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Shading and GLSLEDA 221

Jacob Munkberg

EDA 221 - Computer graphics: Introduction to 3D

Today• Wrap up animation

• Lighting and Shading

• Chapter 5 (some material about GLSL from Chapter 2)

• Phong, texture mapping, cube mapping & bump mapping

• Light sources, GLSL

2

http://cs.lth.se/eda221/



Cubic Hermite Interpolation

3

p(t) = [1 t t2 t3]

2

664

1 0 0 00 0 1 0�3 3 �2 �12 �2 1 1

3

775

2

664

p0

p1

p00

p01

3

775

z

y

xp0

p’0

p1p’1

p(t) = c0 + c1t+ c2t2 + c3t

3

p(t) = [1 t t2 t3]

2

664

c0c1c2c3

3

775

p(t) = tTM�1q




Smoothstep• Useful special (1D) case of cubic

interpolation- performs smooth Hermite interpolation between

0 and 1 when a < x < b.

- Useful in cases where a threshold function with a smooth transition is desired.

- Tangents : 0 at x=a and 0 at x=b

4a b

x




Smoothstep

5

float smoothstep(float x, float a, float b){ float t = clamp((x-a)/(b-a),0,1); return t*t*(3-2*t);}

Derive formula!

a bx




Demo Smoothstep

6




How to specify tangents?• One simple solution:

7

p0i ⇡

pi+1 � pi�1

2

p0i

pi-2

pi-1 pi

pi+1

pi+2




Catmull-Rom Splines• Given a set of points, define tangents

as: - Curve segment between pi and pi+1 completely

defined by pi-1, pi, pi+1 and pi+2

8

p0i ⇡

pi+1 � pi�1

2

p0i

pi-2

pi-1 pi

pi+1

pi+2




Catmull-Rom Splines

9

p0 p1

p2

p3

p01 =

p2 � p0

2

p02 =

p3 � p1

2

2

664

p(0)p(1)p0(0)p0(1)

3

775 =

2

664

0 1 0 00 0 1 0

�1/2 0 1/2 00 �1/2 0 1/2

3

775

2

664

p0

p1

p2

p3

3

775

p(t)

Four conditions:




Catmull-Rom Splines• Tangent def. gives four conditions

- Insert in Hermite formula:

10

2

664

p(0)p(1)p0(0)p0(1)

3

775 =

2

664

0 1 0 00 0 1 0

�1/2 0 1/2 00 �1/2 0 1/2

3

775

2

664

p0

p1

p2

p3

3

775

q = Np

p(t) = tTM�1q = tTM�1Np

M�1N =1

2

2

664

0 2 0 0�1 0 1 02 �5 4 �1�1 3 �3 1

3

775 FEL I BOKEN!!!




Catmull-Rom Splines

• If we add a tension parameter 𝜏:

the Catmull-Rom spline can be generalized to:

11

p(u) = [1 t t2 t3]

2

664

0 1 0 0�⌧ 0 ⌧ 02⌧ ⌧ � 3 3� 2⌧ �⌧�⌧ 2� ⌧ ⌧ � 2 ⌧

3

775

2

664

pi�1

pi

pi+1

pi+2

3

775

( (=(tension,(how(sharply(the(curve(bends(at(control(points((Keep(within([0,1]((Good(ini-al(value:(0.5%

Tension(

low(high(

p0i = ⌧(pi+1 � pi�1), ⌧ 2 [0, 1]




Animate Colors• Other attributes than position can be

animated- Example: animate green color channel, G = 255*t

12t=0

R=255G=0B=0

R=255G=255B=0

t=1




Light Sources• Ambient light- Equal intensity at all points in scene💡

• Point light- Intensity falloff with distance: 1/r2

• Spotlights- Limit point light to a cone

• Directional lights (sun)- All light rays parallel

13

r☼

🎥




Shading Theory• Describe how surfaces interact

(reflect/refract/absorb) light

• Light-material interactions:- Specular surfaces (mirrors, shiny metals)

reflect light in narrow cone

- Diffuse surfaces (rough metal, paper)reflect incoming light in wide cone

- Translucent surfaces (glass, water, marble, skin)Some light penetrates the surface

