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Show 25 4.2 Geometric Models The Alpha_! Research Project here at the University of Utah performs research on spline-based geometric modeling. The models produced with Alpha.J. are a boundary representation of three-dimensional objects, where an object is formed from a collection of parametric patches [29,33]. The Alpha.J. software was used to create all the geometric models tested in this thesis. 4.3 Surface Subdivision Subroutines from the Alpha_! system were used to perform the subdivision of spline surfaces into sets of triangles. These subroutines divide a sculptured surface in alternating parametric directions [8]. When a surface patch resulting from the subdi_vision of a parent surface meets certain geometric flatness criteria, the surface patch is approximated by a set of triangles. This will be discussed later in relation to the interpolation method used with the radiosity results. 4.4 Octree Creation After surface subdivision, an octree structure was created (for the purposes of ray tracing) from the sets of triangles that approximate the smooth surface. The methods for construction of the octree were described in Section 3.3. Restating briefly, a bounding box was placed around all the objects visible in the model a.nd the point of view. The bounding box contained a list of all the triangles that intersected it. H the bounding box contained more than a given number of triangles, then the bounding box was split into eight child boxes. The subdivision criterion was then recursively applied to the eight child boxes, creating the octree. |
