**Surface Normals:**-
- Illumination models require:
- surface normal vectors at intersection points
- ray-surface intersection computation must also yield a normal
- light-source directions must be established at intersection
- shadow information determined by light-ray intersections with other objects

- Normals to polygons:
- provided by planar normal
- provided by cross product of adjacent edges
- Or use phong normal interpolation if normals specified at vertices

- Normals to any implicit surface (eg. quadrics)
- move from (
*x*,*y*,*z*) to which is*maximally*far from the surface - direction of greatest increase to
*f*(*x*,*y*,*z*)

- move from (
- Taylor series:
- maximality for the
*gradient vector*of*f* - not normalized

- maximality for the
- Normal to a quadric surface

- Illumination models require:
**Normal Transformations:**-
How do affine transformations affect surface normals?
- Let and be any two points on object
- arbitrarily close
- using transpose notation:

- After an affine transformation on , :
we want to be a normal for some transformation

**N**:and this certainly holds if

- Only the upper 3-by-3 portion of
**M**is pertinent for vectors - Translation:
no change to the normal

- Rotation (example):
rotation applied unchanged to normal

- Scale:
reciprocal scale applied to normal

- Let and be any two points on object

CS488/688: Introduction to Interactive Computer Graphics

University of Waterloo

Computer Graphics Lab