14




Phong Reflection Model• Efficient approximation of materials- Very popular in real-time graphics

• Describe materials as a sum of three types of reflection terms:

15

Ambient Diffuse Specular

=++




Phong Reflection Model• Ambient: constant

• Diffuse:

• Specular

16

/ n · l/ (r · v)↵

☼

! " ☀

p

nl rv




Diffuse (Lambertian) Term• Rough surfaces scatter

light in all directions

• Model with Lambert’s law

17

☼

p

nl θ

Rd / cos ✓ = l · n

|l| = |n| = 1




Diffuse (Lambertian) Term• Let kd represent the fraction of incoming

diffuse light Ld that is reflected. The diffuse reflection term is:

18

Id = kd(l · n)Ld ☼

p

nl θ☼




Specular Reflection• Smooth surface reflects

light in one direction

• Phong specular term

- where ks represent the fraction of incoming specular light Ls that is reflected. α represent shininess

19

☼

p

nl

! " ☀

v

r�

Is = ks(cos�)↵Ls = ks(r · v)↵Ls




Reflection operator

20

n̂r

i

i

r = i� 2(n̂ · i)n̂

(n̂ · i)n̂

�2(n̂ · i)n̂




Specular Reflection• Alternative specular term: - Use half vector:

• Alternative Phong specular term

- No reflection operation needed

- Commonly used, called“Blinn-Phong” specular

21

☼

p

n

l

! " ☀

v

h�

h =l+ v

|l+ v|

Is = ks(cos�)↵Ls = ks(n · h)↵Ls




Shininess

22

-1.5 -1 -0.5 0 0.5 1 1.5

0.25

0.5

0.75

1

cos�

cos

2 �

(cos�)10

(cos�)100

(cos�)↵Vary exponent in

↵ ! 1Mirror if




Shininess

23

α=1 α=10 α=100 α=1000

-1.5 -1 -0.5 0 0.5 1 1.5

0.25

0.5

0.75

1




In practice

24

Diffuse Diffuse + Specular




Phong Model• Combine the three terms

• More than one light? Accumulate!

25

I = kaLa + kdLd max(l · n, 0) + ksLs max((r · v)↵, 0)



= ++

C =X

i

(Iambient + Idiffuse + Ispecular)




Phong Materials• In the Phong model, a material is

defined by the coefficients: ka, kd, ks and shininess

• Examples:- Red diffuse material:

- “Gold”:

26

ka = (0, 0, 0)

kd = (1, 0, 0)

ks = (0, 0, 0)

ka = (0, 0, 0)

kd = (0.8, 0.6, 0.2)

ks = (0.3, 0.3, 0.3)shininess=100

shininess=0




Graphics Hardware• Pipeline that accelerates the costly

tasks of rendering

27

Vertex Shader

Rasterizer

Pixel Shader

Transform geometry(Lecture 2 & 3)

Compute visibilityper pixel

Compute color per pixel




Graphics Hardware

28

Vertex Shader

Rasterizer

Pixel Shader

GLSL vertex shader

program

GLSL pixel shader

program




Passing Geometry Info• We need position and a set of vectors

• All vectors need to be defined in the same coordinate space- One of the most common bugs in shaders

- Angle between vectors requires a common space

• The vertex shader transforms position and vectors

• Pixel shader evaluates Phong model

29




Geometry setup for shading• Place object

• Place light source (defines l-vector)

• Place camera (defines v-vectors)

• Pick shading coordinate system

• Transform vectors into common system

30




Geometry setup for shading• Place object

• Place light source (defines l-vector)

• Place camera (defines v-vectors)

• Pick shading coordinate system

• Transform vectors into common system

31

Vertexshader

Applicationcode




GLSL• OpenGL Shading Language

• Domain-specific C-like language- Scalar types: float, int, bool

- Vectors: vec2, vec3, vec4

- Matrices: mat2, mat3, mat4

- Texture samplers

32




Working with vectors

33

vec4 v(1.0, 2.0, 3.0, 4.0);

v[1] = v.y = 2.0;

v.xyz = v.rgb = vec3(1.0, 2.0, 3.0);

