quadric surface vs curved shape

quadric surface and curved shape both are nouns.

Word	Noun	Adjective	Verb	Adverb
quadric surface	Yes	No	No	No
curved shape	Yes	No	No	No

As nouns, curved shape is a hypernym of quadric surface; that is, curved shape is a word with a broader meaning than quadric surface:

quadric surface: a curve or surface whose equation (in Cartesian coordinates) is of the second degree
curved shape: the trace of a point whose direction of motion changes

Other hypernyms of quadric surface include curve.

quadric surface (noun)	curved shape (noun)
a curve or surface whose equation (in Cartesian coordinates) is of the second degree	the trace of a point whose direction of motion changes