# Design and analysis of Bi-cubic hermite surfaces

## Purpose:

Figure 1.6.1

To plot surfaces along with normals, tangent vectors and modify them based on the user inputs

## Learning Outcome:

• Helps in understanding the behavior of surfaces with respect to change in surface parameters (control points, tangents, twist vectors)
• Tool to assist students with their assignments

## Example Problem:

Figure 1.6.2

Determine a point on a Hermite bicubic surface patch corresponding | to u=0.25, w=0.75.

• The position vectors for four corner points are:
P(0,0) = [-50 0 50], P(0,1) =[-50 -50 -50], P(1,0) = [50 -50 50], P(1,1) =[50 0 -50].

The tangent vectors are:

• Pu(0,0)=[50 50 0], Pu(0,1)=[5 5 0], Pu(1,0) = [5 -5 0], Pu(1,1) =[5 -5 0],
• Pw(0,0) = [0 20 -20], Pw(0,1) =[0 -5 -5], Pw(1,0) = [0 5 -5], Pw(1,1) =[0 -5 -5].

The twist vectors are:

• Puw(0,0) =[0 0 0], Puw(0,1) =[0.5 0.5 0.5], Puw(1,0)=[0.5 -0.5 -0.5], Puw(1,1)=[0 0 0].
• Plot the patch and determine unit normal vector at u=0.25, w=0.75.