//Swizzle

v.wwxy = vec4(4.0, 4.0, 1.0, 2.0);




GLSL Matrix & Vector ops

34

mat4 M = ...vec4 v = ...vec4 u = M*v; // Matrix mul

float f = dot(u.xyz, v.xyz);vec3 w = cross(u.xyz, v.xyz);

vec3 n = ...vec3 l = ...vec3 r = reflect(-l,n);float lambert = dot(n,l);




Qualifiers• in, out- Pass vertex attributes to and from shaders

in vec2 tex_coord, out vec4 color;

- Older versions of GLSL use varying keyword and pre-defined variables such as gl_Vertex.

• uniform - variables from application- uniform float time

- Same value for all vertices / pixels

35




Built-in functions• Use these!- Arithmetic: sqrt, pow, abs, clamp

- Trigonometric: sin, cos, ...

- Geometry: length, reflect, dot, cross, smoothstep, ...

36




Output from shaders• Vertex shader output- gl_Position Mandatory output (position) from

vertex shader

- Add additional per-vertex outputs with out keyword. Ex: out vec4 color

• Pixel shader output- Pixel shader must output a vec4 color

- Example: out vec4 fColor

- Older versions of OpenGL use gl_FragColor

37




Simple Vertex Shader• Transform a point- A vertex shader must output a position in clip

coordinates to the rasterizer

38

in vec4 vPos;uniform mat4 MVP; // ModelViewProjection mtx

void main(){ gl_Position = MVP*vPos;}

Matrix [4x4] * Vector [4x1] = Vector[4x1]




Simple Pixel Shader• Set pixel color to red

39

out vec4 fColor;

void main(){ fColor = vec4(1,0,0,1);}




Simple Pixel Shader• Interpolate vertex colors

40

in vec3 vertexColor;out vec4 fColor;

void main(){ fColor = vec4(vertexColor,1.0);}




Coordinate Frames in GLSL• Object (Model) Coordinates

• World Coordinates

• Eye (camera) coordinates

• Clip coordinates

• Normalized Device Coordinates

• Window (screen) coordinates

41




Phong Shading in GLSL

42

uniform vec3 ka; // Material ambientuniform vec3 kd; // Material diffuseuniform vec3 ks; // Material specularuniform float shininess;in vec3 fN; // From vertex shaderin vec3 fL; in vec3 fV;out vec4 fColor;

void main(){! vec3 N = normalize(fN);! vec3 L = normalize(fL);! vec3 V = normalize(fV);! vec3 R = normalize(reflect(-L,N));! vec3 diffuse = kd*max(dot(L,N),0.0);! vec3 specular = ks*pow(max(dot(V,R),0.0), shininess);! fColor.xyz = ka + diffuse + specular;! fColor.w = 1.0;}

Pixel Shader

FEL I BOKEN!!!





43

World space version

Vertex Shaderuniform mat4 ModelViewProj;uniform mat4 World; // Model -> Worlduniform mat4 WorldIT; // Inverse transposeuniform vec3 LightPos; // Defined in world spaceuniform vec3 CamPos; // Defined in world spacein vec3 vPos;in vec3 vNormal;out vec3 fN;out vec3 fV;out vec3 fL;

void main(){ vec3 worldPos = (World*vec4(vPos,1)).xyz;! fN = (WorldIT*vec4(vNormal,0)).xyz; ! fV = CamPos - worldPos; fL = LightPos - worldPos;! gl_Position = ModelViewProj*vec4(vPos,1);}





44

Camera space version

Vertex Shaderuniform mat4 ModelViewProj;uniform mat4 ModelView;uniform mat4 ModelViewIT; // Inverse Transposeuniform mat4 View;uniform vec3 LightPos; // Defined in world spacein vec3 vPos; // From applicationin vec3 vNormal;out vec3 fN; // Send to Pixel shaderout vec3 fV;out vec3 fL;

void main(){ vec3 posCamSpace = (ModelView*vec4(vPos,1)).xyz;! fN = (ModelViewIT*vec4(vNormal,0)).xyz;! fV = -posCamSpace; fL = (View*vec4(LightPos,1)).xyz - posCamSpace;! gl_Position = ModelViewProj*vec4(vPos,1);}




