Modeling and CSG

Modeling:

Constructive Solid Geometry

• How do we model for a Ray Tracer?
• Hierarchical modeling works well, but we can do more easily.
• In Constructive Solid Geometry all primitives are solids.
• New type of internal node: Boolean operation.

  Intersection, Union, Difference

• Thus, our model is a DAG with
  • Leaf nodes representing primitives
  • Interal nodes are transformations, materials, or boolean operations.

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CSG:

The primitives

We will want a rich set of primitives. How do we specify them?

• As a ``canonical'' primitive

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  Sphere()*Scale(2,2,2)*Translate(x,y,z)

• As a transformed canonical primitive
  • Sphere(r,x,y,z);
  • Cube(x,y,z,dx,dy,dz);
  • Cone(width,height,x,y,z,dx,dy,dz);

CSG:

Traversing the transformation tree

• After transformation are applied, our primitives will be warped.
• Rather than intersect ray with warped primitive (which is worse once we add boolean operations), we will transform the ray.
• On the way down, apply inverse transformation to ray.
• On the way back, apply the transformation to the point and to the normal

  Caution: see notes on transforming normals

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  Note: In this figure, T' is used to denote , T'' denotes

CSG:

Boolean operations

• Could apply boolean operations to transformed primitives and construct a surface for that object.

  Problem: representation too complex

• Idea: perform a complete ray intersect object with each primitive. This gives us a (set of) line segment(s).

  Next, perform boolean operations on line segments.

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• Note that if we transform the ray on the way down, then we must transform the entire segment on the way back
• Also, we must be careful with normals: they flip when we perform difference.