This slide shows the surface decomposition by conjugate roof Roof* A.
Slant triangles on standard cone Cone A are classified into three kinds:
In(Cone A, Roof* A) is the set of all the slant triangles under Roof* A,
Bd(Cone A, Roof* A) is the set of all the slant triangles partially covered by Roof* A,
And In(Cone A, Roof* A) is the set of all the slant triangles above Roof* A.
Shown below is the decomposition of slant triangles on Cone A of the middle figure, where the conjugate roof Roof* A is colored blue.
Shown on the left are the slant triangles under Roof* A and their image on the hyperplane.
Shown on the right are the slant triangles above Roof* A and their image on the hyperplane.
In this example, there are no slant triangles partially covered by Roof* A.