1) Curves Flashcards
1
Q
A
A mapping from an open interval to n dimensional space
2
Q
If a tangent vector is a curve is constant
A
The curve is part of a straight line
3
Q
A
4
Q
The arc length of a curve
A
5
Q
A
6
Q
For φ reparameterization map
A
7
Q
If a curve has Unit speed?
A
8
Q
A
9
Q
Proof of reason for unit speed?
A
10
Q
A
It’s tangent vector is never zero
11
Q
Proof that curve has unit seed reparam iff its tangent vector is never zero
A
12
Q
A curve that never has a zero tangent vector is
A
Regular
13
Q
A
14
Q
Prove that a curve γ has a unit speed reparam iff it’s tangent vector is never zero
A
To the right of iff, that should be the derivative of the reparamterization
15
Q
A parameterisation γ is smooth if
A
Each of the components is smooth <=>
Each derivative exists for for each component
