Functions homo/isomorphic to change in scale

[LogicalTime]

I would like to find out which functions retain the same structure when they are scaled. Particularly I am interested in projections.

For example, a parabola 3d space viewed at another angle can still be represented by at^2 + bt+c. A circle however can not (ellipse)

I am guessing conic sections have this property? Are there any other functions that have this property, and what terms are associated with this property?

 

[Bacle]

I think it would help looking at projective surfaces, with homogeneous coordinates.

 

[HallsofIvy]

I would like to find out which functions retain the same structure when they are scaled. Particularly I am interested in projections.

For example, a parabola 3d space viewed at another angle can still be represented by at^2 + bt+c. A circle however can not (ellipse)

I am guessing conic sections have this property? Are there any other functions that have this property, and what terms are associated with this property?

Have what property? You assert that a parabola, projected onto any plane, is still a parabola (which is not quite true- it can project to a ray) while that is not true for a circle. But parabola and circle are both conic sections.