17.11 for OpenGL commands
 Demo: Run lightposition.exe and lightmaterial.exe in

TUTORS program
 Quattron technology:

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

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

Lighting and Rasterization – Shading
Intended Learning Outcomes
Lighting and Shading Models
Light sources
Slide Number 5
Slide Number 6
Shading
Object properties
Types of Reflection
Ambient reflection
Diffuse Reflection
Slide Number 12
Slide Number 13
Slide Number 14
Specular reflection
Slide Number 16
Slide Number 17
Slide Number 18
Slide Number 19
General Model with n light sources with ambient, diffuse and specular terms
Colour model
Slide Number 22
Slide Number 23
Shading Models /Rendering Models
Flat shading
Slide Number 26
Gouraud shading
Slide Number 28
Slide Number 29
Slide Number 30
Phong shading
Slide Number 32
Incremental form
OpenGL Functions : Lighting
Light source colour
Surface Property
Surface Rendering
Slide Number 38
References

]
)
)(
(
)
(
[
]
)
)(
(
)
(
[
]
)
)(
(
)
(
[
1
1
1
sB
sG
sR
n
i
i
B
i
n
i
dB
lBi
aB
aB
B
n
i
i
G
i
n
i
dG
lGi
aG
aG
G
n
i
i
R
i
n
i
dR
lRi
aR
aR
R
W
k
I
I
k
I
W
k
I
I
k
I
W
k
I
I
k
I
R
V
L
N
R
V
L
N
R
V
L
N
×
+
×
+
=
×
+
×
+
=
×
+
×
+
=
å
å
å
=
=
=
q
q
q

_1380970568.unknown