Quadratic Surfaces

Various types of Quadratic surfaces:-

1. Sphere :-
2. A sphere with radius ‘r’ is defined as the set of points(x,y,z) , that satisfies the following equation:

                           x2  + y2 + z2  = r2

1. Sphere in parametric form :- We can also describe the spherical surface in parametric form, using latitude and longitude angles.

1. Ellipsoid :-
2. An ellipsoidal surface can be described as an extension of a spherical surface, where the radii in three mutually perpendicular directions can have different values.

1. The Cartesian representation for points over the surface of an ellipsoid centered on the origin is

1. Ellipsoid - Parametric representation

1. Superquadrics
2. Superquadrics are formed by incorporating additional parameters into the quadric equations to provide increased flexibility for adjusting object shapes.
3. The number of additional parameters used is equal to the dimension of the object: one parameter for curves and two parameters for surfaces.

e.g. :-

superellipse:-

\ We obtain a Cartesian representation for a superellipse from the corresponding equation for an ellipse by allowing the exponent on the x and y terms to be variable.

Blobby objects :-

• Some objects do not maintain a fixed shape

• They change their surface characteristics in certain motions 

• These objects are referred to as blobby objects, since their shapes show a certain degree of fluidity

 Examples in this class of objects include :-

1. water droplets 

2. melting objects 

3. muscle shapes in the human body.