Builtin Functions

1
Built-in Functions

• Chap 5 of OrangeBook

2
Contents

• Math (trignometry, exponential)
• Geometry
• Matrix, vector
• Texture access
• Fragment processing
• Noise (Perlin)

3
Component-wise!
4
Common Functions
5
More on smoothstep
1.0
1.0
0.6
0.4
Ramp down smoothstep (1.0, 0.6, x)
Ramp up smoothstep (0.4, 1.0, x)
6
Common Functions

• Two versions of min max
• vec min (vec x, vec y)
• vec min (vec x, float y)
• Similarly, for clamp mix
• vec mix (vec x, vec y, float a)
• vec mix (vec x, vec y, vec a)

7
Geometry Functions

• length, distance, dot, cross, normalize
• reflect (I,n) refract
• faceforward

I-(In)n
n
I
reflect I - 2(In)n
(In)n
8
Matrix Functions

• Multiplication
• mat x, y, z, zz
• z x y
• zz matrixCompMult (x,y)

9
Texture Access

• texture2D
• texture2DProj
• texture2DLod
• texture2DProjLod
• shadow2D

10
Fragment Processing

• dFdx
• fwidth
• What are the usage?

11
Characteristics of Noise Functions

• The return values are always in the range -1,1
  and cover at least the range -0.6,0.6 with a
  Gaussian-like distribution.
• The return values have an overall average of 0.
• The functions are repeatable, in that a
  particular input value always produces the same
  return value.
• The spatial frequency is narrowly concentrated,
  centered somewhere between 0.5 and 1.0.
• They are C1 continuous everywhere that is the
  first derivative is continuous.