Difference between parametric continuity and geometric continuity
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Parametric vs. Geometric Continuity
Actually, there are two different notions of what it means to be smooth to kthkth order. The first is called parametric continuity, and is written CkCk; the other is called either geometric or visual continuity, and is written GkGk or VCkVCk. Parametric continuity means smoothness both of the curve and of its parameterization. That is, if a curve F is parametrically smooth, we can make a movie in which a car’s position at time t is F(t) and the motion of the car in that movie will look smooth. Geometric continuity means simply the smoothness of the track that the car leaves in the snow after it passes by.
Actually, there are two different notions of what it means to be smooth to kthkth order. The first is called parametric continuity, and is written CkCk; the other is called either geometric or visual continuity, and is written GkGk or VCkVCk. Parametric continuity means smoothness both of the curve and of its parameterization. That is, if a curve F is parametrically smooth, we can make a movie in which a car’s position at time t is F(t) and the motion of the car in that movie will look smooth. Geometric continuity means simply the smoothness of the track that the car leaves in the snow after it passes by.
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The main difference between parametric continuity and geometric continuity is that parametric can not be defined by the shape of the curve whereas geometric can be only by the curve shape
- Parametric continuity means the curve's smoothness as well as its parameterisation. That is, if a curve F is parametrically smooth, we can make a film where the position of a car at the time t is F(t) and the car's motion in that film will look smooth.
- Geometric continuity simply means the smoothness of the track the car leaves in the snow after passing through.
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