02/19/2002
15-462 Graphics I
4
Implicit Representation
•Curve
in 2D: f(x,y) = 0
–Line:
ax + by + c = 0
–Circle:
x2 + y2 – r2 = 0
•Surface
in 3d: f(x,y,z) = 0
–Plane:
ax + by + cz + d = 0
–Sphere:
x2 + y2 + z2 – r2 = 0
•f(x,y,z)
can describe 3D object:
–Inside:
f(x,y,z) < 0
–Surface:
f(x,y,z) = 0
–Outside:
f(x,y,z) > 0