Hardware Interpolation• Vertex attributes are interpolated for

each pixel by the graphics hardware

45

Vertex Shader

Rasterizer

Pixel Shader




Polygonal Shading• Flat Shading- l, n, v constant for each triangle

- Compute shading once per triangle

• Gouraud Shading- Shade at each vertex

- Interpolate between the three vertexcolors for each fragment within triangle

• Phong Shading- Compute shading for each pixel

46




Gouraud vs Phong

47

Diffuse

Ambient, diffuse & specular

Gouraud Phong




Texture Mapping• “Gift-wrap” geometry

• For each vertex of the mesh, store texture coordinates (s, t)

• Use (s, t) to index into a texture (image)

• Adds detail to a mesh

• “Paste decals” onto geometry

48




Texture Mapping• Specify tex coordinate at each vertex- Hardware interpolates texCoord for each pixel

• Use coordinate to lookup in texture

49

(0,1)

(0,0) (1,0)

(1,1)(s,t)=




Texture Mapping in GLSL

50

in vec3 vPos;in vec2 vTexCoord;

out vec2 texCoord;uniform mat4 MVP;

void main(){! texCoord = vTexCoord.xy;!! gl_Position = MVP * vPos;}

out vec4 fColor;

uniform sampler2D Sampler;in vec2!texCoord;

void main(){! fColor = texture(Sampler,texCoord);}

Vertex shader Pixel shader




Textured Phong Model• Change the diffuse factor (kd) per pixel

51

I = kaLa + kdLd max(l · n, 0) + ksLs max((r · v)↵, 0)


= ++

= ++





Texturing in Graphics

• Map detail from an image onto a 3D object

52





Tangent space• Local coordinate system made up of

the tangent, binormal and normal

• Unique for each point of the surface

• Remember the sphere (lecture 3)

53

Sphere((Surface(

(Tangent,(binormal(




Bump Mapping• Modify surface normal for each pixel

• Store tangent space normal in a texture

54

n

b

t

n0 = ↵t+ �b+ �n

�

↵

�

Sphere((Surface(

(Tangent,(binormal(




Bump Mapping• Modify surface normal for each pixel

• Store tangent space normal in a texture

55

n

b

t

n0 = ↵t+ �b+ �n

�

↵

�

(R,G,B) ! (↵,�, �)

(127, 127, 255) ! (0, 0, 1)

[0, 255] ! [�1, 1]




Coordinate Transform• From tangent space to object space- Normal in tangent space:

- Basis vectors (defined in object space):

- Normal in object space:

56

(↵,�, �)

t, b, n

↵t+ �b+ �n =

2

4| | |t b n| | |

3

5

2

4↵��

3

5




Example : Bump Mapping

+

57

=




Bump Mapping Summary• Derive tangent space - Compute tangent, binormal and normal in vertex

shader and pass to pixel shader

• Find tangent space normal

- Lookup (α,β,𝛾) from texture, and remap from [0,1] to [-1,1] (Colors in GLSL: [0,1] instead of [0,255])

- Express as (object space)

• Transform normal from object space to world space and shade

58

n0 = ↵t+ �b+ �n




Reflection Mapping• Fast (but incorrect) way to

simulate reflection

• Use reflection vector, r, to lookup in a cube map texture

• Instead of (s,t), use a 3D direction- Direction gives a point

on unit sphere

59

! " ☀

p

nr v




Reflection Mapping• Simulate highly

reflective surfaces, such as chrome, mirrors and metals

• How do we express environment?

60




Cube Map• Take six photos

from the same point- With camera looking:

Front, back, left, right, up, down

• The cube approximates the spherical view

61




Reflection Mapping in GLSL

62

out vec4 fColor;uniform samplerCube SkyboxTexture;

void main(){ vec3 V = normalize(...); vec3 N = normalize(...); vec3 R = reflect(-V, N); vec4 reflection = texture(SkyboxTexture, R);! fColor = reflection;}



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