Final Exam will be a take home exam with a time limit.
Remaining presentations will be:
11-Nov |
Student Presentations 4 & 4.5 |
16-Nov |
Student Pres 5 & 6 |
18-Nov |
Student Pres 7 |
23-Nov |
Student Pres 8 |
If I didn't already say it, Read 11.2 through 11.2.2, 11.2.8-9
Factoring the non-linearity out of parametric equations. Tangents.
Hermite and Bezier curves. What are these magic matricies? Making your own basis. 4-point form. Blending functions.
4-point blending functions
M=[0 0 0 1; 1/27 1/9 1/3 1; 8/27 4/9 2/3 1; 1 1 1 1];
syms t;
bc=[t^3 t^2 t^1 1] * inv(M)
bc =
[ -9/2*t^3+9*t^2-11/2*t+1, 27/2*t^3-45/2*t^2+9*t, -27/2*t^3+18*t^2-9/2*t,
9/2*t^3-9/2*t^2+t ]
tvals=0:0.01:1;
for i=1:4
curve(:,i)=subs(bc(i),t,tvals');
end
plot(tvals,curve);
Bezier blending functions
Bezier subdivision.