Surface Textures in the Fragment Shader - Graphics Shaders - page 193

Figure 9.6. Ripples by bump mapping.

dy

line segment has slope m

d = , we can express the slope as the vector [1, m ], as
shown in the diagrams below.

The normal to any line with slope m has slope 1 − m (the negative recipro-
cal of the original slope), so the normal can be expressed as the vector (- m , 1.).
Notice that the dot product is (1, m ) × (− m ,1) = 0, as must be true if the vectors
are perpendicular. So if we want to model a moving “bump” on the surface
with height a , period P d , and time t , we have

2 π x

z a =− ∗ cos − 2 π t

P

d

and its slope, or derivative with respect to x , is

dz
dx

2 π 2 π x

=∗ ∗ a sin − 2 π t

P P

d d

so the vector slope, s , is

2 π 2 π x

s = 10 ., ., a ∗ ∗ sin − 2 π t .

P P

d d