Implicit Surfaces

1
Implicit Surfaces

• Surface is modeled as the level set of a scalar
  function
• F(x,y,z) 0
• Classic example is the sphere

2
Limitations

• Can be difficult to render
• Surfaces that can be modeled effectively are
  limited
• But the field is advancing

3
Advantages

• Analytic representation of the object
• Easy blending
• F(x,y,z) G(x,y,z) 0
• Gives a blend of the surfaces defined by F and G
• Blobs

4
Blending
Adding the field functions at various separation
distances
Can also subtract or take the max
5
Classic Paper

• Jim Blinn 1982
• Modeling molecules
• Represent electron density cloud in a way that
  ball and stick models cant
• Previous implicit surface models primarily
  confined to simple algebraic surfaces such as
  quadrics

6
Blinns Blobs

• Electron density described by exponential
  distribution
• Collection of atoms represented by a sum

7
Blinns Blobs (Cont.)

• For computational simplicity, used Gaussians
  instead
• Surface defined by some threshold

8
Modeling Parameters

• Rearrange the function
• Where and are the radius and
  blobbiness respectively
• Since T is now incorporated into every atom, it
  becomes irrelevant and so is set to 1

9
A Blinn Blob
10
Rendering

• Well suited to ray tracing, which is what Blinn
  used
• The algorithm

11
Other Field Equations

• Meta balls
• Soft objects

Derived from an expansion of a truncated exponenti
al
12
Modern Techniques

• Construct signed distance function
• Fit with radial basis functions
• Challenge is to do this efficiently