Nadradený pojem:
Parametric surface and surface normal
Description
A
space curve has a parametric form x(t)
A surface has a parametric form s(u, v)
The derivative of a surface can be taken with respect to u and v. These derivatives can be used to find the tangent to the surface, which is a now a plane that grazes the surface at a given point.
The surface normal n is a vector orthogonal to the tangent plane.
- This provides a mapping from one variable (t) to R3
A surface has a parametric form s(u, v)
- This provides a mapping from two variables (u, v) to R3
The derivative of a surface can be taken with respect to u and v. These derivatives can be used to find the tangent to the surface, which is a now a plane that grazes the surface at a given point.
The surface normal n is a vector orthogonal to the tangent plane.
Importance
High
Additional information
Exercise:
For simple surfaces, the surface normal can be identified by inspection
- Task 1: draw the normals for the surfaces below
- Task 2: how might you specify or compute them?
